The Analysis of Biological Data Third Edition by Michael C. Whitlock and Dolph Schlute TEST BANK

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Chap 01_3e Indicate the answer choice that best completes the statement or answers the question.

1. Other terms for a "sampling unit" include all of the following, except one. a. Individual b. Replicate c. Statistic d. Subject 2. For the data set: 1, 3, 6, 6, 7, 7, 7, 8, 8, 9 which of the following is true? a. The absolute frequency of "6" is 0.2, and the relative frequency of "7" is 0.3. b. The absolute frequency of "6" is 0.2, and the relative frequency of "7" is 3. c. The absolute frequency of "6" is 2, and the relative frequency of "7" is 0.3. d. The absolute frequency of "6" is 2, and the relative frequency of "7" is 3.

3. If we are conducting a study and seeking to determine the relationship between two variables, but a third variable complicates the situation and makes it hard to figure out the causal relationship, we term this third variable a(n) _____ variable. a. Confounding b. Interfering c. Non-linear d. Random 4. The measurements of one or more variables made on a sample of individuals is called which of the following? a. Data b. Parameters c. Treatments d. Variates 5. Ideal samples are unbiased; which of the following terms is a synonym for unbiased in this context? a. Accurate b. Centered c. Precise d. Proportional 6. Characteristics or measurements that differ from individual to individual are called which of the following? a. Data b. Statistics c. Treatments d. Variables Copyright Macmillan Learning. Powered by Cognero.

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Chap 01_3e 7. Which of the following is the best description of our approach to statistics? a. We calculate statistics to look for mathematical relationships between samples and populations. b. We perform mathematical operations with data values in order to compare the values in samples to the values in populations. c. We take samples from populations in order to calculate parameters, which we can then use to predict the statistics of the population. d. We want to know about a population but can't measure everything, so we use data from a subset to infer what is probable for the population.

8. When we look at a sample, the number of times a specific measurement is observed is called the _____ of the observation. a. Frequency b. Probability c. Proportion d. Statistic 9. If we administered psychological tests to a set of students and then placed these subjects into groups with the labels "anxious," "calm," "angry," and "control," what type of variable have we created for our sample? a. Ordinal categorical b. Ordinal quantitative c. Nominal categorical d. Nominal quantitative 10. Which of the following is correct? a. Populations are described by parameters, whereas samples provide estimates or statistics. b. Populations are described by estimates, whereas samples provide parameters or statistics. c. Populations are described by statistics, whereas samples provide estimates or parameters. d. Populations are described by statistics or parameters, whereas samples provide estimates.

11. Which of the following is the best definition of estimation? a. Increasing a sample yields better data. b. Predicting a measured value before the measurements begin. c. The process of rounding values to specific degrees of accuracy. d. Using sample data to infer population data.

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Chap 01_3e 12. Consider the figure showing the final position of balls dropped that had been aimed at the indentation. Which of the plots shows the situation best described as good accuracy, good precision?

a. Plot A b. Plot B c. Plot C d. Plot D 13. When a researcher takes a sample of individuals because they are easily available, rather than choosing randomly, we say they have done which of the following? a. Taken a "biased sample." b. Taken a "sample of convenience." c. Taken a "saturated sample." d. Taken an "availability sample."

14. When subjects in studies are randomly assigned to treatment groups, we call this a(n) _____ study, whereas if the subjects are in treatment groups for some other reasons, we call this a(n) _____ study. a. case-control : cohort b. cohort : case-control c. experimental : observational d. observational : experimental 15. Sampling error is defined as differences between the estimate and the estimated parameter due to which of the following? a. Bias in the sample. b. Errors due to rounding sample statistics too much. c. Mistakes during sampling. d. Randomness during sampling.

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Chap 01_3e 16. Imagine there is a forest with 2000 trees, and we want to know the average height. Which of the following is the best procedure to generate an unbiased sample of size 50? a. Measure all the heights and then choose the 50 with the heights closest to the average. b. Measure the 50 trees closest to the center of the forest. c. Number all the tree, randomly generate 50 numbers between 1 and 2000, and measure those trees. d. Number all the trees, then starting with the first tree, measure each 2000/50 = 40th tree.

17. When we consider categorical variables, if the categories have no order, we term them _____, whereas if the categories have an order, we term them _____. a. ordinal : nominal b. nominal : ordinal c. random : sequential d. sequential : random 18. The most important probability distribution in statistics looks like a "bell curve" and is called the _____ distribution. a. Control b. Normal c. Proportional d. Symmetric 19. Which best describes the use of statistics to understand reality? a. We use data from a sample and concepts from statistics to make estimates about populations. b. We use data from a population and concepts from statistics to make estimates about samples. c. We use data to compare samples to populations. d. We use concepts from statistics to improve our estimates of sample characteristics.

20. In ______ studies, subjects are randomly assigned to treatment groups, whereas in ______ studies, subjects are assigned to treatment groups for reasons beyond the control of the researchers. a. experimental : observational b. observational : experimental c. scientific : unscientific d. unscientific : scientific

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Chap 01_3e 21. Consider the figure showing the final position of balls dropped that had been aimed at the indentation. Which of the plots shows the situation best described as poor accuracy, good precision?

a. Plot A b. Plot B c. Plot C d. Plot D 22. Variables that describe membership in certain qualitative categories or groups are termed which of the following? a. Categorical b. Numerical c. Non-quantitative d. Separable 23. When we look at the association between two variables, we term the one that predicts or influences the other the _____ variable, whereas the one being influenced is termed the _____ variable. a. baseline : resultant b. causal : influential c. dependent : independent d. explanatory : response 24. When a study recruits people at large and some types of people sign up more because of a systematic difference in their behavior, our sample may be prone to which of the following types of bias? a. Behavioral bias b. Readiness bias c. Sampling bias d. Volunteer bias

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Chap 01_3e 25. If we measured the mass of subjects and then placed these observed individuals into groups with the labels "light," "medium," and "heavy," what type of variable have we created for our sample? a. Ordinal categorical b. Ordinal quantitative c. Nominal categorical d. Nominal quantitative 26. Which of the following is a major benefit of experimental studies over observational ones? a. They are less biased. b. They are more accurate and precise. c. They can separate categorical and numerical variables. d. They can separate explanatory and confounding variables.

27. Consider the figure showing the final position of balls dropped that had been aimed at the indentation. Which of the plots shows the situation best described as good accuracy, poor precision?

a. Plot A b. Plot B c. Plot C d. Plot D 28. For the data set: 1, 1, 1, 2, 3, 3, 4, 5, 5, 5 which of the following is true? a. The absolute frequency of "4" is 1, and the relative frequency of "1" is 3. b. The absolute frequency of "4" is 1, and the relative frequency of "1" is 0.3. c. The absolute frequency of "4" is 0.1, and the relative frequency of "1" is 3. d. The absolute frequency of "4" is 0.1, and the relative frequency of "1" is 0.3.

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Chap 01_3e 29. Consider the figure showing the final position of balls dropped that had been aimed at the indentation. Which of the plots shows the situation best described as poor accuracy, poor precision?

a. Plot A b. Plot B c. Plot C d. Plot D 30. When considering the deviation between calculated statistics and the true parameter, how consistently the statistics generate similar values is referred to as defining their ______ , whereas how close the statistics are to the true parameter defines their ______. a. accuracy : precision b. precision : accuracy c. robustness : quality d. quality : robustness 31. Which of the following is a valid statistical hypothesis? a. The mean blood pressure of a population of people taking an experimental drug is higher than the mean for a population of those who don't. b. The mean temperature of a sample of patients administered ice packs is lower than the mean of a sample given a blanket. c. The range of height values for wild giraffes is larger than the range of heights for giraffes in captivity. d. Colonies of E. Coli exposed to high salt levels reproduce more slowly than ones exposed to low salt levels.

32. Describe what explanatory and response variables are and why these terms are superior to the more traditional terms independent and dependent.

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Chap 01_3e 33. Define the two major types of variables and identify and describe two important subsets within each of these two broad categories.

34. Compare and contrast the following four terms: sample, statistic, parameter, and population.

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Chap 01_3e 35. Magpies are a type of bird that collects colored objects for their nests. Consider the data shown depicting a total of 18 observations of variously colored objects found in a magpie nest.

What are the absolute and relative frequencies of each color?

Blue: Green: Yellow: Orange: Red: Purple: Black: White:

36. The phrase "correlation does not imply causation" is often used to dismiss observed correlations. Explain why this dismissal is not the best approach.

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Chap 01_3e Answer Key 1. c 2. c 3. a 4. a 5. a 6. d 7. d 8. a 9. c 10. a 11. d 12. b 13. b 14. c 15. d 16. c 17. b 18. b 19. a 20. a 21. d 22. a 23. d 24. d 25. a 26. d Copyright Macmillan Learning. Powered by Cognero.

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Chap 01_3e 27. c 28. b 29. a 30. a 31. a 32.

33.

34.

35.

36.

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Chap 02_3e Indicate the answer choice that best completes the statement or answers the question.

1. Strip plots and violin plots are typically used for the same purpose. a. True b. False 2. Preparing figures typically follows data analysis. a. True b. False 3. Effective graphs are designed to accomplish three goals. Which of the following is NOT one of these goals? a. Communicating results to a wider audience. b. Comparing measurements between groups. c. Proving a hypothesis is correct or incorrect. d. Uncovering relationships between variables.

4. There is no strict rule for choosing the number of bins in a histogram. a. True b. False 5. If you saw a graph with rectangles standing on a horizontal axis, what is the best immediate visual clue to determine whether it is likely to be a well-designed bar chart or a histogram? a. If it is in color or shades of gray. b. If the bars are solid or filled with patterns. c. Whether the bars touch or have gaps between them. d. Whether the y-axis goes to zero or some other number.

6. Consider a situation in which bacterial swabs were taken from the ears and noses of 50 study subjects, and the number of swabs that showed the presence of staphylococcus were measured. The table shows the results of the measurements. Which of the grouped bar graphs shown correctly depicts this data?

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Chap 02_3e

a. Plot A b. Plot B c. Plot C d. Plot D 7. Bar graphs are typically superior to pie charts for representing category frequencies. a. True b. False 8. Which of the following is generally true for pie charts? a. Frequencies are easy to compare across different pie charts. b. Frequencies are hard to compare visually when there are many categories. c. Pie charts are better for showing absolute frequencies than relative frequencies. d. Pie charts are better for showing relative frequencies than absolute frequencies.

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Chap 02_3e 9. Consider an experiment in which female and male rats are weighed and then their food consumption is measured. Which of the following is NOT a flaw in the figure showing data from this experiment?

a. The fonts used for the two axes are different and both hard to read. b. The symbols have identical shapes and colors with very similar shades. c. The x-axis should extend all the way to zero to show magnitude. d. The y-axis has a discontinuity, a sudden jump in magnitude.

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Chap 02_3e 10. Consider the data table that indicates how many subjects in a skin cancer study had various numbers of moles on their backs. Which of the histograms correctly depicts the data?

a. Chart A b. Chart B c. Chart C d. Chart D

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Chap 02_3e 11. Consider an experiment in which female and male rats are weighed and then their food consumption is measured. Which of the following is a flaw in the figure showing data from this experiment?

a. Data for an unequal number of subjects for each of the two sexes are displayed. b. The pair of colors, red and green, is used. c. The groups have both different colors and different shapes, which is redundant; only one aspect of the symbols should differ. d. The wrong variables are plotted on the axes; they should be switched.

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Chap 02_3e 12. Consider a lake survey in which the relative amounts of five different types of fish are identified. Which of the following data sets matches the pie chart shown?

a. 25% bass, 20% bullhead, 25% catfish, 15% perch, 15% walleye b. 35% bass, 15% bullhead, 15% catfish, 15% perch, 20% walleye c. 20% bass, 15% bullhead, 25% catfish, 20% perch, 20% walleye d. 30% bass, 20% bullhead, 15% catfish, 15% perch, 20% walleye

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Chap 02_3e 13. Consider an experiment in which an omnivorous species has its stomach contents analyzed. Which of the pie charts correctly depicts the following values for the diet of the omnivore: Fish = 10% Grass = 40%, Insects = 20% Leaves = 30%

a. Chart A b. Chart B c. Chart C d. Chart D

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Chap 02_3e 14. Consider a lake survey in which the relative amounts of five different types of fish are identified. Which of the following data sets matches the pie chart shown?

a. 15% bass, 15% bullhead, 15% catfish, 40% perch, 15% walleye b. 15% bass, 15% bullhead, 15% catfish, 35% perch, 20% walleye c. 20% bass, 15% bullhead, 20% catfish, 30% perch, 15% walleye d. 20% bass, 15% bullhead, 15% catfish, 30% perch, 20% walleye 15. When designing a bar graph, which of the following is NOT something that should generally be done? a. Bar heights should be proportional to the number of observations. b. Bars should stand apart with small gaps between them. c. Nominal categories should be ordered by frequency, from largest to smallest. d. Ordinal categories should be ordered by frequency, from largest to smallest.

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Chap 02_3e 16. Consider an experiment in which rats are given three diets (reduced calorie, control, and increased calorie) and their masses at 6 weeks of age are measured. Which of the following is an aspect of poor design in the figure shown?

a. The different patterns for the groups provide no additional information because they are redundant with the labels. b. The figure is black and white; color is always better when making figures and graphs. c. The unit for mass in the axis label should be spelled out with words instead of abbreviated within the parentheses. d. Since the minimum group mean is 20, dropping the axis all the way down to zero is too far and wastes space.

17. Bar graphs, histograms, and scatter plots should always show the y-axis all the way down to zero. a. True b. False

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Chap 02_3e 18. Consider the histograms of a data set shown. Which of the histograms depicts an asymmetric data set?

a. Chart A b. Chart B c. Chart C d. Chart D 19. The type of figure that uses rectangles, the height of which indicates magnitude, is called which of the following? a. Bar graph b. Box plot c. Pie chart d. Rectangle plot 20. Grouped bar graphs and mosaic plots are typically used for the same purpose. a. True b. False 21. Which of the bar charts shown corresponds to the data table shown?

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Chap 02_3e

a. Chart A Copyright Macmillan Learning. Powered by Cognero.

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Chap 02_3e b. Chart B c. Chart C d. Chart D 22. Mosaic plots and grouped bar graphs display the same basic data, but mosaic plots only show the frequencies, not the raw values. While this may seem to be a weakness, in which way are mosaic plots potentially better than grouped bar graphs? a. They are more widely used and therefore better understood by readers. b. They are not as prone as grouped bars graphs to rounding error, which causes inaccuracy. c. They are often better at indicating associations between treatment and response variables. d. They take up less space on the page.

23. Consider the histograms of a data set shown. Which of the histograms depicts a symmetric data set?

a. Chart A b. Chart B c. Chart C d. Chart D 24. Line graphs are typically used to show trends in time. a. True b. False

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Chap 02_3e 25. Consider a lake survey in which the relative amounts of five different types of fish are identified. Which of the following is not an aspect of poor design in the pie chart shown?

a. The segments are not arranged alphabetically. b. The segments are not arranged in order of magnitude. c. The green and light blue would be hard to tell apart if printed in black and white. d. The yellow and red segments would be hard for most color-blind people to tell apart.

26. Three-dimensional figures are often the best way to represent data a. True b. False

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Chap 02_3e 27. Consider an experiment in which rats are given three diets (reduced calorie, control, and increased calorie) and their masses at 6 weeks of age are measured. Which of the following is NOT an aspect of poor design in the figure shown?

a. The two-dimensional nature of the bars subliminally exaggerates differences between the groups. b. The axis should go to zero to allow true judgement of relative differences. c. The data are shown in a manner that makes judging the values more difficult. d. The unit for mass in the axis label is redundant and makes the label overly wordy.

28. Essentially, all professional statistics software programs can read data files saved as .csv or text files, but not all will read Excel formats. a. True b. False 29. When looking at a color map that uses colors to represent values, blue signifies larger values and red signifies smaller values. a. True b. False

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Chap 02_3e 30. Consider the data table that indicates how many subjects in a skin cancer study had various sizes of moles on their backs. Which of the histograms correctly depicts the data?

a. Chart A b. Chart B c. Chart C d. Chart D Copyright Macmillan Learning. Powered by Cognero.

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Chap 02_3e 31. Consider an experiment in which an omnivorous species has its stomach contents analyzed. Which of the pie charts correctly depicts the following values for the diet of the omnivore: 20% grass, 40% leaves, 20% insects, 20% fish?

a. Chart A b. Chart B c. Chart C d. Chart D

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Chap 02_3e 32. Consider the histogram shown. What two words describe the skew?

a. Left skewed, negative skew b. Left skewed, positive skew c. Right skewed, negative skew d. Right skewed, positive skew 33. The primary purpose of scatter plots is to highlight differences between groups. a. True b. False 34. If you saw a graph with rectangles standing on a horizontal axis, what is the best immediate visual clue to determine whether it is likely to be a well-designed bar chart or a histogram? a. If the x-axis has numbers or labels. b. If the y-axis goes to zero or some other number. c. Whether it is black and white or in color. d. Whether the bars are solid or filled with patterns.

35. When designing a table of data values, the rows should always be arranged such that the category with the largest number of values is at the top with the values descending until the last row has the smallest number of values. a. True b. False 36. Consider a situation in which tumor-prone rats were given an experimental anti-cancer drug or a control.

There were 50 rats in each treatment group, and after 6 weeks they were sacrificed and autopsies performed to determine the presence or absence of liver tumors. The table shows the results of the measurements. Which of the mosaic plots shown correctly depicts this data?

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Chap 02_3e

a. Plot A b. Plot B c. Plot C d. Plot D

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Chap 02_3e 37. Multiple histograms and grouped bar graphs are typically used for the same purpose. a. True b. False 38. What of the following is the best approach to deciding on the number of bins for a histogram? a. The number of bins should be approximately 20% of the number of data values. b. There is a formula, number of bins = 1 + ln(n)/ln(2), that should always be used to set the number of bins. c. There is no strict rule; the number of bins should be chosen to best show patterns. d. There should be no less than 5 bins and no more than 20.

39. Consider the histogram of a data set shown. Which of the following values is the mode of the data set?

a. 6 b. 9 c. 25 d. 30 40. Which of the following is NOT true of relative frequencies for a complete data set? a. All the relative frequency values are less than or equal to one. b. All the relative frequency values sum to one. c. Each relative frequency is less than or equal to the corresponding absolute frequency. d. No two relative frequency values can be the same.

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Chap 02_3e 41. Consider the histogram shown. What two words describe the skew?

a. Left skewed, negative skew b. Left skewed, positive skew c. Right skewed, negative skew d. Right skewed, positive skew

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Chap 02_3e 42. Consider the histogram of a data set shown. Which of the following values is the mode of the data set?

a. 6 b. 7 c. 12 d. 24

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Chap 02_3e 43. Consider an experiment in which rats are weighed and then their food consumption is measured. Which of the following terms is the best technical description of the data shown?

a. A casual relationship. b. A causal relationship. c. A positive relationship. d. An upward relationship.

44. Which of the following is a good thing to do when designing a data table? a. Arrange rows according to the numerical value of the most interesting variable. b. Arrange rows alphabetically. c. Arrange rows and columns so that values in the same row are as similar as possible. d. Arrange rows from smallest sample size to largest sample size.

45. One of the graphical methods in particular was described as being particularly suited to looking at data values over time—which one? a. A grouped bar graph b. A line graph c. A map d. A mosaic plot 46. Consider a situation in which bacterial swabs were taken from the ears and noses of 50 study subjects, and the number of swabs that showed the presence of staphylococcus were measured. The table shows the results of the measurements. Which of the grouped bar graphs shown correctly depicts this data?

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Chap 02_3e

a. Plot A b. Plot B c. Plot C d. Plot D 47. Consider a situation in which bacterial swabs were taken from the ears and noses of 50 study subjects, and the number of swabs that showed the presence of staphylococcus were measured. The table shows the results Copyright Macmillan Learning. Powered by Cognero.

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Chap 02_3e of the measurements. Which of the mosaic plots shown correctly depicts this data?

a. Plot A b. Plot B c. Plot C d. Plot D Copyright Macmillan Learning. Powered by Cognero.

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Chap 02_3e 48. Which of the following is NOT a good thing to do when designing a data table? a. Arrange quantitative categories by order of value. b. Arrange unordered categorical variables in alphabetical order. c. Arrange unordered categorical variables in order of importance. d. Arrange unordered categorical variables in their natural order, if they have one.

49. Which of the following would greatly improve the utility of the data table shown?

a. Instead of a row for each fish species, there should be a column for each species, with the number listed underneath. b. The rows should be sorted alphabetically based on the fish species name. c. The rows should be sorted numerically based on the number of fish caught. d. The scientific names of the fish should be provided on each row.

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Chap 02_3e 50. Consider an experiment in which rats are weighed and then their food consumption is measured. Which of the following terms would be used for the data point indicated with the arrow?

a. A deviation. b. An exception. c. An outlier. d. A scattered point.

51. Distinguish between absolute and relative frequencies with regard to a data set.

52. Sketch out a histogram (with 5 bins of equal size as appropriate) showing the distribution of the following values: 2, 3, 3, 4, 5, 7, 8, 8, 11, 11, 12, 13, 15, 15, 17, 18, 18, 23, 24, 32, 33, 34, 35, 38, 41, 42, 43, 48

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Chap 02_3e 53. Distinguish between nominal and ordered categorical variables.

54. Multiple histograms and group bar graphs both use multiple sets of bars to display data and facilitate certain analyses. Contrast these two graphical methods—what is the main difference in the goal of these figures?

55. Write out a procedure or recipe for how to best work with a set of values you have obtained in order to make a good set of data files. Be clear about what your end result should be in terms of files.

56. Imagine you have length and weight data for two sets of mice: wildtype mice and ones with a genetic mutation for bone growths. Describe a scientific question using these mice that would be best analyzed with a scatter plot and a different question that would be best approached using a violin plot.

57. Draw a graph showing hypothetical data in which two aspects of its design are misleading or bad. Briefly describe each of the two flaws you included and explain how they could be improved.

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Chap 02_3e Answer Key 1. a 2. b 3. c 4. a 5. c 6. d 7. a 8. b 9. c 10. b 11. b 12. d 13. a 14. d 15. d 16. c 17. b 18. b 19. a 20. a 21. c 22. c 23. d 24. a 25. d 26. b Copyright Macmillan Learning. Powered by Cognero.

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Chap 02_3e 27. d 28. a 29. b 30. c 31. c 32. d 33. b 34. a 35. b 36. c 37. b 38. c 39. a 40. d 41. a 42. a 43. c 44. a 45. b 46. d 47. a 48. b 49. c 50. c 51.

52.

53.

54.

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Chap 02_3e 55.

56.

57.

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Chap 03_3e Indicate the answer choice that best completes the statement or answers the question.

1. Imagine we have a symmetric data set for which we have calculated various statistics, but then a single very large outlier is added to it. When we recalculate the statistics, which of the following things is NOT true? a. The mean increases. b. The median increases. c. The standard deviation increases. d. The variance increases.

2. What are the median and interquartile range for the set of data values shown?

Data: 2 4 6 8 10 12 a. Median = 6, interquartile range = 6 b. Median = 6, interquartile range = 7 c. Median = 7, interquartile range = 6 d. Median = 7, interquartile range = 7 3. Using the data table shown, what proportion of the leaves examined have more than two galls?

a. 0.1 b. 0.3 c. 0.5 d. 0.7

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Chap 03_3e 4. If a data set has a bell-shaped distribution, approximately what proportion of the values lie above the mean and within two standard deviations? a. 25% b. 33% c. 38% d. 48% 5. The standard deviation has the same units as the data values, whereas the variance does not. a. True b. False 6. The location is always the most important statistic when considering a data set. a. True b. False 7. Which of the following accurately describes the numerator for the equation to calculate the variance? a. The average of all the values. b. The square root of the standard deviation. c. The sum of the average deviations between the data values and the mean. d. The sum of the squared deviations between the data values and the mean.

8. A large outlier will tend to change the interquartile range more than the standard deviation. a. True b. False 9. The proportion of values in a data set that are less than the median is 0.5. a. True b. False 10. The interquartile range is larger than 50% of the data. a. True b. False

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Chap 03_3e 11. Using the data table shown, what proportion of the leaves examined have four galls?

a. 0.1 b. 0.3 c. 0.5 d. 0.7 12. The rounding of values should only be done for reported values; use extra digits when performing calculations. a. True b. False 13. What are the median and interquartile range for the set of data values shown?

Data: –5 –1 0 1 3 6 13 a. Median = 0.5, interquartile range = 3 b. Median = 1, interquartile range = 4 c. Median = 1.5, interquartile range = 5 d. Median = 2.0, interquartile range = 6

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Chap 03_3e 14. Using the data table shown, what is the mean number of galls found on a set of 30 leaves collected from a plant?

a. 1.0 b. 1.33 c. 1.66 d. 2.0 15. Which of the following must be true for a plot of a cumulative frequency distribution? a. It is centered around the mean. b. It is centered around the median. c. The line has a shape like a bell curve. d. The line moves upward from left to right.

16. Using the data set shown, what are the correct mean and median values for this data set?

Data set: 3, 4, 5, 5, 8, 9, 11, 11 a. Mean = 6, median = 7.5 b. Mean = 6.5, median = 7 c. Mean = 7, median = 6.5 d. Mean = 7.5, median = 6

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Chap 03_3e 17. If we have a data set with a mean of 25 and a variance of 16, what are the new mean and variance if we add 5 to all the values, then multiply them by 4? a. Mean = 79, variance = 48 b. Mean = 79, variance = 144 c. Mean = 87, variance = 48 d. Mean = 87, variance = 144 18. If a data set has a bell-shaped distribution, approximately what proportion of the values lie above the mean and within one standard deviation? a. 25% b. 33% c. 38% d. 48% 19. If a data set has a mean of 25 and a variance of 16, what is the coefficient of variation? a. 16% b. 64% c. 80% d. 156% 20. If we have a data set with a mean of 12 and a variance of 3, what are the new mean and variance if we add 5 to all the values, then multiply them by 2? a. Mean = 29, variance = 6 b. Mean = 29, variance = 12 c. Mean = 34, variance = 6 d. Mean = 34, variance = 12 21. The variance of a data set is always smaller than the sum of squares. a. True b. False 22. If we have a data set with a mean of 25 and a variance of 16, what are the new mean and variance if we multiply the values by 3 and then add 4? a. Mean = 79, variance = 48 b. Mean = 79, variance = 144 c. Mean = 87, variance = 48 d. Mean = 87, variance = 144

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Chap 03_3e 23. Using the data table shown, what is the mean of the number of species' bones found in 40 sets of stomach contents collected from coyotes?

a. 2.0 b. 3.0 c. 4.0 d. 5.0

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Chap 03_3e 24. Using the data table shown, what is the standard deviation of the number of galls found on a set of 30 leaves collected from a plant?

a. 1.0 b. 1.4 c. 2.0 d. 5.5 25. If we have a data set with a mean of 12 and a variance of 3, what are the new mean and variance if we multiply the values by 2 and then add 5? a. Mean = 29, variance = 6 b. Mean = 29, variance = 12 c. Mean = 34, variance = 6 d. Mean = 34, variance = 12 26. The mean and the median will be the same for a symmetric distribution. a. True b. False

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Chap 03_3e 27. Using the data set shown, what is the sample variance for this data set?

Data set: 1, 4, 7, 9, 15, 24 a. 58.0 b. 69.6 c. 73.4 d. 78.4 28. Using the data set shown, what is the mean value for this data set?

Data set: 1, 4, 5, 9, 13, 24 a. 8.33 b. 8.66 c. 9.00 d. 9.33 29. Using the data set shown, what are the correct variance and interquartile range values for this data set?

Data set: 3, 4, 5, 5, 8, 9, 11, 11 a. Variance = 8.75, interquartile range = 5.5 b. Variance = 8.75, interquartile range = 6.5 c. Variance = 10, interquartile range = 5.5 d. Variance = 10, interquartile range = 6.5 30. The coefficient of variation is usually expressed as a percentage. a. True b. False 31. The standard deviation of a data set is always smaller than the variance. a. True b. False

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Chap 03_3e 32. Using the data table shown, what proportion of the stomach contents examined have bones from more than three species?

a. 0.125 b. 0.250 c. 0.375 d. 0.45 33. Consider a sample of foxes in which there are 20 adult females, 25 adult males, 35 juvenile females, and 20 juvenile males. What is the proportion of juvenile females? a. 0.2 b. 0.25 c. 0.35 d. 0.55 34. A percentile of a measurement specifies the number of values from the data set that are less than the measurement. a. True b. False 35. A proportion must be between zero and one and can also be either zero or one. a. True b. False

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Chap 03_3e 36. If we do experiments correctly, the variability in the data values should be zero. a. True b. False 37. Using the data table shown, what is the standard deviation of the number of species' bones found in 40 sets of stomach contents collected from coyotes?

a. 1.8 b. 2.0 c. 2.2 d. 2.4

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Chap 03_3e 38. Using the data table shown, what proportion of the stomach contents examined have bones from three species?

a. 0.125 b. 0.250 c. 0.375 d. 0.45 39. Consider a sample of foxes in which there are 20 adult females, 25 adult males, 35 juvenile females, and 20 juvenile males. What is the proportion of females? a. 0.2 b. 0.25 c. 0.35 d. 0.55 40. The mean is the most important descriptive statistic for a categorical variable. a. True b. False 41. A large outlier will tend to change the mean more than the median. a. True b. False

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Chap 03_3e 42. Which of the following are a possible set of descriptive statistics for a data set? a. Sum of squares of 18, variance of 6, standard deviation of 36 b. Sum of squares of 18, variance of 36, standard deviation of 6 c. Sum of squares of 180, variance of 6, standard deviation of 36 d. Sum of squares of 180, variance of 36, standard deviation of 6 43. Which of the following is not an important source of variability in data? a. Calculation errors. b. Differences between individuals. c. Instrument error. d. Measurement error.

44. The cumulative relative frequency at a given measurement is the proportion of values in the data set that have that measurement. a. True b. False 45. Sketch a boxplot showing data for the following two data sets.

Data set A: 2 Data set B: 3

3 5

5 6

7 8

9 9

11 11

12

46. Calculate the mean, median, variance, standard deviation, coefficient of variation, and interquartile range for the following data set: 9, 13, 14, 16, 17, 21.

47. Calculate the mean, median, variance, standard deviation, coefficient of variation, and interquartile range for the following data set: 5, 7, 10, 11, 14.

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Chap 03_3e 48. Consider an ecological study of the insect populations in a region. Pit traps are set out overnight, and the number of insects in each trap is recorded the next day.

Using the data shown in the table, calculate the mean, median, variance, standard deviation, coefficient of variation, and interquartile range for the data values. Also, what proportion of traps failed to trap any insects?

49. Calculate the mean, median, variance, standard deviation, coefficient of variation, and interquartile range for the following data set: –2, 0, 3, 4, 5.

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Chap 03_3e 50. Consider a study of patients with heart problems that follows them for 5 years after treatment and measures the number of myocardial infarctions (i.e., heart attacks) they experience.

Using the data shown in the table, calculate the mean, median, variance, standard deviation, coefficient of variation, and interquartile range for the data values. Also, what proportion of patients experienced subsequent myocardial infarctions?

51. Calculate the mean, median, variance, standard deviation, coefficient of variation, and interquartile range for the following data set: –2, 2, 4, 6, 8, 12.

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Chap 03_3e Answer Key 1. b 2. c 3. b 4. d 5. a 6. b 7. d 8. b 9. a 10. b 11. a 12. a 13. b 14. d 15. d 16. c 17. d 18. b 19. a 20. d 21. a 22. b 23. b 24. c 25. b 26. a Copyright Macmillan Learning. Powered by Cognero.

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Chap 03_3e 27. b 28. d 29. c 30. a 31. b 32. d 33. c 34. b 35. a 36. b 37. d 38. a 39. d 40. b 41. a 42. d 43. a 44. b 45.

46.

47.

48.

49.

50.

51.

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Chap 04_3e Indicate the answer choice that best completes the statement or answers the question.

1. The population of all sample means that could be obtained from a population is called which of the following? a. The estimation distribution of a population's mean. b. The population distribution of a mean. c. The sampling distribution of a population's mean. d. The universe of probabilities.

2. It is possible for the standard deviation and standard error values in a data set with multiple values to be equal. a. True b. False 3. The sampling distribution of an estimate is the mean and variance of the sample. a. True b. False 4. The mean and standard error bars for four data sets are shown in the figure. Which of the data sets most likely has a variance of 64 and a sample size of 16?

a. Plot A b. Plot B c. Plot C d. Plot D

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Chap 04_3e 5. The mean and 95% confidence interval bars for four data sets are shown in the figure. Which of the data sets most likely has a standard deviation of 4 and a sample size of 64?

a. Plot A b. Plot B c. Plot C d. Plot D 6. For a sample with a mean of 32 and a standard error of 5, which of the following is the best approximation for the 95% confidence interval of the population mean? a. 22 < μ < 42 b. 27 < μ < 37 c. 27 < μ < 47 d. 32 < μ < 42 7. If a sample with 40 values has a standard deviation of 16, what would the standard error be? a. 2.5 b. 5.0 c. 7.5 d. 10.0 8. What is the standard error for a sample of size 33 that has a standard deviation of 56? a. 1.70 b. 9.75 c. 12.24 d. 42.99

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Chap 04_3e 9. If the variance is larger than one, then the standard error will always be less than the standard deviation. a. True b. False 10. If a sample of size of 30 has a confidence interval of approximately 10.58 < μ < 16.42, what would the most likely standard deviation be? a. 6 b. 7 c. 8 d. 9 11. The standard deviation measures the spread of the data values, whereas the standard error measures the uncertainty in our estimate of the population mean. a. True b. False 12. If a sample has a standard deviation of 9 and a sample size of 9, it will have a standard error of 1.0. a. True b. False 13. If a sample with a standard deviation of 20 has a confidence interval of approximately 11.14 < μ < 24.86, what would the most likely sample size be? a. 34 b. 36 c. 38 d. 10 14. The 95% confidence interval is best thought of as the region within which we are 95% confident the population mean lies. a. True b. False 15. Which of the following is the best statement regarding the confidence interval for a mean with a lower limit of 20 and an upper limit of 30? a. We are 95% confident that the population mean lies between 20 and 30. b. We are 95% confident that the sample mean lies between 20 and 30. c. There is a 95% probability that the population mean lies between 20 and 30. d. There is a 95% probability that the sample mean lies between 20 and 30.

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Chap 04_3e 16. If a sample of size of 20 has a confidence interval of approximately 15.8 < μ < 38.2, what would the most likely standard deviation be? a. 19 b. 21 c. 23 d. 25 17. The larger the sample size, the narrower the sampling distribution of the population mean. a. True b. False 18. Error bars on a graph typically indicate the variance of the data values. a. True b. False 19. The mean and 95% confidence interval bars for four data sets are shown in the figure. Which of the data sets most likely has a variance of 81 and a sample size of 36?

a. Plot A b. Plot B c. Plot C d. Plot D 20. The standard error of the mean is the standard deviation of the sampling distribution for a population mean. a. True b. False

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Chap 04_3e 21. If a sample with a standard deviation of 16 has a confidence interval of approximately 3.2 < μ < 16.8, what would the most likely sample size be? a. 20 b. 22 c. 24 d. 26 22. The mean and standard error bars for four data sets are shown in the figure. Which of the data sets most likely has a variance of 144 and a sample size of 4?

a. Plot A b. Plot B c. Plot C d. Plot D 23. The 95% confidence interval is best thought of as the region within which there is a 95% probability that the population mean lies. a. True b. False 24. What is the standard error for a sample of size 20 that has a standard deviation of 40? a. 1.00 b. 3.16 c. 4.47 d. 8.94

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Chap 04_3e 25. It is possible for the variance and standard error values in a data set with multiple values to be equal. a. True b. False 26. Which of the following best describes a confidence interval? a. A range of values around a population parameter that is likely to contain the sample estimate. b. A range of values around a sample estimate that is likely to contain the population parameter. c. The width of the region within which the population mean lies. d. The width of the region within which the sample mean lies.

27. For a sample with a mean of 16 and a standard error of 4, which of the following is the best approximation for the 95% confidence interval of the population mean? a. 4 < μ < 16 b. 8 < μ < 20 c. 8 < μ < 24 d. 12 < μ < 20 28. The mean and 95% confidence interval bars for four data sets are shown in the figure. Which of the data sets most likely has a standard deviation of 32 and a sample size of 81?

a. Plot A b. Plot B c. Plot C d. Plot D 29. The term estimation describes the process of inferring a sample value from population data. a. True b. False Copyright Macmillan Learning. Powered by Cognero.

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Chap 04_3e 30. The symbol σ represents the population standard deviation. a. True b. False 31. Which of the following describes the width of the sampling distribution of the population mean? a. Sampling deviation. b. Sampling error. c. Standard deviation. d. Standard error.

32. A quick and dirty approximation for the 95% confidence interval is to add and subtract the standard error from the sample mean. a. True b. False 33. The mean and standard error bars for four data sets are shown in the figure. Which of the data sets most likely has a standard deviation of 40 and a sample size of 25?

a. Plot A b. Plot B c. Plot C d. Plot D

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Chap 04_3e 34. If a sample with a standard deviation of 16 has a standard error of approximately 4.62, what would the most likely sample size be? a. 8 b. 10 c. 12 d. 14 35. If a sample with a standard deviation of 25 has a standard error of approximately 5.6, what would the most likely sample size be? a. 14 b. 16 c. 18 d. 20 36. The mean and 95% confidence interval bars for four data sets are shown in the figure. Which of the data sets most likely has a variance of 100 and a sample size of 16?

a. Plot A b. Plot B c. Plot C d. Plot D

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Chap 04_3e 37. The mean and standard error bars for four data sets are shown in the figure. Which of the data sets most likely has a standard deviation of 56 and a sample size of 47?

a. Plot A b. Plot B c. Plot C d. Plot D 38. The symbol Ȳ represents the population mean. a. True b. False 39. If a sample with 16 values has a standard deviation of 47, what would the standard error be? a. 2.29 b. 2.94 c. 11.75 d. 11.98 40. If a sample has a standard deviation of 7 and a sample size of 4, it will have a standard error of 3.5. a. True b. False 41. Describe, using technical terms, why a larger sample size results in a more precise estimate of the population mean.

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Chap 04_3e 42. If the 95% confidence interval for a data set with a variance of 1600 is approximately 5 < μ < 25, what is the most likely sample size?

43. Clearly describe what a 95% confidence interval represents.

44. Sketch a figure showing the mean and 95% confidence intervals for two data sets using filled black circles and error bars. For the first, the mean is 30, the standard deviation is 10, and the sample size is 16. For the second, the mean is 40, the standard deviation is 18, and the sample size is 36.

45. If a data set is reported as having a 95% confidence interval from 15 to 23, what does that mean?

46. In your own words, describe a pair of similar experiments in which one suffers from pseudoreplication while the other does not.

47. Sketch a figure showing the mean and standard error values for two data sets using filled black circles and error bars. For the first, the mean is 25, the standard deviation is 9, and the sample size is 9. For the second, the mean is 20, the standard deviation is 35, and the sample size is 25.

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Chap 04_3e 48. Describe the relationship between a population and a sample with respect to how the word "estimation" is used.

49. Compare and contrast the terms standard deviation and standard error. What is their relationship, and what do they represent?

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Chap 04_3e Answer Key 1. c 2. b 3. b 4. a 5. c 6. a 7. a 8. b 9. a 10. c 11. a 12. b 13. a 14. a 15. a 16. d 17. a 18. b 19. d 20. a 21. b 22. c 23. b 24. d 25. a 26. b Copyright Macmillan Learning. Powered by Cognero.

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Chap 04_3e 27. c 28. c 29. b 30. a 31. d 32. b 33. b 34. c 35. d 36. b 37. d 38. b 39. c 40. a 41.

42.

43.

44.

45.

46.

47.

48.

49.

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Chap 05_3e Indicate the answer choice that best completes the statement or answers the question.

1. Discrete probability distributions are used to model the probabilities of continuous numerical variables. a. True b. False 2. The general addition rule states that Pr[A or B] = Pr[A] + Pr[B] - Pr[A and B] a. True b. False 3. Consider a study in which trees of two species (elm and oak) were assayed to determine what the probabilities are of being infected with a disease. The data collected are shown in the accompanying table.

Which of the mosaic plots below accurately represents the probability values in the data table?

a. Plot A b. Plot B c. Plot C d. Plot D

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Chap 05_3e 4. Consider a collection of 100 birds where 20 of them are penguins, 25 are ostriches, 15 are hawks, and 40 are doves. Penguins and ostriches are unable to fly, whereas hawks and doves can. If a bird is randomly chosen from this population, what is the probability it will not be a dove? a. 0.40 b. 0.60 c. 0.75 d. 0.85 5. Discrete probability distributions are used to model the probabilities of categorical variables. a. True b. False 6. Consider a collection of 100 birds where 20 of them are penguins, 25 are ostriches, 15 are hawks, and 40 are doves. Penguins and ostriches are unable to fly, whereas hawks and doves can. If a bird is randomly chosen from this population, what is the probability it will be either a hawk or unable to fly? a. 0 b. 0.20 c. 0.40 d. 0.60 7. Consider the probabilities of people taking HIV tests. Assume that the true probability of having HIV for all people who take the test is 4%. If HIV tests give a positive result in 99% of the cases in which the person has HIV and give a negative result in 99% of the cases in which the person does not have HIV, what is the probability that a person who gets a positive test result does not have HIV? a. 0.125 b. 0.155 c. 0.165 d. 0.195 8. Consider the probabilities of people taking HIV tests. Assume that the true probability of having HIV for all people who take the test is 3%. If HIV tests give a positive result in 99% of the cases in which the person has HIV and give a negative result in 99% of the cases in which the person does not have HIV, what is the probability that a person who gets a positive test result truly has HIV? a. 0.50 b. 0.75 c. 0.95 d. 0.99 9. When we sample without replacement, the probabilities of events may change as we take our sample. a. True b. False Copyright Macmillan Learning. Powered by Cognero.

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Chap 05_3e 10. Pairs of events that do not influence the probability of occurring for the other are called mutually exclusive. a. True b. False 11. Discrete probability distributions are used to model the probabilities of all numerical variables. a. True b. False 12. Which of the following statements is correct for a pair of independent events? a. Pr[A and B] = Pr[A] + Pr[B] b. Pr[A or B] = Pr[A] + Pr[B] c. Pr[A and B] = Pr[A] × Pr[B] d. Pr[A or B] = Pr[A] × Pr[B] 13. Full body scans are becoming popular even for people who have no symptoms. At any given time, a person's risk of having lung cancer is approximately 1 in 1000. If a full body scan can detect lung cancer 95% of the time (i.e., gives a positive result when a person has lung cancer) but returns a positive result 2% of the time if a person does not have lung cancer, what is the probability that a person who gets a positive test result does not have lung cancer? a. 0.955 b. 0.975 c. 0.995 d. 0.999 14. Imagine we are catching fish from a small pond that contains 6 catfish, 10 perch, and 4 walleye. When we catch a fish, we return it to the water so it may be caught again. Individuals of all species are equally likely to be caught, and fish are no more or less likely to be caught a second time than they were the first. What is the probability of catching a catfish, followed by a perch, followed by a walleye in the first three catches? a. 0.007 b. 0.015 c. 0.021 d. 0.030 15. Which of the following statements correctly describes a pair of mutually exclusive events? a. Pr[A and B] = Pr[A] + Pr[B] b. Pr[A or B] = Pr[A] + Pr[B] c. Pr[A and B] = Pr[A] × Pr[B] d. Pr[A or B] = Pr[A] × Pr[B]

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Chap 05_3e 16. If A and B are mutually exclusive events and Pr[A] = 0.2 and Pr[B] = 0.3, then what is Pr[A and B]? a. 0 b. 0.06 c. 0.5 d. 0.6 17. Which of the following statements correctly describes a pair of mutually exclusive events? a. Pr[A and B] = 0 b. Pr[A or B] = 0 c. Pr[A and B] = 1 d. Pr[A or B] = 1 18. Pairs of events that cannot both occur are called mutually exclusive. a. True b. False 19. Imagine we are catching fish from a small pond that contains 6 catfish, 10 perch, and 4 walleye. When we catch a fish, we keep it in the boat and catch the next fish from the remaining fish in the pond. Individuals of all species are equally likely to be caught, and fish are no more or less likely to be caught a second time than they were the first. What is the probability of catching a catfish, followed by a perch, followed by a walleye in the first three catches? a. 0.007 b. 0.015 c. 0.035 d. 0.030 20. The general multiplication rule states that Pr[A and B] = Pr[A] × Pr[B]. a. True b. False 21. Consider a collection of 100 birds where 20 of them are penguins, 25 are ostriches, 15 are hawks, and 40 are doves. Penguins and ostriches are unable to fly, whereas hawks and doves can. If a bird is randomly chosen from this population, what is the probability it will be a penguin or a dove? a. 0 b. 0.20 c. 0.40 d. 0.60 22. Continuous probability distributions are used to model the probabilities of all numerical variables. a. True b. False Copyright Macmillan Learning. Powered by Cognero.

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Chap 05_3e 23. Imagine we are catching fish from a small pond that contains 6 catfish, 10 perch, and 4 walleye. When we catch a fish, we return it to the water so it may be caught again. Individuals of all species are equally likely to be caught, and fish are no more or less likely to be caught a second time than they were the first. What is the probability of catching a catfish followed by a perch in the first two catches? a. 0.150 b. 0.160 c. 0.480 d. 0.600 24. Consider a collection of 100 birds where 20 of them are penguins, 25 are ostriches, 15 are hawks, and 40 are doves. Penguins and ostriches are unable to fly, whereas hawks and doves can. If a bird is randomly chosen from this population, what is the probability it will be a hawk? a. 0.15 b. 0.20 c. 0.25 d. 0.40 25. If A and B are independent events and Pr[A] = 0.2 and Pr[B] = 0.3, then what is Pr[A and B]? a. 0 b. 0.06 c. 0.5 d. 0.6 26. Consider a collection of 240 snakes where 40 of them are cobras, 60 are rattlesnakes, 60 are boas, and 80 are anacondas. Cobras and rattle snakes are venomous, whereas boas and anacondas are not. If a snake is randomly chosen from this population, what is the probability it will not be venomous? a. 0.167 b. 0.333 c. 0.417 d. 0.583 27. Full body scans are becoming popular even for people who have no symptoms. At any given time, a person's risk of having lung cancer is approximately 1 in 1000. If a full body scan can detect lung cancer 95% of the time (i.e., gives a positive result when a person has lung cancer) but returns a positive result 1% of the time if a person does not have lung cancer, what is the probability that a person who gets a positive test result truly has lung cancer? a. 0.012 b. 0.056 c. 0.087 d. 0.115 Copyright Macmillan Learning. Powered by Cognero.

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Chap 05_3e 28. Imagine we are catching fish from a small pond that contains 6 catfish, 10 perch, and 4 walleye. When we catch a fish, we keep it in the boat and catch the next fish from the remaining fish in the pond. Individuals of all species are equally likely to be caught, and fish are no more or less likely to be caught a second time than they were the first. What is the probability of catching a catfish followed by a perch in the first two catches? a. 0.150 b. 0.158 c. 0.526 d. 0.600 29. Consider a study in which swabs from the skin of a random sample of college students were tested for the presence of drug-resistant Staphylococcus Aureus. The probabilities that resulted are shown in the probability tree. Which of the columns in the data table below accurately represents the probability values in the probability tree?

a. Plot A b. Plot B c. Plot C d. Plot D

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Chap 05_3e 30. Consider a study in which swabs from the skin of a random sample of college students were tested for the presence of drug-resistant Staphylococcus Aureus. The data collected are shown in the accompanying table.

Which of the mosaic plots below accurately represents the probability values in the data table?

a. Plot A b. Plot B c. Plot C d. Plot D

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Chap 05_3e 31. Consider a study in which trees of two species (elm and oak) were assayed to determine what the probabilities are of being infected with a disease. The probabilities that resulted are shown in the probability tree. Which of the columns in the data table below accurately represents the probability values in the probability tree?

a. Plot A b. Plot B c. Plot C d. Plot D 32. Consider a collection of 240 snakes where 40 of them are cobras, 60 are rattlesnakes, 60 are boas, and 80 are anacondas. Cobras and rattle snakes are venomous, whereas boas and anacondas are not. If a snake is randomly chosen from this population, what is the probability it will be either a boa or venomous? a. 0.167 b. 0.417 c. 0.583 d. 0.666

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Chap 05_3e 33. The addition rule states that Pr[A and B] = Pr[A] + Pr[B]. a. True b. False 34. Bayes' theorem states that the sum of all mutually exclusive probabilities is one. a. True b. False 35. Consider a collection of 240 snakes where 40 of them are cobras, 60 are rattlesnakes, 60 are boas, and 80 are anacondas. Cobras and rattle snakes are venomous, whereas boas and anacondas are not. If a snake is randomly chosen from this population, what is the probability it will be a cobra or a boa? a. 0.167 b. 0.333 c. 0.417 d. 0.583 36. When we sample with replacement, we don't need to worry about conditional probabilities. a. True b. False 37. Consider a collection of 240 snakes where 40 of them are cobras, 60 are rattlesnakes, 60 are boas, and 80 are anacondas. Cobras and rattle snakes are venomous, whereas boas and anacondas are not. If a snake is randomly chosen from this population, what is the probability it will be either a cobra or venomous? a. 0.167 b. 0.417 c. 0.583 d. 0.666 38. Consider a collection of 100 birds where 20 of them are penguins, 25 are ostriches, 15 are hawks, and 40 are doves. Penguins and ostriches are unable to fly, whereas hawks and doves can. If a bird is randomly chosen from this population, what is the probability it will be either a penguin or unable to fly? a. 0.05 b. 0.25 c. 0.45 d. 0.65

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Chap 05_3e 39. The probability of an event is the _____ of times the event would occur if we repeated a random trial many times. a. Number b. Opposite c. Proportion d. Sum 40. Consider a collection of 240 snakes where 40 of them are cobras, 60 are rattlesnakes, 60 are boas, and 80 are anacondas. Cobras and rattle snakes are venomous, whereas boas and anacondas are not. If a snake is randomly chosen from this population, what is the probability it will be a boa? a. 0.167 b. 0.250 c. 0.333 d. 0.600 41. If A and B are mutually exclusive events and Pr[A] = 0.2 and Pr[B] = 0.3, then what is Pr[A or B]? a. 0.06 b. 0.5 c. 0.6 d. Cannot be determined from the information 42. If A and B are independent events and Pr[A] = 0.2 and Pr[B] = 0.3, then what is Pr[A or B]? a. 0.06 b. 0.5 c. 0.6 d. Cannot be determined from the information 43. Describe the difference between sampling with replacement and sampling without replacement with respect to calculating probabilities.

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Chap 05_3e 44. A fabella is a small bone in the knee found in a tendon behind the femur in some species of mammals, including humans. Historically, it has been rare, but recently it has become more common. Probability data for birth year and presence or absence of the bone is presented in the table. Imagine we examined 200 skeletons of individuals born in 1900 and 100 skeletons of individuals born in 2000. Draw a probability tree diagram depicting the probabilities of a random individual from our study having or not having a fabella in their skeleton.

45. Describe what a Venn diagram is and how it is used to compute probabilities.

46. Describe a real-world example of something that has a probability of 10%.

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Chap 05_3e 47. Under what circumstances is drawing a probability tree most useful?

48. A fabella is a small bone in the knee found in a tendon behind the femur in some species of mammals, including humans. Historically, it has been rare, but recently it has become more common. Probability data for birth year and presence or absence of the bone is presented in the table. Imagine we examined 200 skeletons of individuals born in 1900 and 100 skeletons of individuals born in 2000. Draw a mosaic plot depicting the probabilities of a random individual from our study having or not having a fabella in their skeleton.

49. When we make a probability tree, we look at outcomes for two different events and draw a diagram from left to right with one event and then the other. Invent a simple example with numbers and clearly show that the order we depict the events in a probability tree does not alter the final probabilities. (Hint: Draw two trees for the same probabilities)

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Chap 05_3e 50. Describe the difference between discrete and continuous probability distributions. In particular, how are they different in how they compute probabilities for certain outcomes?

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Chap 05_3e Answer Key 1. b 2. a 3. d 4. b 5. a 6. d 7. d 8. b 9. a 10. b 11. b 12. c 13. a 14. d 15. b 16. a 17. a 18. a 19. c 20. b 21. d 22. b 23. a 24. a 25. b 26. d Copyright Macmillan Learning. Powered by Cognero.

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Chap 05_3e 27. c 28. b 29. b 30. c 31. a 32. d 33. b 34. b 35. c 36. b 37. b 38. c 39. c 40. b 41. b 42. d 43.

44.

45.

46.

47.

48.

49.

50.

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Chap 06_3e Indicate the answer choice that best completes the statement or answers the question.

1. Which of the following is correct? a. We generally prefer doing one-sided tests followed by a two-sided test. b. We generally prefer doing two-sided tests followed by a one-sided test. c. We generally prefer doing one-sided tests unless we have a genuinely good reason to do a two-sided test. d. We generally prefer doing two-sided tests unless we have a genuinely good reason to do a one-sided test.

2. Consider a situation in which we calculate a 95% confidence interval that ranges from 35 to 45. If we conducted a two-sided test with the null hypothesis of the population mean equaling 43, what would the likely result of our test be? a. A P-value larger than 0.05 and we fail to reject the null hypothesis. b. A P-value larger than 0.05 and we reject the null hypothesis. c. A P-value smaller than 0.05 and we fail to reject the null hypothesis. d. A P-value smaller than 0.05 and we reject the null hypothesis.

3. The most commonly used significance level in biology is a value of 0.05. a. True b. False 4. If a two-sided statistical test returns a P-value less than 0.05, then what can be said about the parameter value specified in the null hypothesis? a. It is guaranteed to be inside the 95% confidence interval for the parameter. b. It is guaranteed to be outside the 95% confidence interval for the parameter. c. It is very likely inside the 95% confidence interval for the parameter. d. It is very likely outside the 95% confidence interval for the parameter.

5. Statistical hypotheses are statements about population values whereas scientific hypotheses are statements about natural phenomena that may account for population values. a. True b. False 6. The value of the significance level is the probability of making a Type II error. a. True b. False

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Chap 06_3e 7. Which of the following describes a Type II error? a. Failing to reject a false alternative hypothesis b. Failing to reject a false null hypothesis c. Rejecting a true alternative hypothesis d. Rejecting a true null hypothesis 8. The ability of a statistical test to correctly reject a false null hypothesis is called which of the following? a. Accuracy b. Power c. Precisions d. Reliability 9. Which of the following statements is correct? a. Larger P-values will tend to give nonsignificant results. b. Larger P-values will tend to give significant results. c. Lower P-values will tend to give insignificant results. d. Lower P-values will tend to give unsignificant results.

10. P-values range between –1 and 1. a. True b. False 11. Which of the following is true for a one-sided test? a. The alternative hypothesis specifies a range of values. b. The null hypothesis includes only a single value for the parameter of interest. c. We calculate our P-value using the extremes of the null distribution. d. We make a decision about using this test after looking at the data.

12. Nonsignificant tests are uninformative. a. True b. False 13. Generally speaking, if we fail to reject the null hypothesis, we should therefore conclude that the null hypothesis is true. a. True b. False 14. The y-axis for a null distribution is probability values. a. True b. False

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Chap 06_3e 15. The power of a statistical test is best described as which of the following? a. The probability that the test will correctly accept a false alternative hypothesis. b. The probability that the test will correctly accept a false null hypothesis. c. The probability that the test will correctly reject a false alternative hypothesis. d. The probability that the test will correctly reject a false null hypothesis.

16. Hypothesis testing quantifies how unusual the data are, assuming that the alternative hypothesis is true. a. True b. False 17. When calculating the 95% confidence intervals for the parameter value used in a nonsignificant statistical test, the region would usually (but not always) include the value specified in the null hypothesis. a. True b. False 18. Consider a hypothetical study in which ecologists looked at the sex ratios of clutches of frog eggs. In their sample, there were more clutches with a majority of males compared to those with a majority of females. The P-value of their test was 0.008. What is their best conclusion based on the evidence provided? a. The frequencies of male and female majority clutches seem to differ in the population. b. The frequencies of male and female majority clutches don't seem to differ in the population. c. There are more female majority clutches than male majority clutches in the population. d. There are more male majority clutches than female majority clutches in the population.

19. When presenting your results in a research paper or report, which of the following is not one of the pieces of information you should always include? a. The P-value b. The range of values c. The sample size d. The value of the test statistic 20. As studies increase in sample size, they tend to have more statistical power. a. True b. False 21. The alternative hypothesis is usually the hypothesis we would be most interested in determining is correct. a. True b. False

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Chap 06_3e 22. Increasing the value of the significance level tends to do which of the following? a. Increases Type I error and increases Type II error b. Increases Type I error and reduces Type II error c. Reduces Type I error and increases Type II error d. Reduces Type I error and reduces Type II error 23. Consider a null hypothesis in which we state that the mean mass of male and female robins in a population is the same. Which of the following is an appropriate alternative hypothesis? a. The mean mass of female robins is different from the mean mass of male robins. b. The mean mass of female robins is equal to the mean mass of male robins. c. The mean mass of female robins is less than the mean mass of male robins. d. The mean mass of female robins is more than the mean mass of male robins.

24. The value of the significance level is the probability of making a Type I error. a. True b. False 25. Which of the following is the best description of what a "two-sided" test means? a. Either the null or alternative hypothesis may be false. b. Either the null or alternative hypothesis may be true. c. The alternative hypothesis includes parameter values of both sides of the null hypothesis parameter value. d. The alternative hypothesis includes statistical values of both sides of the null hypothesis statistic value 26. The null hypothesis is a specific claim about the value of a sample statistic. a. True b. False 27. Which of the following describes a Type I error? a. Failing to reject a false alternative hypothesis b. Failing to reject a false null hypothesis c. Rejecting a true alternative hypothesis d. Rejecting a true null hypothesis

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Chap 06_3e 28. Consider a hypothetical study in which ecologists looked at the sex ratios of clutches of frog eggs. In their sample, there were more clutches with a majority of males compared to those with a majority of females. The P-value of their test was 0.08. What is their best conclusion based on the evidence provided? a. The frequencies of male and female majority clutches seem to differ in the population. b. The frequencies of male and female majority clutches don't seem to differ in the population. c. There are more female majority clutches than male majority clutches in the population. d. There are more male majority clutches than female majority clutches in the population.

29. The sampling distribution for a test statistic if the null hypothesis is true is called which of the following? a. The hypothetical distribution b. The null distribution c. The test distribution d. The true distribution 30. Consider a situation in which we calculate a 95% confidence interval that ranges from 18 to 23. If we conducted a two-sided test with the null hypothesis of the population mean equaling 17, what would the likely result of our test be? a. A P-value larger than 0.05 and we fail to reject the null hypothesis. b. A P-value larger than 0.05 and we reject the null hypothesis. c. A P-value smaller than 0.05 and we fail to reject the null hypothesis. d. A P-value smaller than 0.05 and we reject the null hypothesis.

31. The probabilities of Type I and Type II errors always add up to 1.0. a. True b. False 32. Which of the following is not one of the basic steps in hypothesis testing? a. State the hypothesis. b. Compute the test statistic with the data. c. Estimate the population parameter with the data. d. Determine the P-value.

33. If a one-sided test rejects the null hypothesis, then a two-sided test would have rejected the null hypothesis as well. a. True b. False 34. The null distribution is always centered around zero. a. True b. False

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Chap 06_3e 35. Which of the following is our best attitude to a test result that returns a nonsignificant result? a. The null hypothesis is conclusively demonstrated to be correct. b. The null hypothesis is conclusively demonstrated to be incorrect. c. The overall study is inconclusive and the null hypothesis is incorrect. d. The overall study is inconclusive and we shouldn't make a definitive decision.

36. It is recommended practice to look at the data values prior to deciding whether to perform a one-sided or two-sided test. a. True b. False 37. The P-value is the probability that the null hypothesis is true. a. True b. False 38. Typically, the null hypothesis is the statement that we are interested in _____. a. Accepting b. Disproving c. Proving d. Rejecting 39. Describe a data set and make two scientific hypotheses: one must be appropriate for studying with a twosided test and the other must be appropriate for studying with a one-sided test.

40. Is the null hypothesis always what we expect or hope to be true? Explain why or why not.

41. When describing the results of a study, we should report three things. What are these three values and why should we include each of them?

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Chap 06_3e 42. Describe the major problem with using a nonsignificant result as evidence that the null hypothesis is true.

43. In your own words, describe what a P-value is and how we use it to evaluate statistical hypotheses.

44. There is a risk relating to P-values when we look at our data before deciding on a one-sided or two-sided test. Describe this risk with specific reference to the P-value we calculate if we do the wrong test.

45. Describe the U.S. criminal justice system's assumptions about guilt and innocence using Type I and Type II terminology. Include reference to the concept of significance level as used in the system.

46. Describe the relationship between a statistical hypothesis and a scientific hypothesis.

47. Describe the relationship between the P-value of a two-sided statistical test and the confidence interval around the value listed in the null hypothesis.

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Chap 06_3e Answer Key 1. d 2. a 3. a 4. d 5. a 6. b 7. b 8. b 9. a 10. b 11. a 12. b 13. b 14. a 15. d 16. b 17. a 18. d 19. b 20. a 21. a 22. b 23. a 24. a 25. c 26. b Copyright Macmillan Learning. Powered by Cognero.

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Chap 06_3e 27. d 28. b 29. b 30. d 31. b 32. c 33. b 34. b 35. d 36. b 37. b 38. d 39.

40.

41.

42.

43.

44.

45.

46.

47.

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Chap 07_3e Indicate the answer choice that best completes the statement or answers the question.

1. What is the 95% confidence interval, using the Agresti-Coull method, for the proportion when there are 7 observed successes out of a total of 50 trials? a. 0.014 < p < 0.213 b. 0.044 < p < 0.236 c. 0.067 < p < 0.266 d. 0.104 < p < 0.282 2. Consider a binomial distribution with a sample size of 10 and a success probability of 0.9. What is the probability that there are more than 8 successes? a. 0.193 b. 0.349 c. 0.387 d. 0.736 3. Given a fixed proportion of successes in the population, the width of the sampling distribution for the number of successes gets narrower as the sample size gets larger. a. True b. False 4. If we have a sample with 25 values and a sample proportion of 0.36, what would the standard error of the proportion be?

a. 0.072 b. 0.096 c. 0.177 d. 0.215 5. Which of the following is not an assumption of the binomial distribution? a. All trials are independent of the others. b. The number of trials is a fixed value. c. The probability of success is less than 0.5. d. The same probability of success for each trial.

6. When we do a binomial test and obtain a P-value smaller than 0.05, then the 95% confidence interval for the proportion will almost certainly not include the proportion we hypothesized. a. True b. False

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Chap 07_3e 7. Imagine that we are rolling a six-sided die and we do that seven times. What is the probability that we roll a "one" either six or seven times? a. 0.00010 b. 0.00011 c. 0.00012 d. 0.00013 8. The standard error of a proportion is used to estimate how much variation there is in the sample data. a. True b. False 9. Consider the claim that 60% of the members of a population of bacteria have a plasmid conferring antibiotic resistance. If we collected 11 bacterial samples and 4 proved to have the resistance plasmid, what would the P-value of a binomial test of this hypothesis be? a. 0.0666 b. 0.0701 c. 0.1401 d. 0.3636 10. The probability distribution for the number of "successes" in a fixed number of independent trials, when the probability of success is the same for each, is called which of the following? a. Binomial distribution b. Bivariate distribution c. Joint distribution d. Pairwise distribution 11. The value of 8! / 5! is which of the following? a. 40 b. 336. c. 1,300 d. 14,630 12. Consider a bird has laid a clutch of six eggs that all hatch. Assuming the binomial distribution is appropriate, what is the probability that there is an equal number of male and female chicks that hatch? a. 0.279 b. 0.313 c. 0.346 d. 0.500

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Chap 07_3e 13. If a study with a total sample size of 15 measures 6 successes, in how many different sequences could these successes have occurred?? a. 2,002 b. 3,003 c. 4,004 d. 5,005 14. What is the 95% confidence interval, using the Wald method, for the proportion when there are 7 observed successes out of a total of 50 trials? a. 0.014 < p < 0.213 b. 0.044 < p < 0.236 c. 0.074 < p < 0.259 d. 0.104 < p < 0.282 15. Using the Wald method, what is the 95% confidence interval for the proportion when there are 15 observed successes and 25 observed failures? a. 0.240 < p < 0.540 b. 0.235 < p < 0.535 c. 0.230 < p < 0.530 d. 0.225 < p < 0.525 16. Consider the claim that 60% of the members of a population of bacteria have a plasmid conferring antibiotic resistance. If we collected some random bacterial samples and the P-value of a binomial test was 0.015, what would our conclusion be? a. We fail to reject the null hypothesis and therefore conclude that the true proportion of bacteria with resistance plasmids differs from 60%. b. We fail to reject the null hypothesis and therefore conclude that the true proportion of bacteria with resistance plasmids does not differ from 60%. c. We reject the null hypothesis and therefore conclude that the true proportion of bacteria with resistance plasmids differs from 60%. d. We reject the null hypothesis and therefore conclude that the true proportion of bacteria with resistance plasmids does not differ from 60%.

17. Using the Agresti-Coull method, what is the 95% confidence interval for the proportion when there are 15 observed successes and 25 observed failures? a. 0.243 < p < 0.529 b. 0.253 < p < 0.519 c. 0.263 < p < 0.509 d. 0.273 < p < 0.499

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Chap 07_3e 18. Imagine a surgery that is known to have a 10% chance of serious side effects. An internal hospital review shows that three out of eight of a particular doctor's patients have these side effects. If we conducted a binomial test of whether this doctor's patients are experiencing unusually low or high rates of side effects, what would our conclusion be? a. We fail to reject the null hypothesis and therefore conclude that the rate of side effects for this doctor differs from the usual 10%. b. We fail to reject the null hypothesis and therefore conclude that the rate of side effects for this doctor does not seem to differ from the usual 10%. c. We reject the null hypothesis and therefore conclude that the rate of side effects for this doctor differs from the usual 10%. d. We reject the null hypothesis and therefore conclude that the rate of side effects for this doctor does not seem to differ from the usual 10%.

19. 10! < 1,000 a. True b. False 20. Consider a class of 10 students in a school district with a 20% prevalence of students with special needs.

Assuming the binomial distribution is appropriate, what is the probability that exactly 2 of those students have special needs? a. 0.201 b. 0.302 c. 0.403 d. 0.504 21. Consider a set of nine separate water samples from a region where the prevalence of bacterial contamination is 30%. Assuming the binomial distribution is appropriate, what is the probability that exactly three of the samples indicate contamination? a. 0.267 b. 0.333 c. 0.350 d. 0.400 22. If a study reveals five successes and eight failures, in how many different ways (i.e., sequences) could this have occurred?? a. 789 b. 839 c. 1,287 d. 1,716

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Chap 07_3e 23. When calculating binomial probabilities, we use the term "success" for the desired outcome of each individual trial. a. True b. False 24. Consider the claim that 60% of the members of a population of bacteria have a plasmid conferring antibiotic resistance. If we collected some random bacterial samples and the P-value of a binomial test was 0.15, what would our conclusion be? a. We fail to reject the null hypothesis and therefore conclude that the true proportion of bacteria with resistance plasmids differs from 60%. b. We fail to reject the null hypothesis and therefore conclude that the true proportion of bacteria with resistance plasmids does not differ from 60%. c. We reject the null hypothesis and therefore conclude that the true proportion of bacteria with resistance plasmids differs from 60%. d. We reject the null hypothesis and therefore conclude that the true proportion of bacteria with resistance plasmids does not differ from 60%.

25. The value of 5! is which of the following? a. 20 b. 120 c. 125 d. 225 26. If the 95% confidence interval for the proportion does not include the value hypothesized in the binomial test, then the test will almost certainly return a P-value greater than 0.05. a. True b. False 27. Imagine a surgery that is known to have a 10% chance of serious side effects. An internal hospital review shows that three out of eight of a particular doctor's patients have these side effects. If we want to know whether this doctor's patients are experiencing unusually low or high rates of side effects, what would the Pvalue of a binomial test of this hypothesis be? a. 0.022 b. 0.044 c. 0.066 d. 0.088 28. When the binomial test returns a P-value less than 0.05, that generally means that the data match the expectations arising from using the binomial distribution to model the population. a. True b. False Copyright Macmillan Learning. Powered by Cognero.

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Chap 07_3e 29. The value of 99! / 97! is which of the following? a. 9,405 b. 9,504 c. 9,603 d. 9,702 30. What is the standard error of the proportion when the sample size is 55 values and the sample proportion is 0.4? a. 0.033 b. 0.066 c. 0.100 d. 0.133 31. Imagine a surgery that is known to have a 10% chance of serious side effects. An internal hospital review shows that 4 out of 8 of a particular doctor's patients have these side effects. If we conducted a binomial test of whether this doctor's patients are experiencing usually low or high rates of side-effects, what would our conclusion be? a. We fail to reject the null hypothesis and therefore conclude that the rate of side effects for this doctor differs from the usual 10%. b. We fail to reject the null hypothesis and therefore conclude that the rate of side effects for this doctor does not seem to differ from the usual 10%. c. We reject the null hypothesis and therefore conclude that the rate of side effects for this doctor differs from the usual 10%. d. We reject the null hypothesis and therefore conclude that the rate of side effects for this doctor does not seem to differ from the usual 10%.

32. The value of 7! is which of the following? a. 1,040 b. 1,840 c. 5,040 d. 12,840 33. 20! > 992 a. True b. False 34. When calculating the standard error of a proportion, if the sample size is small or the population proportion is close to 0 or 1, then the Wald method is preferable to the Agresti-Coull method. a. True b. False Copyright Macmillan Learning. Powered by Cognero.

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Chap 07_3e 35. The term

is stated verbally as "three choose seven."

a. True b. False 36. The value of

is which of the following?

a. 77 b. 330 c. 7,920 d. 37,290 37. The value of 25! / 22! is which of the following? a. 550 b. 2,300 c. 13,800 d. 215,225 38. If we have a sample with 50 values and a sample proportion of 0.40, what would the standard error of the proportion be? a. 0.049 b. 0.059 c. 0.069 d. 0.079 39. The value of

is which of the following?

a. 1,020 b. 1,140 c. 1,260 d. 1,380 40. Consider the claim that 60% of the members of a population of bacteria have a plasmid conferring antibiotic resistance. If we collected 11 bacterial samples and 3 proved to have the resistance plasmid, what would the P-value of a binomial test of this hypothesis be? a. 0.0233 b. 0.0467 c. 0.1774 d. 0.3547

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Chap 07_3e 41. Given a fixed proportion of successes in the population, the width of the sampling distribution for the proportion of successes gets narrower as the sample size gets larger. a. True b. False 42. If a study reveals 10 successes and 12 failures, in how many different ways (i.e., sequences) could this have occurred?? a. 646,646 b. 705,432 c. 801,426 d. 953,664 43. The term

is stated verbally as "ten choose four."

a. True b. False 44. What is the standard error of the proportion when the sample size is 81 values and the sample proportion is 0.35? a. 0.023 b. 0.033 c. 0.043 d. 0.053 45. If a binomial test returns a P-value greater than 0.05, we typically interpret this as meaning there is a match between the data and our expectations arising from using the binomial distribution to model the population. a. True b. False 46. Imagine a surgery that is known to have a 10% chance of serious side effects. An internal hospital review shows that four out of eight of a particular doctor's patients have these side effects. If we want to know whether this doctor's patients are experiencing usually low or high rates of side effects, what would the Pvalue of a binomial test of this hypothesis be? a. 0.009 b. 0.09 c. 0.9 d. 0.5 47. The binomial test uses data to test whether a sample proportion matches the null expectation for the proportion. a. True b. False Copyright Macmillan Learning. Powered by Cognero.

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Chap 07_3e 48. If a study with a total sample size of 14 measures 7 successes, in how many different sequences could these successes have occurred?? a. 3,003 b. 3,432 c. 3,867 d. 4,124 49. Clearly and precisely describe the statistical conclusions that we make when conducting a binomial test.

Describe both results: when we obtain a P-value less than 0.05 and when we obtain a P-value larger than 0.05.

50. Consider a situation in which a group of physiologists are studying the sizes of wings in seagulls. They are interested in whether the gulls show asymmetry or symmetry with respect to the wing sizes. They humanely trap (and subsequently release) 14 seagulls, and after measuring the wings they determine that 10 had larger right wings than left wings and 4 had larger left wings than right wings. Use a binomial test and the calculation of 95% confidence intervals to address this question: Is there sufficient evidence to determine whether the population of seagulls is symmetric with respect to their wing sizes or not?

51. Demonstrate with a hypothetical numerical example how the Agresti-Coull method generates a narrower confidence interval than the Wald method.

52. What is the relationship between the 95% confidence interval for a proportion and the P-value of a binomial test?

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Chap 07_3e 53. Consider a situation in which a group of ecologists are studying the frequency of symbiotic relationships between acacia trees and ant colonies in Bolivia. Previous studies in Colombia have shown the frequency of symbiotic relationships there to be 30%, and the ecologists are interested in whether the same frequency holds in Colombia. They locate 20 trees and determine that 11 of the trees appear to have a symbiotic relationship with an ant colony. Use a binomial test and the calculation of 95% confidence intervals to address this question: Is there sufficient evidence to determine whether the frequency of symbiotic acacia trees in Colombia differs from 30% or not?

54. Draw a bar chart showing the sampling distribution for the proportion of successes for sample size 3 where the population proportion of successes is 0.6. Clearly label each axis and be precise.

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Chap 07_3e Answer Key 1. c 2. d 3. b 4. b 5. c 6. a 7. d 8. b 9. c 10. a 11. b 12. b 13. d 14. b 15. d 16. c 17. a 18. b 19. b 20. b 21. a 22. c 23. b 24. b 25. b 26. b Copyright Macmillan Learning. Powered by Cognero.

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Chap 07_3e 27. c 28. b 29. d 30. b 31. c 32. c 33. a 34. b 35. b 36. b 37. c 38. c 39. b 40. b 41. a 42. a 43. a 44. d 45. a 46. a 47. b 48. b 49.

50.

51.

52.

53.

54.

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Chap 07_3e

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Chap 08_3e Indicate the answer choice that best completes the statement or answers the question.

1. If a set of values exhibits a Poisson distribution with a mean value of 1, then the probability of observing no successes in a given period is equal to 0.368. (Note: The value of e = 2.718.) a. True b. False 2. A χ2 goodness-of-fit test that results in a large P-value supports the null hypothesis. a. True b. False 3. A χ2 goodness-of-fit test can be done when the expected value in one or more categories is less than 1 as long as long as at least one category has an expected value larger than 5. a. True b. False 4. Consider a study testing whether birds were equally likely to rest on each streetlight. Researchers surveyed 30 randomly chosen streetlights in a city known to have many birds and counted the number of birds resting on each streetlight. Data on the number of birds seen on the lights are shown. (Note: No lights had more than three birds.) What is the mean number of birds observed on each light?

a. 1.40 b. 1.60 c. 1.80 d. 2.00

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Chap 08_3e 5. When two heterozygotes are mated, the ratios of the offspring produced should be in a 1:2:1 ratio if normal Mendelian segregation is occurring. If one of the alleles is dominant, then the phenotypes observed should be present in a 3:1 ratio with the dominant phenotype more common than the recessive one. We can use an χ2 goodness-of-fit test to test whether the ratio of offspring is indeed 3:1. Imagine a cross is performed and the number of offspring observed are 67 with the dominant phenotype and 33 with the recessive phenotype.

Using the table of critical values shown, what is the P-value range we would obtain for our test?

a. 0.05 < P b. 0.025 < P < 0.05 c. 0.01 < P < 0.025 d. P < 0.01 6. Consider a situation in which we expect one third of the observed values to be in each of three categories. We can use a χ2 goodness-of-fit test to test whether the frequencies of offspring are as expected. If the numbers of values in each category are 13, 18, and 29, what is the χ2 value we would obtain? a. 6.28 b. 6.42 c. 6.56 d. 6.70 7. A χ2 goodness-of-fit test can be done when the expected value in each category is more than 1. a. True b. False

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Chap 08_3e 8. Consider a situation in which we expect one-third of the observed values to be in each of three categories. We can use an χ2 goodness-of-fit test to test whether the frequencies of offspring are as expected. If the numbers of values in each category are 14, 19, and 27, what is the χ2 value we would obtain? a. 2.05 b. 2.13 c. 4.30 d. 4.39 9. Consider a study testing whether birds were equally likely to rest on each streetlight. Researchers surveyed 30 randomly chosen streetlights in a city known to have many birds and counted the number of birds resting on each streetlight. Data on the number of birds seen on the lights are shown. (Note: No lights had more than three birds.) Assuming a Poisson process, what is the expected number of streetlights without any birds?

a. 3.06 b. 4.06 c. 5.06 d. 6.06

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Chap 08_3e 10. Consider a study testing whether birds were equally likely to rest on each streetlight. Researchers surveyed 30 randomly chosen streetlights in a city known to have many birds and counted the number of birds resting on each streetlight. Data on the number of birds seen on the lights are shown. (Note: No lights had more than three birds.) What is the χ2 value we would obtain for a goodness-of-fit test comparing these data to the expectations from a Poisson process?

a. 2.33 b. 4.33 c. 6.33 d. 8.33

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Chap 08_3e 11. Consider a situation in which we expect the same frequency of 64 total observations to be in each of four categories. We can use an χ2 goodness-of-fit test to test whether the frequencies of offspring are as expected.

If the numbers of values in each category are 12, 26, 8, and 18, and using the table of critical values shown, what is the conclusion of our test?

a. Fail to reject the null hypothesis, we lack the evidence to decide that the frequencies differ from those that were expected. b. Fail to reject the null hypothesis, we have good evidence to decide that the frequencies differ from those that were expected. c. Reject the null hypothesis, we lack the evidence to decide that the frequencies differ from those that were expected. d. Reject the null hypothesis, we have good evidence to decide that the frequencies differ from those that were expected.

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Chap 08_3e 12. When two heterozygotes are mated, the ratios of the offspring produced should be in a 1:2:1 ratio if normal Mendelian segregation is occurring. If one of the alleles is dominant, then the phenotypes observed should be present in a 3:1 ratio with the dominant phenotype more common than the recessive one. We can use an χ2 goodness-of-fit test to test whether the ratio of offspring is indeed 3:1. Imagine a cross is performed and the number of offspring observed are 65 with the dominant phenotype and 35 with the recessive phenotype.

Using the table of critical values shown, what is the P-value range we would obtain for our test?

a. 0.05 < P b. 0.025 < P < 0.05 c. 0.01 < P < 0.025 d. P < 0.01

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Chap 08_3e 13. Consider a situation in which we expect the same frequency of 64 total observations to be in each of four categories. We can use an χ2 goodness-of-fit test to test whether the frequencies of offspring are as expected.

If the numbers of values in each category are 12, 26, 8, and 18, what is the P-value range we would obtain for our test? (Use the table of critical values shown to answer this question.)

a. 0.05 < P b. 0.025 < P < 0.05 c. 0.01 < P < 0.025 d. P < 0.01 14. Consider a study testing whether birds were equally likely to rest on each streetlight. Researchers surveyed 30 randomly chosen streetlights in a city known to have many birds and counted the number of birds resting on each streetlight. Data on the number of birds seen on the lights are shown. (Note: No lights had more than three birds.) What is the variance for the number of birds observed on each light?

a. 0.32 b. 0.52 c. 0.72 d. 0.92

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Chap 08_3e 15. Consider a situation in which we expect the same frequency of 64 total observations to be in each of four categories. We can use an χ2 goodness-of-fit test to test whether the frequencies of offspring are as expected.

If the numbers of values in each category are 12, 24, 10, and 18, and using the table of critical values shown, what is the conclusion of our test?

a. Fail to reject the null hypothesis, we lack the evidence to decide that the frequencies differ from those that were expected. b. Fail to reject the null hypothesis, we have good evidence to decide that the frequencies differ from those that were expected. c. Reject the null hypothesis, we lack the evidence to decide that the frequencies differ from those that were expected. d. Reject the null hypothesis, we have good evidence to decide that the frequencies differ from those that were expected.

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Chap 08_3e 16. Consider a study testing whether the number of birds resting on streetlights is random. Researchers surveyed 30 randomly chosen streetlights in a city known to have many birds and counted the number of birds resting on each streetlight. Data on the number of birds seen on the lights are shown. (Note: No lights had more than three birds.) Assuming a Poisson process, what is the expected number of streetlights with three or more birds?

a. 5.00 b. 6.00 c. 7.00 d. 8.00 17. When two heterozygotes are mated, the ratios of the offspring produced should be in a 1:2:1 ratio if normal Mendelian segregation is occurring. If one of the alleles is dominant, then the phenotypes observed should be present in a 3:1 ratio with the dominant phenotype more common than the recessive one. We can use a χ2 goodness-of-fit test to test whether the ratio of offspring is indeed 3:1. Imagine a cross is performed and the number of offspring observed are 67 with the dominant phenotype and 33 with the recessive phenotype. What is the χ2 value we would obtain? a. 2.895 b. 3.413 c. 3.864 d. 4.273

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Chap 08_3e 18. Consider a study testing whether the number of birds resting on streetlights is random. Researchers surveyed 30 randomly chosen streetlights in a city known to have many birds and counted the number of birds resting on each streetlight. Data on the number of birds seen on the lights are shown. (Note: No lights had more than three birds.) What is the χ2 value we would obtain for a goodness-of-fit test comparing these data to the expectations from a Poisson process?

a. 3.85 b. 5.85 c. 7.85 d. 9.85 19. At the end of the chapter, there was a list of guidelines and procedures for conducting a good statistical study.

Which of the following was not one of the broad procedures listed? a. Complete the ethical permission paperwork accurately. b. Discuss the design with other researchers. c. Keep the design of your experiment as simple as possible. d. List the possible outcomes of your experiment.

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Chap 08_3e 20. When two heterozygotes are mated, the ratios of the offspring produced should be in a 1:2:1 ratio if normal Mendelian segregation is occurring. If one of the alleles is dominant, then the phenotypes observed should be present in a 3:1 ratio with the dominant phenotype more common than the recessive one. We can use an χ2 goodness-of-fit test to test whether the ratio of offspring is indeed 3:1. Imagine a cross is performed and the number of offspring observed are 67 with the dominant phenotype and 33 with the recessive phenotype.

Using the table of critical values shown, what is the conclusion of our test?

a. We fail to reject the null hypothesis and therefore conclude that something other than usual Mendelian segregation is occurring. b. We fail to reject the null hypothesis and therefore conclude that usual Mendelian segregation is occurring. c. We reject the null hypothesis and therefore conclude that something other than usual Mendelian segregation is occurring. d. We reject the null hypothesis and therefore conclude that usual Mendelian segregation is occurring.

21. The P-value obtained using an χ2 goodness-of-fit test is a good indication of the magnitude of the difference in observed and expected proportions. a. True b. False

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Chap 08_3e 22. Consider a situation in which we expect one-third of the observed values to be in each of three categories. We can use an χ2 goodness-of-fit test to test whether the frequencies of offspring are as expected. If the numbers of values in each category are 13, 18, and 29, and using the table of critical values shown, what is the conclusion of our test?

a. Fail to reject the null hypothesis, we lack the evidence to decide that the frequencies differ from those that were expected. b. Fail to reject the null hypothesis, we have good evidence to decide that the frequencies differ from those that were expected. c. Reject the null hypothesis, we lack the evidence to decide that the frequencies differ from those that were expected. d. Reject the null hypothesis, we have good evidence to decide that the frequencies differ from those that were expected.

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Chap 08_3e 23. Consider a situation in which we expect the same frequency of 64 total observations to be in each of four categories. We can use an χ2 goodness-of-fit test to test whether the frequencies of offspring are as expected.

If the numbers of values in each category are 12, 24, 10, and 18, what is the P-value range we would obtain for our test? (Use the table of critical values shown to answer this question.)

a. 0.05 < P b. 0.025 < P < 0.05 c. 0.01 < P < 0.025 d. P < 0.01 24. If a set of values exhibits a Poisson distribution, then the mean of the values is the same as the variance of the values. a. True b. False

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Chap 08_3e 25. Consider a claim that 60% of the mice in a region have parasitic infections. We can use an χ2 goodness-of-fit test to test whether the proportion is indeed 60%. Consider a study in which we collect a random sample of 50 mice and 36 have infections. Calculate the χ2 value, and using the table of critical values shown, what is the P-value range we would obtain for our test?

a. P > 0.05 b. 0.025 < P < 0.05 c. 0.01 < P < 0.025 d. P < 0.01

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Chap 08_3e 26. Consider a claim that 60% of the mice in a region have parasitic infections. We can use an χ2 goodness-of-fit test to test whether the proportion is indeed 60%. Consider a study in which we collect a random sample of 50 mice and 37 have infections. Calculate the χ2 value, and using the table of critical values shown, what is the conclusion of our test?

a. We fail to reject the null hypothesis and therefore conclude that the percentage of mice with infections may indeed be 60% as claimed. b. We fail to reject the null hypothesis and therefore conclude that the percentage of mice with infections is not 60% as claimed. c. We reject the null hypothesis and therefore conclude that the percentage of mice with infections may indeed be 60% as claimed. d. We reject the null hypothesis and therefore conclude that the percentage of mice with infections is not 60% as claimed.

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Chap 08_3e 27. Consider a study testing whether birds were equally likely to rest on each streetlight. Researchers surveyed 30 randomly chosen streetlights in a city known to have many birds and counted the number of birds resting on each streetlight. Data on the number of birds seen on the lights are shown. (Note: No lights had more than three birds.) Assuming a Poisson process, what is the expected number of streetlights without any birds?

a. 3.4 b. 5.4 c. 7.4 d. 9.4 28. Consider a study testing whether birds were equally likely to rest on each streetlight. Researchers surveyed 30 randomly chosen streetlights in a city known to have many birds and counted the number of birds resting on each streetlight. Data on the number of birds seen on the lights are shown. (Note: No lights had more than three birds.) What is the variance for the number of birds observed on each light?

a. 0.87 b. 1.27 c. 1.67 d. 2.07

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Chap 08_3e 29. Consider a situation in which we expect one-third of the observed values to be in each of three categories. We can use an χ2 goodness-of-fit test to test whether the frequencies of offspring are as expected. If the numbers of values in each category are 14, 19, and 27, what is the P-value range we would obtain for our test? (Use the table of critical values shown to answer this question.)

a. 0.05 < P b. 0.025 < P < 0.05 c. 0.01 < P < 0.025 d. P < 0.01 30. The χ2 goodness-of-fit test is a good alternative for the binomial test when there are only two categories and a large number of observations. a. True b. False

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Chap 08_3e 31. Consider a claim that 60% of the mice in a region have parasitic infections. We can use an χ2 goodness-of-fit test to test whether the proportion is indeed 60%. Consider a study in which we collect a random sample of 50 mice and 36 have infections. Calculate the χ2 value, and using the table of critical values shown, what is the conclusion of our test?

a. We fail to reject the null hypothesis and therefore conclude that the percentage of mice with infections may indeed be 60% as claimed. b. We fail to reject the null hypothesis and therefore conclude that the percentage of mice with infections is not 60% as claimed. c. We reject the null hypothesis and therefore conclude that the percentage of mice with infections may indeed be 60% as claimed. d. We reject the null hypothesis and therefore conclude that the percentage of mice with infections is not 60% as claimed.

32. Consider a situation in which we expect the same frequency of 64 total observations to be in each of four categories. We can use a χ2 goodness-of-fit test to test whether the frequencies of offspring are as expected. If the numbers of values in each category are 12, 24, 10, and 18, what is the χ2 value we would obtain? a. 7.50 b. 7.82 c. 9.50 d. 9.82

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Chap 08_3e 33. Consider a study testing whether the number of birds resting on streetlights is random. Researchers surveyed 30 randomly chosen streetlights in a city known to have many birds and counted the number of birds resting on each streetlight. Data on the number of birds seen on the lights are shown. (Note: No lights had more than three birds.) Using the χ2 value we obtained for a goodness-of-fit test comparing these data to the expectations from a Poisson process and the list of critical values shown, what is the conclusion of our test?

a. Fail to reject the null hypothesis, the birds appear randomly distributed on the streetlights. b. Fail to reject the null hypothesis, the birds appear non-randomly distributed on the streetlights. c. Reject the null hypothesis, the birds appear randomly distributed on the streetlights. d. Reject the null hypothesis, the birds appear non-randomly distributed on the streetlights.

34. Consider a study testing whether birds were equally likely to rest on each streetlight. Researchers surveyed 30 randomly chosen streetlights in a city known to have many birds and counted the number of birds resting on each streetlight. Data on the number of birds seen on the lights are shown. (Note: No lights had more than three birds.) What is the mean number of birds observed on each light?

a. 1.40 b. 1.60 c. 1.80 d. 2.00

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Chap 08_3e 35. Consider a situation in which we expect one-third of the observed values to be in each of 3 categories. We can use an χ2 goodness-of-fit test to test whether the frequencies of offspring are as expected. If the numbers of values in each category are 14, 19, and 27, and using the table of critical values shown, what is the conclusion of our test?

a. Fail to reject the null hypothesis, we lack the evidence to decide that the frequencies differ from those that were expected. b. Fail to reject the null hypothesis, we have good evidence to decide that the frequencies differ from those that were expected. c. Reject the null hypothesis, we lack the evidence to decide that the frequencies differ from those that were expected. d. Reject the null hypothesis, we have good evidence to decide that the frequencies differ from those that were expected.

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Chap 08_3e 36. Consider a situation in which we expect one-third of the observed values to be in each of three categories. We can use an χ2 goodness-of-fit test to test whether the frequencies of offspring are as expected. If the numbers of values in each category are 13, 18, and 29, what is the P-value range we would obtain for our test? (Use the table of critical values shown to answer this question.)

a. 0.05 < P b. 0.025 < P < 0.05 c. 0.01 < P < 0.025 d. P < 0.01 37. Consider a study testing whether birds were equally likely to rest on each streetlight. Researchers surveyed 30 randomly chosen streetlights in a city known to have many birds and counted the number of birds resting on each streetlight. Data on the number of birds seen on the lights are shown. (Note: No lights had more than three birds.) Assuming a Poisson process, what is the expected number of streetlights with three or more birds?

a. 5.50 b. 6.50 c. 7.50 d. 8.50 Copyright Macmillan Learning. Powered by Cognero.

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Chap 08_3e 38. When two heterozygotes are mated, the ratios of the offspring produced should be in a 1:2:1 ratio if normal Mendelian segregation is occurring. If one of the alleles is dominant, then the phenotypes observed should be present in a 3:1 ratio with the dominant phenotype more common than the recessive one. We can use an χ2 goodness-of-fit test to test whether the ratio of offspring is indeed 3:1. Imagine a cross is performed and the number of offspring observed are 65 with the dominant phenotype and 35 with the recessive phenotype. What is the χ2 value we would obtain? a. 2.267 b. 3.000 c. 4.396 d. 5.333 39. Consider a situation in which we expect the same frequency of 64 total observations to be in each of four categories. We can use an χ2 goodness-of-fit test to test whether the frequencies of offspring are as expected.

If the numbers of values in each category are 12, 26, 8, and 18, what is the χ2 value we would obtain? a. 10.55 b. 11.50 c. 12.45 d. 13.40 40. Consider a claim that 60% of the mice in a region have parasitic infections. We can use an χ2 goodness-of-fit test to test whether the proportion is indeed 60%. Consider a study in which we collect a random sample of 50 mice and 37 have infections. What is the χ2 value we would obtain? a. 1.500 b. 1.883 c. 4.083 d. 5.094

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Chap 08_3e 41. Consider a claim that 60% of the mice in a region have parasitic infections. We can use an χ2 goodness-of-fit test to test whether the proportion is indeed 60%. Consider a study in which we collect a random sample of 50 mice and 37 have infections. Calculate the χ2 value, and using the table of critical values shown, what is the P-value range we would obtain for our test?

a. 0.05 < P b. 0.025 < P < 0.05 c. 0.01 < P < 0.025 d. P < 0.01 42. Consider a study testing whether birds were equally likely to rest on each streetlight. Researchers surveyed 30 randomly chosen streetlights in a city known to have many birds and counted the number of birds resting on each streetlight. Data on the number of birds seen on the lights are shown. (Note: No lights had more than three birds.) Using the χ2 value we obtained for a goodness-of-fit test comparing these data to the expectations from a Poisson process and the list of critical values shown, what is the conclusion of our test?

a. Fail to reject the null hypothesis, the birds appear randomly distributed on the streetlights b. Fail to reject the null hypothesis, the birds appear non-randomly distributed on the streetlights c. Reject the null hypothesis, the birds appear randomly distributed on the streetlights d. Reject the null hypothesis, the birds appear non-randomly distributed on the streetlights Copyright Macmillan Learning. Powered by Cognero.

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Chap 08_3e 43. When two heterozygotes are mated, the ratios of the offspring produced should be in a 1:2:1 ratio if normal Mendelian segregation is occurring. If one of the alleles is dominant, then the phenotypes observed should be present in a 3:1 ratio with the dominant phenotype more common than the recessive one. We can use an χ2 goodness-of-fit test to test whether the ratio of offspring is indeed 3:1. Imagine a cross is performed and the number of offspring observed are 65 with the dominant phenotype and 35 with the recessive phenotype.

Using the table of critical values shown, what is the conclusion of our test?

a. We fail to reject the null hypothesis and therefore conclude that something other than usual Mendelian segregation is occurring. b. We fail to reject the null hypothesis and therefore conclude that usual Mendelian segregation is occurring. c. We reject the null hypothesis and therefore conclude that something other than usual Mendelian segregation is occurring. d. We reject the null hypothesis and therefore conclude that usual Mendelian segregation is occurring.

44. Consider a claim that 60% of the mice in a region have parasitic infections. We can use an χ2 goodness-of-fit test to test whether the proportion is indeed 60%. Consider a study in which we collect a random sample of 50 mice and 36 have infections. What is the χ2 value we would obtain? a. 1.500 b. 3.000 c. 4.500 d. 6.000 45. Which of the following best describes how the concept of degrees of freedom (df) is used in an χ2 goodnessof-fit test? a. The df describes the strength of our conclusion. b. The df specifies which probability distribution we will use. c. The df is based on a list of how many hypotheses we are testing. d. The df is inversely related to the sample size.

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Chap 08_3e 46. Which of the following best describes how an χ2 goodness-of-fit test is used and performed? a. The observed and expected frequencies are compared and a close match results in a large P-value, which supports rejection of the null hypothesis. b. The observed and expected frequencies are compared and a close match results in a small P-value, which supports rejection of the null hypothesis. c. The observed and expected frequencies are compared and a mismatch results in a large P-value, which supports rejection of the null hypothesis. d. The observed and expected frequencies are compared and a mismatch results in a small P-value, which supports rejection of the null hypothesis.

47. A χ2 goodness-of-fit test directly compares frequencies, not proportions. a. True b. False 48. The χ2 goodness-of-fit test makes a better estimate of the true P-value than the binomial test. a. True b. False 49. Outline the major steps you would take when planning an experiment testing whether a high-fat diet increases obesity in rats. Keep in mind the advice at the end of the chapter (the interleaf) when you describe the steps.

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Chap 08_3e 50. Anthony says that he thinks births at a local hospital will be equally likely to occur on any day of the week, whereas Justin says they probably won't be because doctors or hospitals schedule Caesarian sections for certain days. Imagine they collect data for 105 births and the numbers on each day are as follow: 21, 16, 8, 12, 10, 17, 21. Conduct an χ2 goodness-of-fit test to determine whether the data support Anthony or Sarah.

As part of your answer, present the test statistic and the P-value range it corresponds to (using the table of critical values for 6 degrees of freedom shown).

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Chap 08_3e 51. Sofia says that she thinks births at a local hospital will be equally likely to occur on any day of the week, whereas Isabella says they probably won't be because doctors or hospitals schedule Caesarian sections for certain days. Imagine they collect data for 105 births and the numbers on each day are as follow: 20, 18, 7, 12, 9, 17, 22. Conduct an χ2 goodness-of-fit test to determine whether the data support Sofia or Isabella. As part of your answer, present the test statistic and the P-value range it corresponds to (using the table of critical values for 6 degrees of freedom shown).

52. Consider a Poisson distribution with an integer mean value. Using the equation for the Poisson distribution, show that the probability value for the number of observations equal to the mean and the probability value for a number of observations one less than the mean are equal.

53. Describe how we use critical values to estimate the probability of seeing the χ2 test statistic we calculate.

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Chap 08_3e Answer Key 1. a 2. a 3. b 4. b 5. a 6. d 7. b 8. c 9. d 10. c 11. d 12. c 13. d 14. b 15. a 16. a 17. b 18. d 19. a 20. b 21. b 22. d 23. a 24. a 25. a 26. d Copyright Macmillan Learning. Powered by Cognero.

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Chap 08_3e 27. c 28. a 29. a 30. a 31. a 32. a 33. d 34. a 35. a 36. b 37. b 38. d 39. b 40. c 41. b 42. a 43. c 44. b 45. b 46. d 47. a 48. b 49.

50.

51.

52.

53.

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Chap 09_3e Indicate the answer choice that best completes the statement or answers the question.

1. Consider a study in which people were recruited and followed for 40 years to determine their health problems. The researchers were interested in lung cancer so at the end of the study they counted the number of participants who had died from lung cancer, or currently had it, and those that did not. They also counted how many were non-smokers their whole life or had been smokers at some point in their lives. The number of non-smokers with lung cancer was 36 and the number of non-smokers with no sign of lung cancer was 815.

The number of smokers with lung cancer was 26 and the number of smokers with no sign of lung cancer was 161.

Assuming a null hypothesis of no relationship between smoking and risk of lung cancer, which of the following values is closest to the expected number of smokers who did not get lung cancer? a. 131 b. 146 c. 161 d. 176 2. There are many claims that eating organic food leads to better health outcomes. To study this, a dietician collects data from her patients: she categorizes their blood pressure values into elevated and healthy and she administers a questionnaire from which she is able to classify their diet into high in organic food and low in organic food. The number of patients with high organic food consumption who had elevated and healthy blood pressures were 33 and 74 respectively. The number of patients with low organic food consumption who had elevated and healthy blood pressures were 267 and 395 respectively.

Assuming a null hypothesis of no relationship between type of diet and blood pressure, which of the following values is closest to the expected number of patients who ate a diet low in organic food who would have elevated blood pressure? a. 258 b. 294 c. 348 d. 404

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Chap 09_3e Humans aren't the only animals that get cancer, other organisms get tumors as well and their risk may be influenced by environmental factors. An ecologist decides to study whether pollution in lakes causes cancer so he collects 100 fish from each of two lakes, one known to be polluted and the other known to be pristine. He then dissects them and determines if they have tumors in their tissues or not. His data is shown below.

Tumors present No tumors

Polluted 26 74

Pristine 15 85

3. To determine whether there appears to be a statistically significant relationship between exposure to pollution and risk of developing tumors he decides to conduct a χ2 analysis. Based on the results of this analysis, which of the following is the most appropriate conclusion? a. Fish appear to be at a significantly higher risk of tumors in the polluted lake compared to the pristine lake (P < 0.05). b. Fish appear to be at a significantly higher risk of tumors in the polluted lake compared to the pristine lake (P > 0.05). c. Fish appear to be at a significantly lower risk of tumors in the polluted lake compared to the pristine lake (P < 0.05). d. These data do not provide sufficient evidence that the risk of tumors differs in polluted or pristine lakes (P < 0.05).

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Chap 09_3e A microbial ecologist is interested in whether the microbial community of a pond changes when it rains. She knows that rainfall will increase the number of bacteria, but she is interested in the pattern of diversity. She collects a water sample from a pond two days before a rainfall and two days after and plates her samples on agar (a method to measure bacteria) and counts the number of colonies she observes for each of three bacteria: E. Coli, Salmonella, and Giardia. In the pre-rain sample she observes 21, 57, and 32 colonies respectively. In the post-rain sample she observes 59, 83, and 88 colonies respectively.

4. To determine whether there appears to be a statistically significant relationship between rainfall and bacterial diversity she would conduct a χ2 analysis. When performing this analysis, which of the values below is closest to the χ2 statistic she would obtain? a. 2.6 b. 6.2 c. 6.7 d. 7.6 5. To determine whether there appears to be a statistically significant relationship between rainfall and bacterial diversity she would conduct a χ2 analysis. After performing this analysis, which of the ranges below best describes the P value she would obtain? a. P > 0.05 b. 0.05 > P > 0.025 c. 0.025 > P > 0.01 d. P < 0.01

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Chap 09_3e Consider an experiment in which adult laboratory mice were fed one of three diets: high fat, low fat, and a control diet. The mice were weighed, received these diets for 2 weeks, and then were weighed again. The table below shows the results of the experiment.

Diet High Fat Low Fat Control

Gained weight 79 30 70

Lost weight 21 69 30

6. Assuming a null hypothesis of no relationship between diet and weight gain, which of the following values is closest to the expected count of individuals in the control group that gained weight? a. 20 b. 40 c. 60 d. 70 Consider the following values for numbers of major traffic accidents involving male and female drivers. The accidents are divided into ones involving a fatality and ones that did not. What is the relative risk for male drivers with regard to fatal accidents?

Fatal Non-fatal

Males 275 3024

Females 142 564

7. What is the odds ratio of fatal accidents for males versus females? a. 10.38 b. 2.77 c. 0.10 d. 0.36

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Chap 09_3e 8. Consider a study in which people were recruited and followed for 40 years to determine their health problems. The researchers were interested in lung cancer so at the end of the study they counted the number of participants who had died from lung cancer, or currently had it, and those that did not. They also counted how many were non-smokers their whole life or had been smokers at some point in their lives. The number of non-smokers with lung cancer was 36 and the number of non-smokers with no sign of lung cancer was 815.

The number of smokers with lung cancer was 26 and the number of smokers with no sign of lung cancer was 161.

To determine whether there appears to be a significant relationship between smoking and risk of lung cancer we would conduct a χ2 analysis. When performing this analysis, which of the values below is closest to the contribution to the χ2 statistic from the "never smoked : had lung cancer"? a. 0.97 b. 2.54 c. 4.33 d. 11.17 Consider an experiment in which a pharmaceutical company is testing a new drug that they hope will lower cholesterol levels. They administer three treatments: A dose of the drug, a dose of a placebo, and a control group that receives neither drug nor placebo. after 24 hours they then measured the cholesterol levels and compared the values to baseline levels measured prior to treatment. The table below shows the results of the experiment.

Treatment

Chol. lower

Drug Placebo Control

64 51 48

Chol. increased or the same 36 49 52

9. To determine whether there appears to be a statistically significant relationship between diet and weight gain or loss they would conduct a χ2 analysis. When performing this analysis, which of the values below is closest to the contribution to the χ2 statistic from the "drug : cholesterol lower" category? a. 1.72 b. 1.91 c. 2.05 d. 2.21

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Chap 09_3e A microbial ecologist is interested in whether the microbial community of a pond changes when it rains. She knows that rainfall will increase the number of bacteria, but she is interested in the pattern of diversity. She collects a water sample from a pond two days before a rainfall and two days after and plates her samples on agar (a method to measure bacteria) and counts the number of colonies she observes for each of three bacteria: E. Coli, Salmonella, and Giardia. In the pre-rain sample she observes 21, 57, and 32 colonies respectively. In the post-rain sample she observes 59, 83, and 88 colonies respectively.

10. To determine whether there appears to be a statistically significant relationship between rainfall and bacterial diversity she would conduct a χ2 analysis. After performing this analysis, which of the following best describes the conclusion she could make from the data? a. There appears to be no statistically significant relationship between rainfall and bacterial diversity. b. There is a statistically significant relationship between rainfall and bacterial diversity, the E.coli is less common (relative to the other bacteria) after rainfall than before. c. There is a statistically significant relationship between rainfall and bacterial diversity, the Salmonella is less common (relative to the other bacteria) after rainfall than before. d. There is a statistically significant relationship between rainfall and bacterial diversity, the Giardia is less common (relative to the other bacteria) after rainfall than before.

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Chap 09_3e Consider an experiment in which a pharmaceutical company is testing a new drug that they hope will lower cholesterol levels. They administer three treatments: A dose of the drug, a dose of a placebo, and a control group that receives neither drug nor placebo. after 24 hours they then measured the cholesterol levels and compared the values to baseline levels measured prior to treatment. The table below shows the results of the experiment.

Treatment

Chol. lower

Drug Placebo Control

64 51 48

Chol. increased or the same 36 49 52

11. To determine whether there appears to be a statistically significant relationship between the treatment and changes in cholesterol level they would conduct a χ2 analysis. When performing this analysis, which of the values below is closest to the χ2 statistic they would obtain? a. 3.77 b. 4.32 c. 5.83 d. 6.94 Humans aren't the only animals that get cancer, other organisms get tumors as well and their risk may be influenced by environmental factors. An ecologist decides to study whether pollution in lakes causes cancer so he collects 100 fish from each of two lakes, one known to be polluted and the other known to be pristine. He then dissects them and determines if they have tumors in their tissues or not. His data is shown below.

Tumors present No tumors

Polluted 26 74

Pristine 15 85

12. What proportion of all fish have tumors? a. 15% b. 20% c. 26% d. 41%

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Chap 09_3e Consider an experiment in which a pharmaceutical company is testing a new drug that they hope will lower cholesterol levels. They administer three treatments: A dose of the drug, a dose of a placebo, and a control group that receives neither drug nor placebo. after 24 hours they then measured the cholesterol levels and compared the values to baseline levels measured prior to treatment. The table below shows the results of the experiment.

Treatment

Chol. lower

Drug Placebo Control

64 51 48

Chol. increased or the same 36 49 52

13. To determine whether there appears to be a statistically significant relationship between the treatment and changes in cholesterol level they would conduct a χ2 analysis. When performing this analysis, which of the following best describes the conclusion they could make from the data? a. These data do not provide sufficient evidence that treatment type is associated with changes in cholesterol level. b. There is a statistically significant relationship between treatment and changes in cholesterol level, the drug lowers cholesterol more than the other treatments. c. There is a statistically significant relationship between treatment and changes in cholesterol level, the placebo lowers cholesterol more than the other treatments. d. There is a statistically significant relationship between treatment and changes in cholesterol level, the control group showed lower cholesterol compared to the other treatments.

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Chap 09_3e A microbial ecologist is interested in whether the microbial community of a pond changes when it rains. She knows that rainfall will increase the number of bacteria, but she is interested in the pattern of diversity. She collects a water sample from a pond two days before a rainfall and two days after and plates her samples on agar (a method to measure bacteria) and counts the number of colonies she observes for each of three bacteria: E. Coli, Salmonella, and Giardia. In the pre-rain sample she observes 21, 57, and 32 colonies respectively. In the post-rain sample she observes 59, 83, and 88 colonies respectively.

14. To determine whether there appears to be a statistically significant relationship between rainfall and bacterial diversity she would conduct a χ2 analysis. When performing this analysis, which of the values below is closest to the contribution to the χ2 statistic from the "pre-rainfall : Salmonella" category? a. 1.01 b. 2.02 c. 3.03 d. 4.04

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Chap 09_3e Sea star wasting disease kills sea stars (i.e., starfish) and has no known cause. It is currently a major problem on the West Coast and many sea stars are infected and dying. Consider a study in which a researcher is interested in whether susceptibility varies between the species. He travels to a site known to show wasting and counts the numbers of healthy and wasting individuals from three different species. His data is shown in the histogram below.

15. To determine whether there appears to be a statistically significant relationship between species and prevalence of wasting disease he would conduct a χ2 analysis. When performing this analysis, which of the values below is closest to the contribution to the χ2 statistic from the "Healthy : Pycnopodia" category? a. 0.47 b. 0.82 c. 1.59 d. 2.14

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Chap 09_3e 16. Consider a study in which people were recruited and followed for 40 years to determine their health problems. The researchers were interested in lung cancer so at the end of the study they counted the number of participants who had died from lung cancer, or currently had it, and those that did not. They also counted how many were non-smokers their whole life or had been smokers at some point in their lives. The number of non-smokers with lung cancer was 36 and the number of non-smokers with no sign of lung cancer was 815.

The number of smokers with lung cancer was 26 and the number of smokers with no sign of lung cancer was 161.

To determine whether there appears to be a statistically significant relationship between smoking and risk of lung cancer we would conduct a χ2 analysis. When performing this analysis, which of the values below is closest to the χ2 statistic we would obtain? a. 21.54 b. 23.35 c. 25.54 d. 27.35 17. Consider a study in which people were recruited and followed for 40 years to determine their health problems. The researchers were interested in lung cancer so at the end of the study they counted the number of participants who had died from lung cancer, or currently had it, and those that did not. They also counted how many were non-smokers their whole life or had been smokers at some point in their lives. The number of non-smokers with lung cancer was 36 and the number of non-smokers with no sign of lung cancer was 815.

The number of smokers with lung cancer was 26 and the number of smokers with no sign of lung cancer was 161.

To determine whether there appears to be a statistically significant relationship between smoking and risk of lung cancer we would conduct a χ2 analysis. Based on the results of this analysis, which of the following is the most appropriate conclusion? a. Smoking appears to significantly elevate the risk of lung cancer (P > 0.05) b. Smoking appears to significantly elevate the risk of lung cancer (P < 0.05) c. Smoking appears to significantly reduce the risk of lung cancer (P < 0.01) d. These data do not provide sufficient evidence that smoking changes the risk of lung cancer (P < 0.05)

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Chap 09_3e 18. There are many claims that eating organic food leads to better health outcomes. To study this, a dietician collects data from her patients: she categorizes their blood pressure values into elevated and healthy and she administers a questionnaire from which she is able to classify their diet into high in organic food and low in organic food. The number of patients with high organic food consumption who had elevated and healthy blood pressures were 33 and 74 respectively. The number of patients with low organic food consumption who had elevated and healthy blood pressures were 267 and 395 respectively.

To determine whether there appears to be a statistically significant relationship between type of diet and blood pressure she would conduct a χ2 analysis. When performing this analysis, which of the values below is closest to the contribution to the χ2 statistic from the "high organic diet : elevated blood pressure" group? a. 1.3 b. 1.8 c. 2.3 d. 2.8 Consider an experiment in which a pharmaceutical company is testing a new drug that they hope will lower cholesterol levels. They administer three treatments: A dose of the drug, a dose of a placebo, and a control group that receives neither drug nor placebo. after 24 hours they then measured the cholesterol levels and compared the values to baseline levels measured prior to treatment. The table below shows the results of the experiment.

Treatment

Chol. lower

Drug Placebo Control

64 51 48

Chol. increased or the same 36 49 52

19. To determine whether there appears to be a statistically significant relationship between the treatment and changes in cholesterol level they would conduct a χ2 analysis. When performing this analysis, which of the values below is closest to the χ2 value they would compare the calculated value to in order to determine significance at the 5% level? a. 3.841 b. 5.991 c. 7.815 d. 9.488

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Chap 09_3e Humans aren't the only animals that get cancer, other organisms get tumors as well and their risk may be influenced by environmental factors. An ecologist decides to study whether pollution in lakes causes cancer so he collects 100 fish from each of two lakes, one known to be polluted and the other known to be pristine. He then dissects them and determines if they have tumors in their tissues or not. His data is shown below.

Tumors present No tumors

Polluted 26 74

Pristine 15 85

20. To determine whether there appears to be a statistically significant relationship between exposure to pollution and risk of developing tumors he decides to conduct a χ2 analysis. When performing this analysis, which of the values below is closest to the χ2 statistic he would obtain? a. 3.7 b. 5.7 c. 7.7 d. 9.7

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Chap 09_3e A microbial ecologist is interested in whether the microbial community of a pond changes when it rains. She knows that rainfall will increase the number of bacteria, but she is interested in the pattern of diversity. She collects a water sample from a pond two days before a rainfall and two days after and plates her samples on agar (a method to measure bacteria) and counts the number of colonies she observes for each of three bacteria: E. Coli, Salmonella, and Giardia. In the pre-rain sample she observes 21, 57, and 32 colonies respectively. In the post-rain sample she observes 59, 83, and 88 colonies respectively.

21. Which of the mosaic tables shown correctly depicts this data? a. Graph A b. Graph B c. Graph C d. Graph D

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Chap 09_3e Consider the following values for numbers of major traffic accidents involving male and female drivers. The accidents are divided into ones involving a fatality and ones that did not. What is the relative risk for male drivers with regard to fatal accidents?

Fatal Non-fatal

Males 275 3024

Females 142 564

22. To determine whether there appears to be a statistically significant relationship between sex of the driver and fatality of their accidents we would conduct a χ2 analysis. Based on the results of this analysis, which of the following is the most appropriate conclusion? a. Males appear to be at a significantly higher relative risk of fatal accidents (P > 0.05) b. Males appear to be at a significantly higher relative risk of fatal accidents (P < 0.05) c. Males appear to be at a significantly lower relative risk of fatal accidents (P < 0.05) d. These data do not provide sufficient evidence that sex of driver changes the relative risk of fatal accidents (P < 0.05) 23. What proportion of all accidents involve one or more fatalities? a. 10% b. 13% c. 19% d. 43%

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Chap 09_3e Sea star wasting disease kills sea stars (i.e., starfish) and has no known cause. It is currently a major problem on the West Coast and many sea stars are infected and dying. Consider a study in which a researcher is interested in whether susceptibility varies between the species. He travels to a site known to show wasting and counts the numbers of healthy and wasting individuals from three different species. His data is shown in the histogram below.

24. To determine whether there appears to be a statistically significant relationship between species and prevalence of wasting disease he would conduct a χ2 analysis. After performing this analysis, which of the ranges below best describes the P value he would obtain? a. P > 0.05 b. 0.05 > P > 0.025 c. 0.025 > P > 0.01 d. P < 0.01

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Chap 09_3e Consider an experiment in which adult laboratory mice were fed one of three diets: high fat, low fat, and a control diet. The mice were weighed, received these diets for 2 weeks, and then were weighed again. The table below shows the results of the experiment.

Diet High Fat Low Fat Control

Gained weight 79 30 70

Lost weight 21 69 30

25. To determine whether there appears to be a statistically significant relationship between diet and weight gain or loss we would conduct a χ2 analysis. When performing this analysis, which of the values below is closest to the χ2 statistic we would obtain? a. 4 b. 14 c. 34 d. 54 Consider the following values for numbers of major traffic accidents involving male and female drivers. The accidents are divided into ones involving a fatality and ones that did not. What is the relative risk for male drivers with regard to fatal accidents?

Fatal Non-fatal

Males 275 3024

Females 142 564

26. Assuming a null hypothesis of no relationship between sex of the driver and fatality of their accidents, which of the following values is closest to the expected number of fatal accidents involving male drivers? a. 73.5 b. 13.6 c. 343.5 d. 63.82

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Chap 09_3e Sea star wasting disease kills sea stars (i.e., starfish) and has no known cause. It is currently a major problem on the West Coast and many sea stars are infected and dying. Consider a study in which a researcher is interested in whether susceptibility varies between the species. He travels to a site known to show wasting and counts the numbers of healthy and wasting individuals from three different species. His data is shown in the histogram below.

27. To determine whether there appears to be a statistically significant relationship between species and prevalence of wasting disease he would conduct a χ2 analysis. When performing this analysis, which of the values below is closest to the χ2 statistic he would obtain? a. 3.3 b. 5.7 c. 9.5 d. 11.2

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Chap 09_3e A microbial ecologist is interested in whether the microbial community of a pond changes when it rains. She knows that rainfall will increase the number of bacteria, but she is interested in the pattern of diversity. She collects a water sample from a pond two days before a rainfall and two days after and plates her samples on agar (a method to measure bacteria) and counts the number of colonies she observes for each of three bacteria: E. Coli, Salmonella, and Giardia. In the pre-rain sample she observes 21, 57, and 32 colonies respectively. In the post-rain sample she observes 59, 83, and 88 colonies respectively.

28. Assuming a null hypothesis of no relationship between rainfall and bacterial diversity, which of the following values is closest to the expected count of E. coli colonies from the post-rain sample? a. 39 b. 44 c. 49 d. 54

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Chap 09_3e Humans aren't the only animals that get cancer, other organisms get tumors as well and their risk may be influenced by environmental factors. An ecologist decides to study whether pollution in lakes causes cancer so he collects 100 fish from each of two lakes, one known to be polluted and the other known to be pristine. He then dissects them and determines if they have tumors in their tissues or not. His data is shown below.

Polluted 26 74

Tumors present No tumors

Pristine 15 85

29. What is the odds ratio for tumors for fish in the polluted lake compared to the pristine lake? a. 1.11 b. 1.73 c. 1.99 d. 2.85 Consider the following values for numbers of major traffic accidents involving male and female drivers. The accidents are divided into ones involving a fatality and ones that did not. What is the relative risk for male drivers with regard to fatal accidents?

Fatal Non-fatal

Males 275 3024

Females 142 564

30. What is the relative risk of fatal accidents for males versus females? a. 1.94 b. 2.41 c. 0.41 d. 0.36

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Chap 09_3e 31. There are many claims that eating organic food leads to better health outcomes. To study this, a dietician collects data from her patients: she categorizes their blood pressure values into elevated and healthy and she administers a questionnaire from which she is able to classify their diet into high in organic food and low in organic food. The number of patients with high organic food consumption who had elevated and healthy blood pressures were 33 and 74 respectively. The number of patients with low organic food consumption who had elevated and healthy blood pressures were 267 and 395 respectively.

To determine whether there appears to be a statistically significant relationship between type of diet and blood pressure she would conduct a χ2 analysis. Based on the results of her analysis, which of the following is the most appropriate conclusion? a. Eating higher amounts of organic food appears to significantly reduce the risk of high blood pressure (P > 0.05). b. Eating higher amounts of organic food appears to significantly reduce the risk of high blood pressure (P < 0.05). c. Eating higher amounts of organic food appears to significantly elevate the risk of high blood pressure (P < 0.05). d. These data do not provide sufficient evidence that eating higher amounts of organic food changes the risk of high blood pressure (P > 0.05).

Consider an experiment in which adult laboratory mice were fed one of three diets: high fat, low fat, and a control diet. The mice were weighed, received these diets for 2 weeks, and then were weighed again. The table below shows the results of the experiment.

Diet High Fat Low Fat Control

Gained weight 79 30 70

Lost weight 21 69 30

32. What proportion of mice in the experiment gained weight? a. 0.40 b. 0.60 c. 0.80 d. 0.90

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Chap 09_3e 33. Consider a study in which people were recruited and followed for 40 years to determine their health problems. The researchers were interested in lung cancer so at the end of the study they counted the number of participants who had died from lung cancer, or currently had it, and those that did not. They also counted how many were non-smokers their whole life or had been smokers at some point in their lives. The number of non-smokers with lung cancer was 36 and the number of non-smokers with no sign of lung cancer was 815.

The number of smokers with lung cancer was 26 and the number of smokers with no sign of lung cancer was 161.

What is the relative risk of lung cancer for participants who were smokers? a. 3.29 b. 3.66 c. 4.02 d. 4.55 Consider an experiment in which a pharmaceutical company is testing a new drug that they hope will lower cholesterol levels. They administer three treatments: A dose of the drug, a dose of a placebo, and a control group that receives neither drug nor placebo. after 24 hours they then measured the cholesterol levels and compared the values to baseline levels measured prior to treatment. The table below shows the results of the experiment.

Treatment

Chol. lower

Drug Placebo Control

64 51 48

Chol. increased or the same 36 49 52

34. What proportion of individuals in the experiment showed cholesterol levels that increased or stayed the same? a. 0.38 b. 0.46 c. 0.54 d. 0.62

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Chap 09_3e Sea star wasting disease kills sea stars (i.e., starfish) and has no known cause. It is currently a major problem on the West Coast and many sea stars are infected and dying. Consider a study in which a researcher is interested in whether susceptibility varies between the species. He travels to a site known to show wasting and counts the numbers of healthy and wasting individuals from three different species. His data is shown in the histogram below.

35. Assuming a null hypothesis of no relationship between species and prevalence of wasting disease, which of the following values is closest to the expected count of Solaster with wasting disease? a. 10.69 b. 13.65 c. 15.13 d. 17.22

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Chap 09_3e Consider an experiment in which a pharmaceutical company is testing a new drug that they hope will lower cholesterol levels. They administer three treatments: A dose of the drug, a dose of a placebo, and a control group that receives neither drug nor placebo. after 24 hours they then measured the cholesterol levels and compared the values to baseline levels measured prior to treatment. The table below shows the results of the experiment.

Treatment

Chol. lower

Drug Placebo Control

64 51 48

Chol. increased or the same 36 49 52

36. Assuming a null hypothesis of no relationship between diet and weight gain, which of the following values is closest to the expected count of individuals in the placebo group that showed lower cholesterol levels? a. 46 b. 49 c. 51 d. 54

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Chap 09_3e Sea star wasting disease kills sea stars (i.e., starfish) and has no known cause. It is currently a major problem on the West Coast and many sea stars are infected and dying. Consider a study in which a researcher is interested in whether susceptibility varies between the species. He travels to a site known to show wasting and counts the numbers of healthy and wasting individuals from three different species. His data is shown in the histogram below.

37. To determine whether there appears to be a statistically significant relationship between species and prevalence of wasting disease he would conduct a χ2 analysis. When performing this analysis, which of the values below is closest to the number of degrees of freedom he would use? a. 1 b. 2 c. 3 d. 4

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Chap 09_3e 38. There are many claims that eating organic food leads to better health outcomes. To study this, a dietician collects data from her patients: she categorizes their blood pressure values into elevated and healthy and she administers a questionnaire from which she is able to classify their diet into high in organic food and low in organic food. The number of patients with high organic food consumption who had elevated and healthy blood pressures were 33 and 74 respectively. The number of patients with low organic food consumption who had elevated and healthy blood pressures were 267 and 395 respectively.

What is the odds ratio for elevated blood pressure for participants with diets high in organic food? a. 0.66 b. 0.76 c. 0.91 d. 1.52 39. There are many claims that eating organic food leads to better health outcomes. To study this, a dietician collects data from her patients: she categorizes their blood pressure values into elevated and healthy and she administers a questionnaire from which she is able to classify their diet into high in organic food and low in organic food. The number of patients with high organic food consumption who had elevated and healthy blood pressures were 33 and 74 respectively. The number of patients with low organic food consumption who had elevated and healthy blood pressures were 267 and 395 respectively.

What proportion of all participants had elevated blood pressure? a. 19% b. 29% c. 39% d. 49%

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Chap 09_3e Consider the following values for numbers of major traffic accidents involving male and female drivers. The accidents are divided into ones involving a fatality and ones that did not. What is the relative risk for male drivers with regard to fatal accidents?

Fatal Non-fatal

Males 275 3024

Females 142 564

40. To determine whether there appears to be a statistically significant relationship between sex of the driver and fatality of their accidents we would conduct a χ2 analysis. When performing this analysis, which of the values below is closest to the contribution to the χ2 statistic from the "non-fatal : female" category? a. 1.52 b. 7.42 c. 13.66 d. 63.82 41. There are many claims that eating organic food leads to better health outcomes. To study this, a dietician collects data from her patients: she categorizes their blood pressure values into elevated and healthy and she administers a questionnaire from which she is able to classify their diet into high in organic food and low in organic food. The number of patients with high organic food consumption who had elevated and healthy blood pressures were 33 and 74 respectively. The number of patients with low organic food consumption who had elevated and healthy blood pressures were 267 and 395 respectively.

To determine whether there appears to be a statistically significant relationship between type of diet and blood pressure she would conduct a χ2 analysis. When performing this analysis, which of the values below is closest to the χ2 statistic she would obtain? a. 2.51 b. 3.49 c. 5.23 d. 8.11

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Chap 09_3e 42. Consider a study in which people were recruited and followed for 40 years to determine their health problems. The researchers were interested in lung cancer so at the end of the study they counted the number of participants who had died from lung cancer, or currently had it, and those that did not. They also counted how many were non-smokers their whole life or had been smokers at some point in their lives. The number of non-smokers with lung cancer was 36 and the number of non-smokers with no sign of lung cancer was 815.

The number of smokers with lung cancer was 26 and the number of smokers with no sign of lung cancer was 161.

What proportion of all participants had been, or currently were, smokers? a. 6% b. 18% c. 24% d. 30% Humans aren't the only animals that get cancer, other organisms get tumors as well and their risk may be influenced by environmental factors. An ecologist decides to study whether pollution in lakes causes cancer so he collects 100 fish from each of two lakes, one known to be polluted and the other known to be pristine. He then dissects them and determines if they have tumors in their tissues or not. His data is shown below.

Tumors present No tumors

Polluted 26 74

Pristine 15 85

43. What is the relative risk of tumors for fish in the polluted lake compared to the pristine lake? a. 1.11 b. 1.73 c. 1.99 d. 2.85 44. To determine whether there appears to be a statistically significant relationship between exposure to pollution and risk of developing tumors he decides to conduct a χ2 analysis. When performing this analysis, which of the values below is closest to the contribution to the χ2 statistic from the "No tumors : pristine" category? a. 0.38 b. 1.48 c. 2.58 d. 3.68

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Chap 09_3e 45. There are many claims that eating organic food leads to better health outcomes. To study this, a dietician collects data from her patients: she categorizes their blood pressure values into elevated and healthy and she administers a questionnaire from which she is able to classify their diet into high in organic food and low in organic food. The number of patients with high organic food consumption who had elevated and healthy blood pressures were 33 and 74 respectively. The number of patients with low organic food consumption who had elevated and healthy blood pressures were 267 and 395 respectively.

What is the relative risk of elevated blood pressure for participants with diets high in organic food? a. 0.66 b. 0.76 c. 0.91 d. 1.52 Consider an experiment in which adult laboratory mice were fed one of three diets: high fat, low fat, and a control diet. The mice were weighed, received these diets for 2 weeks, and then were weighed again. The table below shows the results of the experiment.

Diet High Fat Low Fat Control

Gained weight 79 30 70

Lost weight 21 69 30

46. To determine whether there appears to be a statistically significant relationship between diet and weight gain or loss we would conduct a χ2 analysis. When performing this analysis, which of the values below is closest to the contribution to the χ2 statistic from the "low fat : lost weight" category? a. 6 b. 9 c. 14 d. 21

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Chap 09_3e Humans aren't the only animals that get cancer, other organisms get tumors as well and their risk may be influenced by environmental factors. An ecologist decides to study whether pollution in lakes causes cancer so he collects 100 fish from each of two lakes, one known to be polluted and the other known to be pristine. He then dissects them and determines if they have tumors in their tissues or not. His data is shown below.

Tumors present No tumors

Polluted 26 74

Pristine 15 85

47. Assuming a null hypothesis of no relationship between exposure to pollution and risk of developing tumors, which of the following values is closest to the expected number of fish with tumors in the polluted lake? a. 15.5 b. 20.5 c. 25.5 d. 30.5 48. Consider a study in which people were recruited and followed for 40 years to determine their health problems. The researchers were interested in lung cancer so at the end of the study they counted the number of participants who had died from lung cancer, or currently had it, and those that did not. They also counted how many were non-smokers their whole life or had been smokers at some point in their lives. The number of non-smokers with lung cancer was 36 and the number of non-smokers with no sign of lung cancer was 815.

The number of smokers with lung cancer was 26 and the number of smokers with no sign of lung cancer was 161.

What is the odds ratio of lung cancer for participants who were smokers? a. 3.29 b. 3.66 c. 4.02 d. 4.55

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Chap 09_3e Consider an experiment in which adult laboratory mice were fed one of three diets: high fat, low fat, and a control diet. The mice were weighed, received these diets for 2 weeks, and then were weighed again. The table below shows the results of the experiment.

Diet High Fat Low Fat Control

Gained weight 79 30 70

Lost weight 21 69 30

49. To determine whether there appears to be a statistically significant relationship between diet and weight gain or loss we would conduct a χ2 analysis. When performing this analysis, which of the values below is closest to the number of degrees of freedom we would use? a. 2 b. 3 c. 4 d. 5

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Chap 09_3e A microbial ecologist is interested in whether the microbial community of a pond changes when it rains. She knows that rainfall will increase the number of bacteria, but she is interested in the pattern of diversity. She collects a water sample from a pond two days before a rainfall and two days after and plates her samples on agar (a method to measure bacteria) and counts the number of colonies she observes for each of three bacteria: E. Coli, Salmonella, and Giardia. In the pre-rain sample she observes 21, 57, and 32 colonies respectively. In the post-rain sample she observes 59, 83, and 88 colonies respectively.

50. To determine whether there appears to be a statistically significant relationship between rainfall and bacterial diversity she would conduct a χ2 analysis. When performing this analysis, which of the values below is closest to the number of degrees of freedom she would use? a. 1 b. 2 c. 3 d. 4

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Chap 09_3e Consider the following values for numbers of major traffic accidents involving male and female drivers. The accidents are divided into ones involving a fatality and ones that did not. What is the relative risk for male drivers with regard to fatal accidents?

Fatal Non-fatal

Males 275 3024

Females 142 564

51. To determine whether there appears to be a statistically significant relationship between sex of the driver and fatality of their accidents we would conduct a χ2 analysis. When performing this analysis, which of the values below is closest to the χ2 statistic we would obtain? a. 86.5 b. 569.1 c. 60.0 d. 21.94 52. The relative risk and odds ratio measure similar, but distinct, things. Each has an advantage over the other so both are often calculated. For each of these two statistics, what is the advantage it has compared to the alternative?

53. What is the main benefit of the Fisher's Exact test compared to a traditional χ2 analysis?

54. Under what circumstances are the relative risk and odds ratio most similar?

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Chap 09_3e 55. There are two situations having to do with expected frequencies that create problems for χ2 analyses.

Describe these two situations and two solutions that resolve these issues.

56. Consider an observational study in which a sample of individuals with a certain condition are compared to a second reference group that do not have the condition. Proportions of individuals with risk factor in each group can then be compared. (a) This type of study is called a(n) _______ - _______ study. (b) With this type of data we can do a(n) _______ - _______ analysis, but not a(n) _______ - _______ .

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Chap 09_3e Answer Key 1. d 2. a 3. d 4. d 5. c 6. c 7. d 8. c 9. a 10. c 11. c 12. b 13. a 14. c 15. c 16. c 17. b 18. b 19. b 20. a 21. b 22. c 23. a 24. a 25. d 26. c Copyright Macmillan Learning. Powered by Cognero.

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Chap 09_3e 27. a 28. d 29. c 30. c 31. d 32. b 33. a 34. b 35. b 36. d 37. b 38. a 39. c 40. b 41. b 42. b 43. b 44. a 45. b 46. d 47. b 48. b 49. a 50. b 51. a 52.

53.

54.

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Chap 09_3e 55.

56.

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Chap 10_3e Indicate the answer choice that best completes the statement or answers the question.

1. Which of the following is not a property of the normal distribution? a. It is a continuous distribution. b. It is a discrete distribution. c. It is a symmetric distribution. d. Its mean and mode are equal.

2. The Declaration of Helsinki states that when testing a new treatment, control patients _______. a. must be compensated financially to prevent abuse. b. should receive an inactive yet safe chemical. c. should receive no chemicals or drugs at all. d. should receive the best current treatment.

3. Which equation shown is correct for a normal distribution with a mean of 20 and a variance of 10? a. b. c. d.

4. When mating two heterozygotes for alleles in which one is dominant to the other, if the usual Mendelian segregation process is occurring, the ratio of the offspring phenotypes produced should be 3:1. The dominant phenotype would be more common than the recessive one. Imagine a situation in which two heterozygotes are mated and among their 200 offspring, 160 show the dominant phenotype while 40 show the recessive phenotype. What is the P-value of a two-sided binomial test using the normal distribution to approximate the binomial? a. 0.015 b. 0.031 c. 0.060 d. 0.121 5. The standard normal deviate describes how many standard deviations away from the mean that a value is. a. True b. False

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Chap 10_3e 6. Crossbill finches have beaks that overlap with the top beak to one side or the other of the lower beak. Most populations have 50:50 ratios of "right-handed" and "left-handed" beaks, and the handedness of the beaks is thought to be randomly determined, so we expect to see equal numbers of right-beak and left-beak finches.

Consider a survey of 140 crossbill finches, which reveals 82 with right beaks and 58 with left beaks. What is the P-value of a two-sided binomial test using the normal distribution to approximate the binomial? a. 0.026 b. 0.052 c. 0.078 d. 0.104 7. Consider a population of 900 values that are normally distributed with a mean of 90 and standard deviation of 6. What proportion of values are larger than 78? a. 0.0228 b. 0.8666 c. 0.9772 d. 0.9975 8. Imagine a population consisting of 1,500 values that are normally distributed around a mean of 60, which exhibits a standard deviation of 8. What proportion of values in the population are larger than 63? a. 0.334 b. 0.354 c. 0.374 d. 0.394 9. When mating two heterozygotes for alleles in which one is dominant to the other, if the usual Mendelian segregation process is occurring, the ratio of the offspring phenotypes produced should be 3:1. The dominant phenotype would be more common than the recessive one. Imagine a situation in which two heterozygotes are mated and among their 200 offspring, 160 show the dominant phenotype while 40 show the recessive phenotype. What is the conclusion of a two-sided binomial test using the normal distribution to approximate the binomial? a. Fail to reject null hypothesis, we lack evidence that anything other than usual Mendelian segregation is occurring. b. Fail to reject null hypothesis, we have evidence that something other than usual Mendelian segregation is occurring. c. Reject null hypothesis, we lack evidence that anything other than usual Mendelian segregation is occurring. d. Reject null hypothesis, we have evidence that something other than usual Mendelian segregation is occurring.

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Chap 10_3e 10. Consider a population of 900 values that are normally distributed with a mean of 90 and standard deviation of 6. To the nearest integer, how many values are greater than 84? a. 757 b. 769 c. 785 d. 791 11. Imagine a population consisting of 1,500 values that are normally distributed around a mean of 60, which exhibits a standard deviation of 8. To the closest integer, how many values in the population are between 58 and 65? a. 502 b. 509 c. 519 d. 529 12. Consider a population of 900 values that are normally distributed with a mean of 90 and standard deviation of 6. To the nearest integer, how many values are less than 93? a. 562 b. 582 c. 622 d. 692 13. Imagine a population consisting of 1,500 values that are normally distributed around a mean of 60, which exhibits a standard deviation of 8. What population value is larger than exactly 40% of the population? a. 57.06 b. 57.36 c. 57.66 d. 57.96 14. Crossbill finches have beaks that overlap with the top beak to one side or the other of the lower beak. Most populations have 50:50 ratios of "right-handed" and "left-handed" beaks, and the handedness of the beaks is thought to be randomly determined, so we expect to see equal numbers of right-beak and left-beak finches.

Consider a survey of 140 crossbill finches, which reveals 84 with right beaks and 56 with left beaks. What is the conclusion of a two-sided binomial test using the normal distribution to approximate the binomial? a. Fail to reject null hypothesis, we lack evidence that the handedness of the beaks is non-random. b. Fail to reject null hypothesis, we have evidence that the handedness of the beaks is non-random. c. Reject null hypothesis, we lack evidence that the handedness of the beaks is non-random. d. Reject null hypothesis, we have evidence that the handedness of the beaks is non-random.

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Chap 10_3e 15. Imagine a population consisting of 1,500 values that are normally distributed around a mean of 60, which exhibits a standard deviation of 8. The 75th percentile most closely corresponds to which value of Z? a. 65.0 b. 65.2 c. 65.4 d. 65.6 16. The equation for a normal distribution with a mean of 30 and a variance of 20 is

a. True b. False 17. When mating two heterozygotes for alleles in which one is dominant to the other, if the usual Mendelian segregation process is occurring, the ratio of the offspring phenotypes produced should be 3:1. The dominant phenotype would be more common than the recessive one. Imagine a situation in which two heterozygotes are mated and among their 200 offspring, 165 show the dominant phenotype while 35 show the recessive phenotype. What is the conclusion of a two-sided binomial test using the normal distribution to approximate the binomial? a. Fail to reject null hypothesis, we lack evidence that anything other than usual Mendelian segregation is occurring. b. Fail to reject null hypothesis, we have evidence that something other than usual Mendelian segregation is occurring. c. Reject null hypothesis, we lack evidence that anything other than usual Mendelian segregation is occurring. d. Reject null hypothesis, we have evidence that something other than usual Mendelian segregation is occurring.

18. For the equation for a normal distribution shown, what are the mean and variance?

a. Mean = 4, variance = 4 b. Mean = 4, variance = 16 c. Mean = 16, variance = 4 d. Mean = 16, variance = 16

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Chap 10_3e 19. The central limit theorem states that the means of a large number of samples from a population is approximately normally distributed. a. True b. False 20. Imagine a population consisting of 1,500 values that are normally distributed around a mean of 60, which exhibits a standard deviation of 8. To the closest integer, how many values in the population are less than 62? a. 599 b. 898 c. 1,103 d. 1,314 21. Imagine a population consisting of 1,500 values that are normally distributed around a mean of 60, which exhibits a standard deviation of 8. To the closest integer, how many values in the population are greater than 54? a. 1,140 b. 1,150 c. 1,160 d. 1,170 22. Imagine a population consisting of 1,500 values that are normally distributed around a mean of 60, which exhibits a standard deviation of 8. Which value below is closest to the IQR for the population? a. 8.0 b. 8.6 c. 10.2 d. 10.8 23. Consider a population of 900 values that are normally distributed with a mean of 90 and standard deviation of 6. To the nearest integer, how many values are between 87 and 99? a. 278 b. 562 c. 703 d. 840 24. The term for the observation that the medical conditions of patients often improve when they are given inactive chemical substances is called which of the following? a. Confidence-based improvement b. Dose response improvement c. Placebo effect d. Positive feedback Copyright Macmillan Learning. Powered by Cognero.

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Chap 10_3e 25. The standard normal distribution has a mean of zero and variance of one. a. True b. False 26. The total area under the normal probability distribution is equal to which of the following? a. 0 b. 0.5 c. 1.0 d. This value depends on the mean and variance.

27. Crossbill finches have beaks that overlap with the top beak to one side or the other of the lower beak. Most populations have 50:50 ratios of "right-handed" and "left-handed" beaks, and the handedness of the beaks is thought to be randomly determined, so we expect to see equal numbers of right-beak and left-beak finches.

Consider a survey of 140 crossbill finches, which reveals 82 with right beaks and 58 with left beaks. What is the conclusion of a two-sided binomial test using the normal distribution to approximate the binomial? a. Fail to reject null hypothesis, we lack evidence that the handedness of the beaks is non-random. b. Fail to reject null hypothesis, we have evidence that the handedness of the beaks is non-random. c. Reject null hypothesis, we lack evidence that the handedness of the beaks is non-random. d. Reject null hypothesis, we have evidence that the handedness of the beaks is non-random.

28. Consider a population of 900 values that are normally distributed with a mean of 90 and standard deviation of 6. What value of Z below most closely corresponds to the 65th percentile? a. 91.7 b. 91.9 c. 92.1 d. 92.3 29. The values in normal distribution tables correspond to the probability that the value indicated will be chosen in a random sample. a. True b. False 30. Consider a population of 900 values that are normally distributed with a mean of 90 and standard deviation of 6. What value below is closest to the value larger than exactly 55% of the population? a. 90.6 b. 90.8 c. 91.0 d. 91.2

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Chap 10_3e 31. For a normal distribution, the IQR is larger than two standard deviations. a. True b. False 32. Using the normal approximation to the binomial distribution is most accurate when the proportion is closest to 0.5. a. True b. False 33. Using the normal distribution instead of the exact binomial distribution is slightly more accurate when sample sizes get very large. a. True b. False 34. For a set of samples taken from a normally distributed population, which of the following is not generally true? a. The distribution of sample means is centered around the population mean. b. The distribution of sample means is normal. c. The distribution of sample means is wider for larger population variances. d. The distribution of sample means is wider for larger sample sizes.

35. Consider a population of 900 values that are normally distributed with a mean of 90 and standard deviation of 6. Which value below is closest to the IQR? a. 8.1 b. 8.3 c. 8.5 d. 8.7 36. For the equation for a normal distribution shown, what are the mean and standard deviation?

a. Mean = 40, variance = 4 b. Mean = 40, variance = 8 c. Mean = 40, variance = 16 d. Mean = 40, variance = 24

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Chap 10_3e 37. Crossbill finches have beaks that overlap with the top beak to one side or the other of the lower beak. Most populations have 50:50 ratios of "right-handed" and "left-handed" beaks, and the handedness of the beaks is thought to be randomly determined, so we expect to see equal numbers of right-handed and left-handed finches. Consider a survey of 140 crossbill finches, which reveals 84 with right beaks and 56 with left beaks.

What is the P-value of a two-sided binomial test using the normal distribution to approximate the binomial? a. 0.015 b. 0.020 c. 0.023 d. 0.033 38. Which of the following is not a good rule of thumb for data values exhibiting a normal distribution? a. Approximately 95% of the values lie within two standard deviations of the mean. b. Approximately two-thirds of the values lie within one standard deviation of the mean. c. Exactly half of the values lie at or above the mean. d. Exactly half of the values lie within one standard deviation of the mean.

39. For values from a data set, when we take the value, subtract the mean, and then divide by the standard deviation, we create new values called which of the following?? a. Scaled normal deviate b. Scaled normal value c. Standard normal deviate d. Standard normal value 40. To calculate probabilities using the normal probability distribution, we look at the area under the curve between the values we are interested in. a. True b. False 41. When mating two heterozygotes for alleles in which one is dominant to the other, if the usual Mendelian segregation process is occurring, the ratio of the offspring phenotypes produced should be 3:1. The dominant phenotype would be more common than the recessive one. Imagine a situation in which two heterozygotes are mated and among their 200 offspring, 165 show the dominant phenotype while 35 show the recessive phenotype. What is the P-value of a two-sided binomial test using the normal distribution to approximate the binomial? a. 0.018 b. 0.036 c. 0.054 d. 0.072

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Chap 10_3e 42. Which equation shown is correct for a normal distribution with a median of 25 and a standard deviation of 5? a. b. c. d.

43. The placebo effect appears equally effective at improving a wide variety of conditions, including pain, cholesterol levels, and blood pressure. a. True b. False 44. The equation for a normal distribution with a mean of 20 and a variance of 30 is

a. True b. False 45. Carlos says that he thinks that while humans are more right-handed than left-handed, the same probably isn't true for gorillas. Luis disagrees and says they probably are asymmetric too, but maybe they're more lefthanded. Imagine they collect handedness data for 60 gorillas based on videos of the gorillas eating and 37 of the gorillas appear to be right-handed. Use the normal distribution to approximate the binomial distribution to answer this question. Does the data support Carlos or Luis? As part of your answer, present the test statistic and the P-value it corresponds to.

46. Imagine that your friend comes down with a cold and after being sick for a few days takes a supplement called "essence of wormroot" and gets better soon afterward. She then credits the supplement for her recovery. Based on what you know about the likely mechanism of how placebos work, what is the likely explanation for her recovery?

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Chap 10_3e 47. Explain the primary benefit of using the normal distribution to model the binomial distribution when calculating P-values.

48. For a population of 240 values that exhibit a normal distribution in which the mean is 75 and the variance is 11, answer the following questions. What are the mean, median, mode, standard deviation, coefficient of variation, and IQR? How many values are between 76 and 80 and how many are larger than 90?

49. For a population of 180 values that exhibit a normal distribution in which the mean is 20 and the variance is 6, answer the following questions. What are the mean, median, mode, standard deviation, coefficient of variation, and IQR? How many values are between 18 and 22 and how many are larger than 25?

50. Explain why we should use a correction for continuity when using the normal distribution to model the binomial distribution.

51. Carlos says that he thinks that while humans are more right-handed than left-handed, the same probably isn't true for gorillas. Luis disagrees and says they probably are asymmetric too, but maybe they're more lefthanded. Imagine they collect handedness data for 60 gorillas based on videos of the gorillas eating and 39 of the gorillas appear to be right-handed. Use the normal distribution to approximate the binomial distribution to answer this question. Does the data support Carlos or Luis? As part of your answer, present the test statistic and the P-value it corresponds to.

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Chap 10_3e Answer Key 1. b 2. d 3. b 4. d 5. a 6. b 7. c 8. b 9. a 10. a 11. a 12. c 13. d 14. d 15. c 16. a 17. d 18. d 19. a 20. b 21. c 22. d 23. b 24. c 25. a 26. c Copyright Macmillan Learning. Powered by Cognero.

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Chap 10_3e 27. a 28. d 29. b 30. b 31. b 32. a 33. b 34. d 35. a 36. c 37. c 38. d 39. c 40. a 41. a 42. c 43. b 44. b 45.

46.

47.

48.

49.

50.

51.

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Chap 11_3e Indicate the answer choice that best completes the statement or answers the question.

1. We must use the t-distribution instead of the Z-distribution to calculate probabilities for real- world data sets because of what reason? a. Sampling error causing the sample and population means to differ. b. Sampling error causing the samples and populations to differ. c. Uncertainty about the sample's standard deviation. d. Uncertainty about the population's standard deviation.

2. How many standard errors in width is the 95% confidence interval for a sample with 20 values? a. 1.73 b. 2.09 c. 3.46 d. 4.18 3. Using your table of critical t-values, what values of t correspond to the ones that bound a central region containing 90% of the distribution when there are 16 degrees of freedom? a. –1.753 to 1.753 b. –1.746 to 1.746 c. –2.131 to 2.131 d. –2.120 to 2.120 4. For a pair of samples with the same standard deviation, but where the second has a sample size twice as large, the 95% confidence interval for the second sample is half as wide as the first. a. True b. False 5. Consider a data sample consisting of 12 values with a mean of 22 and standard deviation of 1.5. What is the 95% confidence interval for the variance? a. 0.75 < σ2 < 4.32 b. 0.87 < σ2 < 2.08 c. 1.02 < σ2 < 2.87 d. 1.13 < σ2 < 6.49 6. The t-distribution is wider than the normal distribution. a. True b. False

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Chap 11_3e 7. Consider two t-distributions overlaid on the same figure—one for 18 degrees of freedom and one for 20 degrees of freedom. Which of the following corresponds to the location farthest right (i.e., the largest t-value)? a. The 5% critical value for df = 18 b. The 5% critical value for df = 20 c. The 2% critical value for df = 18 d. The 2% critical value for df = 20 8. Consider an experiment in which Shireen measures 20 Arabidopsis plants in a pasture that an agricultural company claims have an average height of exactly 23 cm. Her plants have a mean of 24.53 cm with a standard deviation of 2.33 cm, however. Based on her t-test statistic, and using your table of critical t values, which of the following P-value ranges matches the one for the t-value she obtains? a. P > 0.05 b. 0.02 < P < 0.05 c. 0.01 < P < 0.02 d. P < 0.01 9. Consider a situation in which Rosa measures the diameter of 15 trees from a population that she thinks (based on published reports) has an average diameter of 240 cm. Her sample has a mean of 253.1 cm with a standard deviation of 25.21 cm. Based on her t-test statistic, which of the following best describes her conclusion? a. She fails to reject the null hypothesis of the t-test and concludes that the mean diameter of the trees seems to differ from 240 cm. b. She fails to reject the null hypothesis of the t-test and concludes that the mean diameter of the trees doesn't seem to differ from 240 cm. c. She rejects the null hypothesis of the t-test and concludes that the mean diameter of the trees seems to differ from 240 cm. d. She rejects the null hypothesis of the t-test and concludes that the mean diameter of the trees doesn't seem to differ from 240 cm.

10. The critical t-value represented by t 0.025(2),20 is the one appropriate for which combination of critical value and degrees of freedom? a. A 5% critical value and 19 degrees of freedom. b. A 5% critical value and 20 degrees of freedom. c. A 2.5% critical value and 19 degrees of freedom. d. A 2.5% critical value and 20 degrees of freedom.

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Chap 11_3e 11. What is the correct representation for the 5% critical t-value for a sample with 9 degrees of freedom? a. t 0.05(2),8 b. t 0.05(2),9 c. t 0.025(2),8 d. t 0.025(2),9 12. Consider a data sample consisting of 12 values with a mean of 22 and variance of 1.5. What is the 95% confidence interval for the variance? a. 0.75 < σ2 < 4.32 b. 0.87 < σ2 < 2.08 c. 1.02 < σ2 < 2.87 d. 1.03 < σ2 < 8.26 13. For a t-test using a sample of 35 values which returns a positive value, how big must the t-test statistic be to reject the null hypothesis? a. 1.69 b. 2.03 c. 2.44 d. 2.72 14. Which of the following does not describe one of the assumptions used in the one sample t-test? a. The population values have a normally distribution. b. The population values are normally distributed. c. The sample values were randomly chosen from the population. d. The sample values were non-randomly chosen from the population.

15. Consider a situation in which Jamal measures the resting heart rate of 16 individuals from a population that he thinks (based on published reports) has an average resting heart rate of 72 beats per minute. His sample has a mean of 75.2 with a standard deviation of 6.2 cm. Based on his t-test statistic, and using your table of critical t-values, which of the following P-value ranges matches the one for the t-value he obtains? a. P > 0.05 b. 0.02 < P < 0.05 c. 0.01 < P < 0.02 d. P < 0.01 16. The t-test is very sensitive to deviations from normality in the population sampled, especially for large sample sizes. a. True b. False Copyright Macmillan Learning. Powered by Cognero.

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Chap 11_3e 17. Consider a situation in which Jamal measures the resting heart rate of 16 individuals from a population that he thinks (based on published reports) has an average resting heart rate of 72 beats per minute. His sample has a mean of 75.2 with a standard deviation of 6.2 cm. If he conducts a one-sample t-test of his data, what t-value would he obtain? a. 2.065 b. 2.135 c. 2.205 d. 2.275 18. In tables of critical t-values, what value of t would correspond to the location with 95% of the distribution less and 5% of the distribution greater when there are 15 degrees of freedom? a. 1.753 b. 1.746 c. 1.740 d. 1.734 19. To calculate the confidence intervals for variance and standard deviation, we use the t-distribution. a. True b. False 20. If a t-test results in a sample mean the same as the hypothesized population mean, then the t-statistic and Pvalue of the test would be which of the following (respectively)? a. 0, 0. b. 0, 1. c. 1, 0. d. 1, 1.

21. Which region contains the smallest total area? a. From t = –5 to t = –1 in a t distribution. b. From t = –1 to t = 0 in a t distribution. c. From Z = –5 to Z = –1 in a normal distribution. d. From Z = –1 to Z = 0 in a normal distribution.

22. For a sample of 8 values, what are the critical values we would use to calculate the 95% and 99% confidence intervals? a. 1.89 and 2.36 b. 2.36 and 3.50 c. 3.00 and 3.50 d. 1.89 and 3.50

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Chap 11_3e 23. Consider a data sample consisting of 12 values with a mean of 22 and variance of 1.5. What is the approximate 95% confidence interval for the standard deviation? a. 0.75 < σ < 4.32 b. 0.87 < σ < 2.08 c. 1.02 < σ < 2.87 d. 1.03 < σ < 8.26 24. The one-sample t-test compares the mean of the sample to the sample mean specified in the null hypothesis. a. True b. False 25. In tables of critical t-values, what value of t would correspond to the location with 99% of the distribution less and 1% of the distribution greater when there are 13 degrees of freedom? a. 1.771 b. 2.160 c. 2.282 d. 2.650 26. If the 95% confidence interval of the population mean includes the value specified in the null hypothesis, then we expect the P-value of the one-sample t-test to be larger than 0.05. a. True b. False 27. For a pair of samples with the same sample size, but where the second has a standard deviation twice as large, the 95% confidence interval for the second sample is twice as wide as the first. a. True b. False 28. The t-distribution is wider for larger sample sizes than for smaller ones. a. True b. False 29. If a sample with 34 values has a mean of 33 and a standard deviation of 35, how many degrees of freedom does it have? a. 32 b. 33 c. 34 d. 35

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Chap 11_3e 30. If we have a sample of 14 values that gives us a 99% confidence interval of 5.76 < μ < 8.54, what is the standard deviation of the sample? a. 1.87 b. 1.91 c. 1.95 d. 1.72 31. If we have a 95% confidence interval of 14.69 < μ < 15.85 based on a sample of 18 values, what is the standard deviation of the sample? a. 1.17 b. 1.39 c. 1.44 d. 1.49 32. If we have a sample of 11 values with a mean of 15.00 and a standard deviation of 1.30, what is the 95% confidence interval? a. 13.86 < μ < 16.16 b. 13.96 < μ < 16.06 c. 14.06 < μ < 15.96 d. 14.14 < μ < 15.86 33. Consider an experiment in which Shireen measures 20 Arabidopsis plants in a pasture that an agricultural company claims have an average height of exactly 23 cm. Her plants have a mean of 24.53 cm with a standard deviation of 2.33 cm, however. Based on her t-test statistic, which of the following best describes her conclusion? a. She fails to reject the null hypothesis of the t-test and concludes that the mean height of the plants seems to differ from 23 cm. b. She fails to reject the null hypothesis of the t-test and concludes that the mean height of the plants doesn't seem to differ from 23 cm. c. She rejects the null hypothesis of the t-test and concludes that the mean height of the plants seems to differ from 23 cm. d. She rejects the null hypothesis of the t-test and concludes that the mean height of the plants doesn't seem to differ from 23 cm.

34. When a one sample t-test rejects the null hypothesis, then the 95% confidence interval of the population mean would typically include the value specified in the null hypothesis. a. True b. False

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Chap 11_3e 35. For a sample of 13 values that has a mean of 5.6 with a standard deviation of 0.7, what would the 99% confidence interval be? a. 4.8 < μ < 6.4 b. 4.9 < μ < 6.3 c. 5.0 < μ < 6.2 d. 5.1 < μ < 6.1 36. Consider an experiment in which Shireen measures 20 Arabidopsis plants in a pasture that an agricultural company claims have an average height of exactly 23 cm. Her plants have a mean of 24.53 cm with a standard deviation of 2.33 cm, however. If she conducts a one-sample t-test of her data, what t-value would she obtain? a. 2.091 b. 2.547 c. 2.937 d. 3.411 37. If a population is hypothesized to have a mean value of 15, but the 95% confidence interval based of a sample of 14 values is 16 < μ < 24, what is the t-statistic of the corresponding one sample t-test? a. 2.65 b. 2.70 c. 2.75 d. 2.80 38. Consider a data sample consisting of 12 values with a mean of 22 and standard deviation of 1.5. What is the approximate 95% confidence interval for the standard deviation? a. 0.75 < σ < 4.32 b. 0.87 < σ < 2.08 c. 1.06 < σ < 2.55 d. 1.03 < σ < 8.26 39. Calculation of the confidence intervals for variance and standard deviation may be highly prone to error if the population is not normally distributed. a. True b. False

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Chap 11_3e 40. Consider the figure shown indicating the number of moles on the skin of a set of 30 patients examined by a dermatologist. Published reports claim that the mean number for the population these patients come from is 3.4 moles. Conduct a one-sample t-test on this data and determine whether this seems to be true. Assume a = 0.5. In your answer, present the following: your calculated t-value, an exact P-value using a computer or a range for the P-value using a table of critical values, and a statement about whether the population mean appears to be 3.4 or not based on the sample.

41. For the data set shown below, calculate the following values: sample mean, 95% confidence interval for the population mean, sample variance, 95% confidence interval for the population variance, sample standard deviation, approximate 95% confidence interval for the population standard deviation.

Data: 2 2 3 3 3 4 4 4 4 4 5 5 5 5 5 5 5 6 6 6 6 6 7 7 7 8 8

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Chap 11_3e 42. Consider a sample with 25 values that has sample mean of 8.00 and a standard deviation of 5.00. Does this sample provide sufficient evidence to conclude that the mean of the population it was sampled from differs from 6.00? Answer in two ways. (a) Describe the P-value and conclusion you obtain from a one-sample t-test. (b) Illustrate the logic of the test by drawing the hypothesized population mean, the sample mean, and 95% confidence interval for the population mean on a number line.

43. Consider the figure shown indicating the number of moles on the skin of a set of 25 patients examined by a dermatologist. Published reports claim that the mean number for the population these patients come from is 3.5 moles. Conduct a one-sample t-test on this data and determine whether this seems to be true. Assume a = 0.5. In your answer present the following: your calculated t-value, an exact P-value using a computer or a range for the P-value using a table of critical values, and a statement about whether the population mean appears to be 3.5 or not based on the sample.

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Chap 11_3e 44. For the data set shown below, calculate the following values: sample mean, 95% confidence interval for the population mean, sample variance, 95% confidence interval for the population variance, sample standard deviation, approximate 95% confidence interval for the population standard deviation.

Data: 1 2 2 2 3 3 3 3 4 4 4 4 4 4 5 5 5 5 6 6 6 7

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Chap 11_3e 45. Consider a study on the diet of coyotes. The table shown indicates an analysis of the bones found in the stomachs of 26 roadkill coyotes, and the number of species found in each was measured. Previous studies claim that the mean number of species eaten by coyotes (i.e., the number of species expected in the stomach contents) is 3.4 species per coyote. Conduct a one-sample t-test on this data and determine whether this seems to be true. Assume a = 0.5. In your answer, present the following: your calculated t-value, an exact Pvalue using a computer or a range for the P-value using a table of critical values, and a statement about whether the population mean appears to be 3.4 or not based on the sample.

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Chap 11_3e 46. Consider a sample with 21 values that has sample mean of 8.00 and a standard deviation of 4.00. Does this sample provide sufficient evidence to conclude that the mean of the population it was sampled from differs from 6.00? Answer in two ways. (a) Describe the P-value and conclusion you obtain from a one-sample t-test. (b) Illustrate the logic of the test by drawing the hypothesized population mean, the sample mean, and 95% confidence interval for the population mean on a number line.

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Chap 11_3e 47. Consider a study on the diet of coyotes. The table shown indicates an analysis of the bones found in the stomachs of 40 roadkill coyotes, and the number of species found in each was measured. Previous studies claim that the mean number of species eaten by coyotes (i.e., the number of species expected in the stomach contents) is 4.5 species per coyote. Conduct a one-sample t-test on this data and determine whether this seems to be true. Assume a = 0.5. In your answer, present the following: your calculated t-value, an exact Pvalue using a computer or a range for the P-value using a table of critical values, and a statement about whether the population mean appears to be 4.5 or not based on the sample.

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Chap 11_3e Answer Key 1. d 2. d 3. b 4. b 5. d 6. a 7. c 8. d 9. b 10. d 11. b 12. a 13. b 14. d 15. a 16. b 17. a 18. a 19. b 20. b 21. c 22. b 23. b 24. b 25. d 26. a Copyright Macmillan Learning. Powered by Cognero.

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Chap 11_3e 27. a 28. b 29. b 30. d 31. a 32. d 33. c 34. b 35. c 36. c 37. b 38. c 39. a 40.

41.

42.

43.

44.

45.

46.

47.

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Chap 12_3e Indicate the answer choice that best completes the statement or answers the question.

1. If the mean of population A is significantly different from 20, but the mean of group B is not significantly different from 20, then the mean of the two population are different from one another. a. True b. False 2. When doing a paired t-test, if the confidence interval for the differences includes zero, we expect the results of our t-test to be which of the following? a. P > 0.05 and we fail to reject the null hypothesis of equal means. b. P > 0.05 and we reject the null hypothesis of equal means. c. P < 0.05 and we fail to reject the null hypothesis of equal means. d. P < 0.05 and we reject the null hypothesis of equal means.

3. Consider urban ecologists who are interested in whether the presence of high-voltage power lines influences the number of eggs laid by birds nearby. They plan to conduct a two-sample t-test and will assume that the population variances are equal. Their data are as follows: Near (group 1): mean = 6.1, SD = 0.35, n = 9 Far (group 2): mean = 5.8, SD = 0.30, n = 12 Based on the t-test statistic, and using your table of critical t-values, which of the following P-value ranges matches the one for the t-value? a. 0.05 < p b. 0.02 < p < 0.05 c. 0.01 < p < 0.02 d. p < 0.01

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Chap 12_3e 4. Consider a situation in which Chris predicts that an impending drainage connection will alter the number of fish in a set of six small lakes. She uses a large net (a seine) and counts the number of fish and obtains the values shown. What is the 95% confidence interval for the difference in the values?

a. –7.6 < μ < 1.55 b. –6.4 < μ < 1.36 c. –5.9 < μ < –1.26 d. –5.4 < μ < –1.76 5. Consider an urban ecologist who is interested in whether the presence of high-voltage power lines influences the number of eggs laid by birds nearby. He plans to conduct a two-sample t-test and will assume that the population variances are equal. His data are as follows: Near (group 1): mean = 6.1, SD = 0.35, n = 9 Far (group 2): mean = 5.8, SD = 0.30, n = 12 What is the 95% confidence interval for the difference between the two means? a. –0.017 < m1 – m2 < 0.617 b. –0.004 < m1 – m2 < 0.604 c. 0.003 < m1 – m2 < 0.597 d. 0.013 < m1 – m2 < 0.587

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Chap 12_3e 6. Consider a situation in which Chris predicts that an impending drainage connection will alter the number of fish in a set of six small lakes. She uses a large net (a seine) and counts the number of fish and obtains the values shown. What is the t-test statistic for a paired t-test of the difference in the mean values?

a. –1.29 b. –1.69 c. –2.09 d. –2.49 7. The paired t-test is essentially the same as a one-sample t-test of the set of differences with a hypothesized mean of zero for the differences. a. True b. False 8. When analyzing the set of differences in a paired t-test procedure, if the confidence interval for the differences does not include zero, we expect the results of our t-test to be which of the following? a. P > 0.05 and we fail to reject the null hypothesis of equal means. b. P > 0.05 and we reject the null hypothesis of equal means. c. P < 0.05 and we fail to reject the null hypothesis of equal means. d. P < 0.05 and we reject the null hypothesis of equal means.

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Chap 12_3e 9. Consider an urban ecologist who is interested in whether the presence of high-voltage power lines influences the number of eggs laid by birds nearby. She plans to conduct a two-sample t-test and will assume that the population variances are equal. Her data are as follows: Near (group 1): mean = 6.1, SD = 0.35, n = 12 Far (group 2): mean = 5.8, SD = 0.30, n = 9 What is the conclusion of the t-test? a. Fail to reject the null hypothesis, the mean number of eggs do not seem to differ in the two types of locations. b. Fail to reject the null hypothesis, the mean number of eggs seem to differ in the two types of locations. c. Reject the null hypothesis, the mean number of eggs do not seem to differ in the two types of locations. d. Reject the null hypothesis, the mean number of eggs seem to differ in the two types of locations.

10. Consider urban ecologists who are interested in whether the presence of high-voltage power lines influences the number of eggs laid by birds nearby. They plan to conduct a two-sample t-test and will assume that the population variances are equal. Their data are as follows: Near (group 1): mean = 6.1, SD = 0.35, n = 9 Far (group 2): mean = 5.8, SD = 0.30, n = 12 What is the t-statistic for the t-test? a. 1.83 b. 1.95 c. 2.03 d. 2.11

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Chap 12_3e 11. Imagine a series of turbidity (cloudiness) measurements in the water from two different lakes. The measurements were taken over many different days (30 samples for each lake) and the figure shows the mean turbidity of those measurements along with bars representing 95% confidence intervals. What can we conclude about the appropriate null hypothesis and mean turbidity of the two lakes?

a. Fail to reject the null hypothesis, we lack evidence that the turbidity differs between the lakes. b. Reject the null hypothesis, we have evidence that the turbidity differs between the lakes. c. Reject the null hypothesis, we lack evidence that the turbidity differs between the lakes. d. We can't really tell from this figure whether the null hypothesis will be rejected or not.

12. When a figure shows means and bars indicating one standard error above and below each mean, and the range defined by the bars in one group overlaps the mean of the other, then the results of a t-test would always fail to reject the null hypothesis that the means are equal. a. True b. False 13. Consider urban ecologists who are interested in whether the presence of high-voltage power lines influences the number of eggs laid by birds nearby. They plan to conduct a two-sample t-test and will assume that the population variances are equal. Their data are as follows: Near (group 1): mean = 6.1, SD = 0.35, n = 9 Far (group 2): mean = 5.8, SD = 0.30, n = 12 What is the conclusion of the t-test? a. Fail to reject the null hypothesis, the mean number of eggs do not seem to differ in the two types of locations. b. Fail to reject the null hypothesis, the mean number of eggs seem to differ in the two types of locations. c. Reject the null hypothesis, the mean number of eggs do not seem to differ in the two types of locations. d. Reject the null hypothesis, the mean number of eggs seem to differ in the two types of locations.

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Chap 12_3e 14. Consider an urban ecologist who is interested in whether the presence of high-voltage power lines influences the number of eggs laid by birds nearby. She plans to conduct a two-sample t-test and will assume that the population variances are equal. Her data are as follows: Near (group 1): mean = 6.1, SD = 0.35, n = 12 Far (group 2): mean = 5.8, SD = 0.30, n = 9 What is the standard error of the difference between the two means? a. 0.142 b. 0.145 c. 0.148 d. 0.151 15. The paired t-test can be used even in some cases in which the population values are highly non-normal. a. True b. False 16. When we have two data sets that reveal 95% confidence intervals that differ from a hypothesized value and don't overlap, what conclusion can we make? a. Although these groups differ from the hypothesized value, they don't differ from one another. b. These groups are not significantly different from one another. c. These groups are significantly different from one another. d. We lack good evidence to decide whether these groups are significantly different from one another or not.

17. Consider an urban ecologist who is interested in whether the presence of high-voltage power lines influences the number of eggs laid by birds nearby. She plans to conduct a two-sample t-test and will assume that the population variances are equal. Her data are as follows: Near (group 1): mean = 6.1, SD = 0.35, n = 12 Far (group 2): mean = 5.8, SD = 0.30, n = 9 Based on the t-test statistic, and using your table of critical t-values, which of the following P-value ranges matches the one for the t-value? a. 0.05 < p b. 0.02 < p < 0.05 c. 0.01 < p < 0.02 d. p < 0.01 18. In a paired design, both treatments are applied to every sampled unit. a. True b. False

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Chap 12_3e 19. Consider a situation in which Chris predicts that an impending drainage connection will alter the number of fish in a set of six small lakes. She uses a large net (a seine) and counts the number of fish and obtains the values shown. Based on the t-test statistic, which of the following best described the results of Chris's paired t-test?

a. Fail to reject the null hypothesis, the storm did not seem to change the number of fish in the lakes. b. Fail to reject the null hypothesis, the storm seemed to reduce the number of fish in the lakes. c. Reject the null hypothesis, the storm did not seem to change the number of fish in the lakes. d. Reject the null hypothesis, the storm seemed to reduce the number of fish in the lakes.

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Chap 12_3e 20. Imagine a series of turbidity (cloudiness) measurements in the water from two different lakes. The measurements were taken over many different days (30 samples for each lake) and the figure shows the mean turbidity of those measurements along with bars representing 95% confidence intervals. What can we conclude about the appropriate null hypothesis and mean turbidity of the two lakes?

a. Fail to reject the null hypothesis, we lack evidence that the turbidity differs between the lakes. b. Reject the null hypothesis, we have evidence that the turbidity differs between the lakes. c. Reject the null hypothesis, we lack evidence that the turbidity differs between the lakes. d. We can't really tell from this figure whether the null hypothesis will be rejected or not.

21. Consider an urban ecologist who is interested in whether the presence of high-voltage power lines influences the number of eggs laid by birds nearby. He plans to conduct a two-sample t-test and will assume that the population variances are equal. His data are as follows: Near (group 1): mean = 6.1, SD = 0.35, n = 9 Far (group 2): mean = 5.8, SD = 0.30, n = 12 What is the standard error of the difference between the two means? a. 0.142 b. 0.145 c. 0.148 d. 0.151

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Chap 12_3e 22. Consider a situation in which Chris predicts that an impending drainage connection will alter the number of fish in a set of six small lakes. She uses a large net (a seine) and counts the number of fish and obtains the values shown. Based on the 95% confidence interval for the difference in the mean values, what do you predict the results of a paired t-test to be?

a. Fail to reject the null hypothesis, the storm did not seem to change the number of fish in the lakes. b. Fail to reject the null hypothesis, the storm seemed to reduce the number of fish in the lakes. c. Reject the null hypothesis, the storm did not seem to change the number of fish in the lakes. d. Reject the null hypothesis, the storm seemed to reduce the number of fish in the lakes.

23. The pooled sample variance is the mean of the variances, weighted by their degrees of freedom. a. True b. False 24. Consider an urban ecologist who is interested in whether the presence of high-voltage power lines influences the number of eggs laid by birds nearby. She plans to conduct a two-sample t-test and will assume that the population variances are equal. Her data are as follows: Near (group 1): mean = 6.1, SD = 0.35, n = 12 Far (group 2): mean = 5.8, SD = 0.30, n = 9 What is the t-statistic for the t-test? a. 1.96 b. 2.06 c. 2.16 d. 2.26 Copyright Macmillan Learning. Powered by Cognero.

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Chap 12_3e 25. In a paired design, numerical values from each treatment are compared with the numerical values from the other treatment that are most similar. a. True b. False 26. Consider a situation in which Chris predicts that an impending drainage connection will alter the number of fish in a set of six small lakes. She uses a large net (a seine) and counts the number of fish and obtains the values shown. Based on the 95% confidence interval for the difference in the mean values, what do you predict the results of a paired t-test to be?

a. Fail to reject the null hypothesis, the storm did not seem to change the number of fish in the lakes. b. Fail to reject the null hypothesis, the storm seemed to reduce the number of fish in the lakes. c. Reject the null hypothesis, the storm did not seem to change the number of fish in the lakes. d. Reject the null hypothesis, the storm seemed to reduce the number of fish in the lakes.

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Chap 12_3e 27. Consider a situation in which Chris predicts that an impending drainage connection will alter the number of fish in a set of six small lakes. She uses a large net (a seine) and counts the number of fish and obtains the values shown. What is the difference in the mean population density values?

a. –1.0 b. –2.0 c. –3.0 d. –4.0 28. If we collect blood pressure values for a set of patients before talking with a psychiatrist and then blood pressure values from a second set of individuals after talking with a psychiatrist, what type of test is most appropriate? a. Paired test b. Separation test c. Temporal test d. Two-sample test 29. Welch's t-test may only be used when the population variances are equal. a. True b. False 30. If the means of two populations are both significantly different from the same value, then they are significantly different from one another. a. True b. False Copyright Macmillan Learning. Powered by Cognero.

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Chap 12_3e 31. Consider an urban ecologist who is interested in whether the presence of high-voltage power lines influences the number of eggs laid by birds nearby. She plans to conduct a two-sample t-test and will assume that the population variances are equal. Her data are as follows: Near (group 1): mean = 6.1, SD = 0.35, n = 12 Far (group 2): mean = 5.8, SD = 0.30, n = 9 What is the pooled sample variance? a. 0.099 b. 0.104 c. 0.109 d. 0.114 32. Consider a situation in which Chris predicts that an impending drainage connection will alter the number of fish in a set of six small lakes. She uses a large net (a seine) and counts the number of fish and obtains the values shown. What is the difference in the mean population density values?

a. –1.0 b. –2.0 c. –3.0 d. –4.0 33. When a figure shows means and bars showing the 95% confidence interval, and the range defined by the bars in one group overlaps the mean of the other, then the results of a t-test would always fail to reject the null hypothesis that the means are equal. a. True b. False Copyright Macmillan Learning. Powered by Cognero.

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Chap 12_3e 34. Consider a situation in which Chris predicts that an impending drainage connection will alter the number of fish in a set of six small lakes. She uses a large net (a seine) and counts the number of fish and obtains the values shown. What is the 95% confidence interval for the difference in the values?

a. –8.9 < μ < 0.9 b. –7.9 < μ < –0.1 c. –7.4 < μ < –0.6 d. –5.9 < μ < –2.1 35. The F-test for comparing variances has a stringent assumption that is often not met in data sets we are analyzing. What is it? a. The data distributions must have equal means. b. The data distributions must have equal variances. c. The data must be binomially distributed. d. The data must be normally distributed.

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Chap 12_3e 36. Consider an urban ecologist who is interested in whether the presence of high-voltage power lines influences the number of eggs laid by birds nearby. She plans to conduct a two-sample t-test and will assume that the population variances are equal. Her data are as follows: Near (group 1): mean = 6.1, SD = 0.35, n = 12 Far (group 2): mean = 5.8, SD = 0.30, n = 9 What is the 95% confidence interval for the difference between the two means? a. 0.017 < μ1 – μ2 < 0.583 b. 0.010 < μ1 – μ2 < 0.590 c. 0.003 < μ1 – μ2 < 0.597 d. –0.004 < μ1 – μ2 < 0.604 37. Which of the following is not an advantage of Levene's test versus the F-test as a test of population variances? a. It can compare more than two groups. b. It is more robust to deviations from normality in the data distributions. c. It is more robust to deviations from symmetry in the data distributions. d. It uses the normal distribution instead of the F distribution.

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Chap 12_3e 38. Consider a situation in which Chris predicts that an impending drainage connection will alter the number of fish in a set of six small lakes. She uses a large net (a seine) and counts the number of fish and obtains the values shown. Based on the t-test statistic, and using your table of critical t-values, which of the following P-value ranges matches the one for the t-value she obtains?

a. 0.05 < p b. 0.02 < p < 0.05 c. 0.01 < p < 0.02 d. p < 0.01

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Chap 12_3e 39. Consider a situation in which Chris predicts that an impending drainage connection will alter the number of fish in a set of six small lakes. She uses a large net (a seine) and counts the number of fish and obtains the values shown. Based on the t-test statistic, which of the following best described the results of Chris's paired t-test?

a. Fail to reject the null hypothesis, the storm did not seem to change the number of fish in the lakes. b. Fail to reject the null hypothesis, the storm seemed to reduce the number of fish in the lakes. c. Reject the null hypothesis, the storm did not seem to change the number of fish in the lakes. d. Reject the null hypothesis, the storm seemed to reduce the number of fish in the lakes.

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Chap 12_3e 40. Imagine a series of turbidity (cloudiness) measurements in the water from two different lakes. The measurements were taken over many different days (30 samples for each lake) and the figure shows the mean turbidity of those measurements along with bars representing 95% confidence intervals. What can we conclude about the appropriate null hypothesis and mean turbidity of the two lakes?

a. Fail to reject the null hypothesis, we lack evidence that the turbidity differs between the lakes. b. Reject the null hypothesis, we have evidence that the turbidity differs between the lakes. c. Reject the null hypothesis, we lack evidence that the turbidity differs between the lakes. d. We can't really tell from this figure whether the null hypothesis will be rejected or not.

41. If the 95% confidence interval for the difference between the means includes the value zero, then we are likely to get a P-value less than 0.05 when we do a two-sample t-test. a. True b. False

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Chap 12_3e 42. Consider a situation in which Chris predicts that an impending drainage connection will alter the number of fish in a set of six small lakes. She uses a large net (a seine) and counts the number of fish and obtains the values shown. What is the t-test statistic for a paired t-test of the difference in the mean values?

a. –2.04 b. –2.54 c. –3.04 d. –3.54

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Chap 12_3e 43. Consider a situation in which Chris predicts that an impending drainage connection will alter the number of fish in a set of six small lakes. She uses a large net (a seine) and counts the number of fish and obtains the values shown. Based on the t-test statistic, and using your table of critical t-values, which of the following P-value ranges matches the one for the t-value she obtains?

a. 0.05 < p b. 0.02 < p < 0.05 c. 0.01 < p < 0.02 d. p < 0.01 44. Consider an urban ecologist who is interested in whether the presence of high-voltage power lines influences the number of eggs laid by birds nearby. He plans to conduct a two-sample t-test and will assume that the population variances are equal. His data are as follows: Near (group 1): mean = 6.1, SD = 0.35, n = 9 Far (group 2): mean = 5.8, SD = 0.30, n = 12 What is the pooled sample variance? a. 0.104 b. 0.109 c. 0.114 d. 0.119

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Chap 12_3e 45. When a figure shows means and bars indicating one standard deviation above and below each mean, and the range defined by the bars in one group overlaps the mean of the other, then the results of a t-test would always fail to reject the null hypothesis that the means are equal. a. True b. False 46. If we collect blood pressure values for a set of patients before talking with a psychiatrist and then blood pressure values from the same individuals after talking with a psychiatrist, what type of test is most appropriate? a. Paired test b. Separation test c. Temporal test d. Two-sample test 47. Draw a flowchart to describe the steps you would take when presented with data from two different groups, and the goal is to identify if the means of the groups differ. You may assume the data values are normally distributed. Include each possible statistical test.

48. Consider a study in which two sets of 20 mice were given different amounts of caffeine in their drinking water.

Members of the control group got none and members of the experimental group received 0.01% caffeine in their water. Their activity levels were measured using the mean number of minutes each mouse spent running on the wheel in their cage over a series of 14 nights.

Control treatment: mean = 305 minutes, standard deviation = 50 minutes Caffeine treatment: mean = 340 minutes, standard deviation = 60 minutes You may assume that the variances are equal for the purposes of conducting a two-sample t-test.

Perform a complete two-sample t-test. Summarize your results with a statement about the 95% confidence interval for the difference between the means, draw a figure showing the 95 confidence intervals for each treatment, present the t-test statistic and P-value for the two-sample test, and state your conclusion with regard to accepting or rejecting the null hypothesis and what this means for the effects of caffeine on mouse activity levels.

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Chap 12_3e 49. Consider a study in which two sets of 20 mice were given different amounts of caffeine in their drinking water.

Members of the control group got none and members of the experimental group received 0.01% caffeine in their water. Their activity levels were measured using the mean number of minutes each mouse spent running on the wheel in their cage over a series of 14 nights.

Control treatment: mean = 305 minutes, standard deviation = 40 minutes Caffeine treatment: mean = 340 minutes, standard deviation = 70 minutes Because the variances may be different, use the Welch's t-test approach for this data.

Perform a complete two-sample t-test. Summarize your results with a statement about the 95% confidence interval for the difference between the means, draw a figure showing the 95% confidence intervals for each treatment, present the t-test statistic and P-value for the two-sample test, and state your conclusion with regard to accepting or rejecting the null hypothesis and what this means for the effects of caffeine on mouse activity levels.

50. Consider a study in which two sets of 20 mice were given different amounts of caffeine in their drinking water.

Members of the control group got none and members of the experimental group received 0.01% caffeine in their water. The number of minutes each mouse spent running on the wheel in their cage was measured over a series of 14 nights. a. Describe why the appropriate sampling unit is the mean number of minutes for each of the 40 mice rather than the number of minutes during each of the 280 nights. b. What are the sample sizes you would use when comparing this running data in the two groups?

51. Describe a study to measure a physiological variable using twins that would be appropriate for a paired t-test and another design of the experiment, also using twins, that would not be appropriate for analyzing with a paired t-test.

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Chap 12_3e 52. Consider a study in which two sets of 20 mice were given different amounts of caffeine in their drinking water.

Members of the control group got none and members of the experimental group received 0.01% caffeine in their water. Their activity levels were measured using the mean number of minutes each mouse spent running on the wheel in their cage over a series of 14 nights.

Control treatment: mean = 305 minutes, standard deviation = 30 minutes Caffeine treatment: mean = 340 minutes, standard deviation = 60 minutes.

Because the variances may be different, use the Welch's t-test approach for this data Perform a complete two-sample t-test. Summarize your results with a statement about the 95% confidence interval for the difference between the means, draw a figure showing the 95% confidence intervals for each treatment, present the t-test statistic and P-value for the two-sample test, and state your conclusion with regard to accepting or rejecting the null hypothesis and what this means for the effects of caffeine on mouse activity levels.

53. Consider a study in which two sets of 20 mice were given different amounts of caffeine in their drinking water.

Members of the control group got none and members of the experimental group received 0.01% caffeine in their water. Their activity levels were measured using the mean number of minutes each mouse spent running on the wheel in their cage over a series of 14 nights.

Control treatment: mean = 305 minutes, standard deviation = 40 minutes Caffeine treatment: mean = 340 minutes, standard deviation = 50 minutes You may assume that the variances are equal for the purposes of conducting a two-sample t-test.

Perform a complete two-sample t-test. Summarize your results with a statement about the 95% confidence interval for the difference between the means, draw a figure showing the 95% confidence intervals for each treatment, present the t-test statistic and P-value for the two-sample test, and state your conclusion with regard to accepting or rejecting the null hypothesis and what this means for the effects of caffeine on mouse activity levels.

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Chap 12_3e Answer Key 1. b 2. a 3. b 4. a 5. b 6. b 7. a 8. d 9. a 10. d 11. d 12. a 13. d 14. a 15. a 16. c 17. a 18. a 19. d 20. b 21. b 22. a 23. b 24. b 25. b 26. d Copyright Macmillan Learning. Powered by Cognero.

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Chap 12_3e 27. c 28. d 29. b 30. b 31. c 32. d 33. a 34. c 35. d 36. c 37. d 38. b 39. a 40. a 41. b 42. c 43. a 44. a 45. b 46. a 47.

48.

49.

50.

51.

52.

53.

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Chap 13_3e Indicate the answer choice that best completes the statement or answers the question.

1. It is acceptable practice to try multiple transformations and choose the one that results in the smallest P-value for your statistical test. a. True b. False 2. Data transformations are only applied to the values that cause a distribution to deviate from normality. a. True b. False 3. For the data transformation Y' = ln[Y], what is the back transformation? a. Y = eY' b. Y = 10Y' c. Y = Log10[Y'] d. Y = L[Y'] 4. Log transformation is most useful for all of the following types of data except which? a. Highly variable data b. Left-skewed data c. Right-skewed data d. Values that are ratios 5. The Mann-Whitney U-test compares which of the following properties in two groups? a. The location and shape of their distributions. b. The location and variance of their distributions. c. The mean and shape of their distributions. d. The mean and variance of their distributions.

6. The square-root transformation is most often used for what types of data? a. Counts b. Highly symmetric distributions c. Proportions d. Ratios 7. Which of the following is not a commonly used data transformation? a. Arcsine transformation b. Log transformation c. Squared-value transformation d. Square-root transformation Copyright Macmillan Learning. Powered by Cognero.

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Chap 13_3e 8. Hallmarks of a non-normal population distribution include all of the following except which pattern? a. A histogram of the sample that has outliers. b. A histogram of the sample that is skewed heavily to one side. c. A histogram of the sample that is strongly bimodal. d. A histogram of the sample that is symmetric around the mean.

9. The sign test can be performed with highly skewed data sets. a. True b. False 10. When calculating your U-values to obtain your U-statistic, the two U values will sum up to the product of the two sample sizes. a. True b. False 11. The Wilcoxon signed rank test can be performed on skewed data sets. a. True b. False 12. If we calculate a 95% confidence interval for a square-root transformed (using the 1/2 factor) set of data and get 5.33 < μ' < 9.33, what is the 95% confidence interval in the original values? a. 27.91 < μ < 83.53 b. 27.91 < μ < 86.55 c. 30.86 < μ < 83.53 d. 30.86 < μ < 86.55 13. When sample sizes are large and all assumptions are met, a sign test has approximately ____% of the power of the one-sample t-test and the Mann-Whitney U-test has approximately ____% of the power of the twosample t-test. a. 65%; 75%. b. 65%; 95%. c. 75%; 95%. d. 95%; 75%.

14. If we calculate a 95% confidence interval for a square-root transformed (using the 1/2 factor) set of data and get 15.5 < μ' < 22.5, what is the 95% confidence interval in the original values? a. 225 < μ < 484 b. 225 < μ < 505.75 c. 239.75 < μ < 484 d. 239.75 < μ < 505.75

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Chap 13_3e 15. Randomly rearranging the values when we do a permutation test allows us to do which of the following? a. Estimate the sampling error. b. Filter out the asymmetry. c. Model a null hypothesis distribution. d. Simulate a data set with more precision.

16. In order for a two-sided sign test to be capable of rejecting the null hypothesis = 0.05 it must use a sample of at least 8 values. a. True b. False 17. When performing a permutation analysis, we remove values from a pool, and they can't be chosen more than once for each new data set. This process is called ___________. a. sampling with replacement. b. sampling without replacement. c. single sampling. d. unique sampling.

18. To figure out whether our sample appears to have come from a population exhibiting a normal distribution, which of the following is least useful? a. Creating a histogram of the data and looking at it carefully. b. Judging the linearity of values on a quantile plot of the data. c. Measuring the mean and variance to see if they are equal. d. Performing a Shapiro-Wilk test on the data.

19. The central limit theorem allows the assumption of normality to be ignored for F tests when we use extremely large samples. a. True b. False 20. When comparing two groups with a t-test, which is the best approach? a. Either test can be used unless the standard deviations differ by a factor of 3 or more, in which case you can only use a two-sample t-test. b. Either test can be used unless the standard deviations differ by a factor of 3 or more, in which case you can only use a Welch's t-test. c. Neither test can be used unless the standard deviations differ by less than a factor of 3, in which case you can use a two-sample t-test. d. Neither test can be used unless the standard deviations differ by less than a factor of 3, in which case you can use a Welch's t-test.

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Chap 13_3e 21. An inflated risk of Type I error is the main reason not to use parametric tests when their assumptions are not met. a. True b. False 22. The t-test is fairly robust to deviations from normality for large sample sizes, even though this is an assumption of the method. This is because the central limit theorem states that ____. a. the distribution of population data will be normal. b. the distribution of population means will be normal. c. the distribution of sample data will be normal. d. the distribution of sample means will be normal.

23. Which of the following is not one of the steps in performing a permutation analysis? a. Calculate the measure of association for the permutated sample. b. Create a permutated set of data with values of the response variable are randomly reordered. c. Estimate the P-value of each permutation. d. Repeat the permutation process many times.

24. As sample sizes increase, their distributions tend to resemble the population from which they are drawn. a. True b. False 25. What assumption does the Wilcoxon signed-rank test make that limits its utility? a. The distribution must be normal. b. The distribution must be symmetric. c. The sample size must be larger than 10. d. The variance must be equal to the mean.

26. An inflated risk of Type II error is the main reason not to use parametric tests when their assumptions are not met. a. True b. False 27. What two values would you get if you apply the square-root transformation with a factor of 1/2 to the numbers 3 and 9? a. 1.58 and 2.92 b. 1.58 and 3.08 c. 1.87 and 2.92 d. 1.87 and 3.08

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Chap 13_3e 28. Often the best way to check for normality in the population is to just look at the shape of the distribution of sample values. a. True b. False 29. If we have two samples of size 18 and 23 that generate a U-statistic value of 250, what Z-statistic does this approximate to? a. 0.604 b. 1.130 c. 1.656 d. 2.253 30. Statistical methods vary in their sensitivity to violations of their assumptions. The methods that are less prone to error when the assumptions are violated are termed which of the following? a. Reliable b. Repeatable c. Resistant d. Robust 31. It is acceptable practice to try multiple transformations and choose the one that makes your data fit the assumptions of the statistical test best. a. True b. False 32. If we have two samples of size 27 and 34 that generate a U-statistic value of 273, what Z-statistic does this approximate to? a. –1.80 b. –2.10 c. –2.40 d. –2.70 33. A quantile plot for a data set is described by which of the following? a. A plot of the numerical values versus the t-value expected for a value at that position in the set. b. A plot of the numerical values versus the Z-value expected for a value at that position in the set. c. A plot of the numerical values versus their frequency in the set. d. A plot of the numerical values versus their position in the set.

34. Permutation tests can be used to compare two means even when the data sets are highly skewed, as long as the skew is similar. a. True b. False Copyright Macmillan Learning. Powered by Cognero.

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Chap 13_3e 35. The Mann-Whitney U-test compares the medians in two groups to see if they are significantly different. a. True b. False 36. The Wilcoxon signed-rank test can be performed with highly skewed data sets. a. True b. False 37. Calculate the means and difference in means for the data sets shown. Now, square-root transform (using a factor of 1/2) the data and show the new means and difference in means.

Set 1: 4 5 7 8 Set 2: 4 4 6 22

38. Draw a flowchart for deciding what test to do when comparing the location of a group to a hypothesized value. Show the options for when the distribution is or is not skewed.

39. Draw a flowchart for deciding what test to do when comparing two groups. Show the options for when the data values are paired, the distributions are or are not skewed, and when the variances are or are not equal.

40. Calculate the means and difference in means for the data sets shown. Now, square-root transform (using a factor of 1/2) the data and show the new means and difference in means.

Set 1: 3 9 12 14 Set 2: 14 12 10 2

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Chap 13_3e Answer Key 1. b 2. b 3. a 4. b 5. a 6. a 7. c 8. d 9. a 10. a 11. b 12. b 13. b 14. d 15. c 16. b 17. b 18. c 19. b 20. b 21. a 22. d 23. c 24. a 25. b 26. b Copyright Macmillan Learning. Powered by Cognero.

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Chap 13_3e 27. d 28. a 29. b 30. d 31. a 32. d 33. b 34. a 35. b 36. b 37.

38.

39.

40.

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Chap 14_3e Indicate the answer choice that best completes the statement or answers the question.

1. A well-designed study will have only one control group. a. True b. False 2. An experimental unit is an individual or a group of individuals who have been assigned to an experimental treatment ___________ other individuals or groups. a. different from b. independently of c. randomly to d. separately from 3. Why is it important to be cautious when judging the results of an experiment comparing extremely different treatments to one another? a. The effect may not scale linearly, so smaller treatment differences may have no effect. b. The effect observed may be not replicable if the experiment is performed again. c. The effect seen may not be due to the extreme treatment used but due to some other factor instead. d. The effect when doing an extreme experiment will always be unrealistic.

4. Experiments with two treatments per block are _____ designs, and experiments with more than two treatments per block are _____ designs. a. single : multiple b. single : variational c. paired : randomized block d. paired : unpaired block 5. An experimental unit is an individual or group of individuals who have been assigned an experimental treatment independently of other individuals or groups. a. True b. False 6. If we do four statistical tests in situations where the null hypothesis is true and use an a = 0.05 threshold, there is a 21.5% chance we have made at least one Type I error. a. True b. False 7. Control groups in clinical trials are always expected to show no change in the variable of interest over time. a. True b. False

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Chap 14_3e 8. Increasing the sample size reduces the magnitude, or risk, of all of the following except which one? a. Bias b. Noise c. Sampling error d. Type II error 9. Randomization should never be carried out by listing subjects and then choosing experimental units for each treatment by alternating back and forth along the sequence. a. True b. False 10. Consider estimating the 95% confidence interval for the difference between two population means with a desired margin of error of 5 cm. What would the approximate (i.e., using the 2SE rule of thumb) minimum sample size be for each of the samples if the population standard deviation is 15 cm? a. n = 60 b. n = 72 c. n = 84 d. n = 96 11. Assigning experimental units to each treatment alphabetically is bad practice. a. True b. False

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Chap 14_3e 12. Consider the figure shown indicating the results on an experiment growing a marine invertebrate in four different environments based on values of two factors. Two different temperatures and two different salinities were used. Which of the following is incorrect?

a. The effect of low versus high temperature depends on the salinity. b. The effect of low versus high salinity depends on the temperature. c. There is no interaction. d. The two factors interact with one another.

13. If the DNA sequences of a bunch of individuals from a family with a history of a specific genetic disease are compared to DNA sequences in a data base, what limits the power of tests to discover the causes of the disease? a. The family members aren't independent, reducing the effective sample size. b. The family members may have different sequences from the individuals in the database. c. The individuals in the database are from different families, reducing the effective sample size. d. The individuals in the database may have different sequences from the individuals in the family.

14. If the experiment involves giving drugs, we provide a ____ to the control group, whereas if the experiment involves surgical procedures, we provide a ____ operation to the control group. a. blank : fake b. fake : blank c. placebo : sham d. sham : placebo

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Chap 14_3e 15. The way that blocks are used in experiments is to assign individuals in a balanced manner to the blocks and then randomly assign each block to one of the treatments. a. True b. False 16. When testing a new drug for an illness, which of these is a major reason to use a control group? a. Control groups eliminate all other factors that may cause statistical noise. b. More than one group is required to perform a statistical test for differences between a response and an expected response. c. People often get better just from thinking they have been treated, regardless of the actual effectiveness of the drug. d. Statistical power is maximized in tests that use two groups compared to those that just use one.

17. When treatments in a study have different sample sizes, we say it is which of the following? a. Clumped b. Dispersed c. Mixed d. Unbalanced 18. If we do four statistical tests in situations where the null hypothesis is true and use an a = 0.05 threshold, there is an 18.5% chance we have made at least one Type I error. a. True b. False 19. Which of these is not a good method to reduce sampling error in experimental results? a. Making sure that non-treatment factors were balanced in different groups. b. Organizing subjects into blocks with treatments varying between blocks. c. Organizing subjects into blocks with treatments varying within blocks. d. The use of large sample sizes.

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Chap 14_3e 20. Consider the figure shown indicating the results on an experiment growing a marine invertebrate in four different environments based on values of two factors. Two different temperatures and two different salinities were used. Which of the following is correct?

a. The effect of low versus high temperature depends on the salinity. b. The effect of low versus high salinity depends on the temperature. c. There is no interaction. d. The two factors interact with one another.

21. Imagine you are estimating the difference between two population means by comparing 95% confidence intervals. If you use the 2SE rule of thumb and have desired margin of error of 5 cm, what is the approximate minimum sample size for each of the samples if the population standard deviation is 15 cm? a. n = 108 b. n = 120 c. n = 132 d. n = 144 22. A clinical trial is a study testing the effects of a new drug, operation, or other medical intervention. a. True b. False 23. Reducing noise by making experimental conditions constant is always a good practice when designing experiments. a. True b. False Copyright Macmillan Learning. Powered by Cognero.

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Chap 14_3e 24. Which of the following aspects of good experimental design is the one that observational studies are unable to provide? a. Balancing b. Controls c. Extreme treatments d. Randomization 25. Why is blinding important when designing studies? a. Researchers may deliberately manipulate results if they know the groups. b. Researchers may accidentally treat genuine and placebo individuals differently. c. Researchers must not be able to know any details about the study subjects. d. Researchers must treat all treatments the exact same way.

26. Estimating the required sample size for an experiment is often done for practical economic reasons. a. True b. False 27. For a given population variance, what is the relationship between sample size and expected margin of error? a. There is a linear pattern (i.e., constant improvement) where larger sample sizes give larger margins of error. b. There is a linear pattern (i.e., constant improvement) where larger sample sizes give smaller margins of error. c. There is a nonlinear pattern (i.e., diminishing improvement) where larger sample sizes give larger margins of error. d. There is a nonlinear pattern (i.e., diminishing improvement) where larger sample sizes give smaller margins of error.

28. What is a control group? a. A group for which the null hypothesis is true. b. A group for which we know all the parameter values. c. A set of experimental units that do not receive the interesting treatment but are otherwise similar. d. A set of experimental units that receive the interesting treatment but under more controlled conditions.

29. To reduce bias, all study subjects should be arranged according to a parameter of interest, and then an alternating procedure (e.g., A, B, A, B, etc.) should be used to assign the participants to the groups. a. True b. False 30. Randomized block design uses three or more treatments. a. True b. False Copyright Macmillan Learning. Powered by Cognero.

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Chap 14_3e 31. Consider a situation in which you are interested in whether there is a 3 cm or larger difference between the means of two populations that each have a population standard deviation is 15 cm. You decide that a power of 0.080 is appropriate for your purposes. If you use a two-sample t-test with a = 0.05, what would the approximate minimum sample size be for each of the samples? a. n = 380 b. n = 390 c. n = 400 d. n = 410 32. Which performing 15 statistical tests, what is the Bonferroni corrected a* value that should be used instead of a = 0.05? a. a* = 0.03 b. a* = 0.015 c. a* = 0.0033 d. a* = 0.0015 33. For a given total sample size, a balanced design will result in the highest statistical power. a. True b. False 34. Using the Bonferroni correction reduces our overall risk of Type I error but increases the risk of Type II error for factors that have minor and moderate effects. a. True b. False 35. If testing for a 4 cm or more difference in means between two populations using a two-sample t-test with a = 0.05, what would the approximate (i.e., using a desired power of 0.80) minimum sample size be for each of the samples if the population standard deviation is 16 cm? a. n = 256 b. n = 266 c. n = 276 d. n = 286 36. We use matching in observational studies to reduce, but not eliminate, bias and sampling error. a. True b. False 37. Experiments with humans should be double-blind, but experiments with animals don't require blinding. a. True b. False

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Chap 14_3e 38. Estimating the required sample size for an experiment is often done to safeguard against undue harm to the study population. a. True b. False 39. Which of the following is the main problem arising when performing many statistical tests? a. After the first test, the accuracy of each additional test decreases. b. After the first test, the precision of each additional test decreases. c. The overall risk of Type I error adds up. d. The overall risk of Type II error adds up.

40. In experiments, when only the study subjects don't know which treatment group they are in, we call this a ____ - blind study, whereas if both the subjects and the people administering the treatment don't know, we call this a ____ - blind study. a. individual : pairwise b. simple : complex c. single : double d. solo : group 41. Doubling the sample size will tend to double the power of a statistical analysis. a. True b. False 42. What are the primary benefits of matching when doing observational studies? a. Matching eliminates bias and sampling error. b. Matching eliminates noise and sampling error. c. Matching reduces bias and sampling error. d. Matching reduces noise and sampling error.

43. When testing a new drug for an illness, which of these is not a major reason to use a control group? a. It allows us to distinguish the effects of different drugs from one another. b. It allows us to distinguish the effects of the stress of being treated from the effects of the drug. c. It allows us to distinguish the effects of typical improvement over time from the effects of the drug. d. It allows us to distinguish the placebo effect from the effects of the drug.

44. With matching, every individual in the treatment group is paired with a control individual having the same or closely similar value of the parameter of interest. a. True b. False

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Chap 14_3e 45. To reduce bias in experimental results, all of these are useful except for which one? a. Assigning participants to each treatment using an alternating procedure. b. Assigning participants to each treatment using random numbers. c. Blinding participants to which treatment they are in. d. Including control treatments.

46. True replication is more than just the absolute number of experimental units; the units considered must be ______ as well. a. Independent b. Measured c. Separate d. Variable 47. When factors interact, that is because we see effects when factors are combined that are not predictable from when each factor is tested in isolation. a. True b. False 48. Explain what blinding and double-blinding are and why they are important for clinical trials. Are they also needed for animal studies?

49. Using an example from everyday life, describe two factors that interact to have an effect on some kind of measurable quantity.

50. When determining the required sample size for an experiment, there are two major concepts that were discussed. Describe each of these and distinguish between them. Also, describe several factors that limit sample size and explain why.

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Chap 14_3e 51. Consider a study in which we wish to see whether the lengths of fish are related to the size of the lake in which they live. Unfortunately, the amount of dissolved nitrogen in the water from farm runoff is also thought to influence fish size. Imagine we are provided with the data shown in the table and wish to perform a matched design study where we compare the sizes of the fish in the largest four lakes to those in the smallest four lakes.

(a) Which fish should be in each of the two observation groups, and how should they be matched? (b) After matching, what is the mean and standard error of the differences in the sizes of the fish? (c) Based on your values in part (b), does there seem to be a difference in the mean size of the fish in the small and large lakes?

52. Compare and contrast "matching" and "adjusting" with respect to experimental design and data analysis. What do they both do, and in which ways do they differ?

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Chap 14_3e 53. Recall that doing many statistical tests increases the overall chance of a Type I error. Consider a situation in which we test 1,200 genes for their influence on a measured factor. If we use an a = 0.05 threshold for each test and obtain 83 significant results, how would we interpret this, and what would the next step be? Be sure to make a quantitative statement about these results in reference to the technical phrase "false discovery rate" in your answer.

54. Consider a study in which we wish to see whether the lengths of fish are related to the size of the lake in which they live. Unfortunately, the amount of dissolved nitrogen in the water from farm runoff is also thought to influence fish size. Imagine we are provided with the data shown in the table and wish to perform a matched design study where we compare the sizes of the fish in the largest four lakes to those in the smallest four lakes.

(a) Which fish should be in each of the two observation groups and how should they be matched? (b) After matching, what is the mean and standard error of the differences in the sizes of the fish? (c) Based on your values in part (b), does there seem to be a difference in the mean size of the fish in the small and large lakes?

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Chap 14_3e 55. Recall that doing many statistical tests increases the overall chance of a Type I error. If we used an a = 0.05 threshold for each test and the null hypothesis is actually true for all the tests, how many tests would we need to do before our risk of making at least one Type I error reaches 50%? Show all the steps in your calculation and remember that logarithms can be useful for solving equations with exponents.

56. Compare and contrast "balancing" and "blocking" with respect to experimental design. What do they both do, and in which ways do they differ?

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Chap 14_3e Answer Key 1. b 2. b 3. a 4. c 5. a 6. b 7. b 8. a 9. a 10. b 11. a 12. b 13. a 14. c 15. b 16. c 17. d 18. a 19. b 20. c 21. a 22. a 23. b 24. d 25. b 26. a Copyright Macmillan Learning. Powered by Cognero.

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Chap 14_3e 27. d 28. c 29. b 30. a 31. c 32. c 33. a 34. a 35. a 36. a 37. b 38. a 39. c 40. c 41. b 42. c 43. a 44. b 45. a 46. a 47. a 48.

49.

50.

51.

52.

53.

54.

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Chap 14_3e 55.

56.

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Chap 15_3e Indicate the answer choice that best completes the statement or answers the question.

1. The error mean square is best described by which of the following? a. It measures how many values there are. b. It measures the variation between all values in all of the groups. c. It measures the variation between the means of the groups. d. It measures the variation between values within each of the groups.

Consider the data table shown with values for five individuals measured in each of four groups (A, B, C, and D). We will conduct an ANOVA analysis of this.

2. What is the value of the F-ratio we will use in the analysis? a. 1.83 b. 2.92 c. 6.34 d. 8.75 3. Which of the following best describes when we would reject the null hypothesis when doing an ANOVA analysis? a. If the variation of group means is less than expected based on the variation between values within each group. b. If the variation of group means is more than expected based on the variation between values within each group. c. If the variation of values within each group is less than expected based on the variation between values of the group means. d. If the variation of values within each group is more than expected based on the variation between values of the group means.

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Chap 15_3e 4. If groups are predefined and of interest themselves, the explanatory variable is called a(n) ____ effect, but if the groups are randomly sampled from a population of possible groups, the explanatory variable is called a(n) ____ effect. a. fixed; random b. focal; independent c. independent; focal d. random; fixed 5. Consider the figure showing the results of a Tukey-Kramer procedure on the means of individuals collected from four different environments. If the bars represent 95% confidence intervals, what letter or combination of letters would the blank have?

a. a b. ab c. b d. c 6. A study examining the heights of multiple individuals in each of a series of families chosen at random from a population would be analyzed using a random-effects ANOVA. a. True b. False 7. In an ANOVA analysis, the R2 measures the total variation in the data. a. True b. False Copyright Macmillan Learning. Powered by Cognero.

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Chap 15_3e 8. Planned comparisons after an ANOVA using the t-test procedure tend to have higher precisions than regular two-sample t-tests. Why is that? a. The chosen pair of groups will always have the largest difference from among all the groups in the ANOVA. b. The degrees of freedom value used to define the confidence intervals is always larger. c. The MSerror is always less than the pooled variance. d. The standard error is always less using all the groups rather than just two.

Consider the partially completed ANOVA table shown.

9. What is the F-ratio for this ANOVA table? a. 9.28 b. 10.28 c. 16.33 d. 17.33

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Chap 15_3e Consider the data table shown with values for six individuals measured in each of four groups (A, B, C, and D). We will conduct an ANOVA analysis of this.

10. Use your calculated F-ratio, the degrees of freedom, and your table of critical F values to make a conclusion for this test? a. P < 0.05, none of the means seem to differ. b. P < 0.05, at least one of the means seems to differ. c. P > 0.05, none of the means seem to differ. d. P > 0.05, at least one of the means seems to differ.

11. Based on the ANOVA table shown, what is the

value for this data?

a. 4.55 b. 4.77 c. 4.99 d. 5.22

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Chap 15_3e Consider the data table shown with values for six individuals measured in each of four groups (A, B, C, and D). We will conduct an ANOVA analysis of this.

12. What is the error mean square? a. 4.66 b. 5.00 c. 5.33 d. 5.66 13. Based on the ANOVA table shown, what is the repeatability for this data?

a. 0.190 b. 0.322 c. 0.345 d. 0.408

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Chap 15_3e 14. A planned comparison when doing an ANOVA must be specified before the analysis, never afterwards. a. True b. False 15. A study examining the heights of single individuals from each of a series of families based on whether the family was vegetarian or not would be analyzed using a random-effects ANOVA. a. True b. False 16. The ANOVA techniques is robust to violations of its assumptions when sample sizes are large. a. True b. False Consider the data table shown with values for six individuals measured in each of four groups (A, B, C, and D). We will conduct an ANOVA analysis of this.

17. What is the SSgroups? a. 72 b. 80 c. 88 d. 96 18. What is the value of the F-ratio we will use in the analysis? a. 5.00 b. 5.25 c. 5.50 d. 5.75 Copyright Macmillan Learning. Powered by Cognero.

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Chap 15_3e 19. Which of the following is not an assumption of the ANOVA? a. The populations exhibit normal distributions. b. The populations have equal variances. c. The values are randomly chosen from the populations. d. The values are randomly chosen from the samples.

20. When using the Tukey-Kramer method, the probability of making a Type I error is α for each pairwise comparison made. a. True b. False 21. In an ANOVA analysis, the R2 is likely to be larger when the P-value is smaller and vice-versa. a. True b. False 22. When studying randomly chosen groups, we don't tend to do which of the following? a. Create an ANOVA table. b. Compare the within-group variance to the between-group variance. c. Estimate variance components. d. Test a null hypothesis.

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Chap 15_3e Consider the data table shown with values for six individuals measured in each of four groups (A, B, C, and D). We will conduct an ANOVA analysis of this.

23. What is the SSerror? a. 64.00 b. 72.00 c. 80.00 d. 88.00 24. Which of the following is what we expect if the samples we use in an ANOVA come from populations with the same means? a. The error mean square will be identical to the group mean square. b. The error mean square will be larger than the group mean square. c. The error mean square will be smaller than the group mean square d. The error mean square will be very close to than the group mean square.

25. A planned comparison is really just a t-test, but using a standard error based on the variance from all the groups. a. True b. False

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Chap 15_3e Consider the data table shown with values for five individuals measured in each of four groups (A, B, C, and D). We will conduct an ANOVA analysis of this.

26. What is the SSerror? a. 108 b. 128 c. 148 d. 168 27. Planned comparisons are slightly more robust to violations of the assumptions of the ANOVA than the ANOVA they follow. a. True b. False 28. The ANOVA technique requires more than two groups. a. True b. False

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Chap 15_3e Consider the data table shown with values for five individuals measured in each of four groups (A, B, C, and D). We will conduct an ANOVA analysis of this.

29. What is the SSgroups? a. 45 b. 60 c. 70 d. 85 30. Which of the following best describes the alternative hypothesis is an ANOVA analysis? a. All the population means are different from at least one other. b. All the population means are different from one another. c. At least one population's mean is different from all the others. d. At least one population's mean is different from at least one other.

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Chap 15_3e Consider the data table shown with values for six individuals measured in each of four groups (A, B, C, and D). We will conduct an ANOVA analysis of this.

31. What is the group mean square? a. 19.33 b. 24.50 c. 29.33 d. 34.50

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Chap 15_3e Consider the partially completed ANOVA table shown.

32. How many values are in each group of the data set this is based on? a. 5 b. 12 c. 14 d. 15 33. If the normality assumption of the single-factor ANOVA is violated, then the Kruskal-Wallis test is a good alternative as long as the sample sizes are large and the distributions are similar. a. True b. False

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Chap 15_3e 34. Consider the figure showing the results of a Tukey-Kramer procedure on the means of individuals collected from four different environments. If the bars represent 95% confidence intervals, what letter or combination of letters would the blank have?

a. a b. ab c. b d. c

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Chap 15_3e Consider the data table shown with values for five individuals measured in each of four groups (A, B, C, and D). We will conduct an ANOVA analysis of this.

35. To test the significance of the F-ratio value, what degrees of freedom would we use? a. df = 3 in the numerator, df = 12 in the denominator b. df = 3 in the numerator, df = 16 in the denominator c. df = 4 in the numerator, df = 12 in the denominator d. df = 4 in the numerator, df = 16 in the denominator 36. What is the group mean square? a. 17.50 b. 19.33 c. 21.50 d. 23.33 37. Usually for an ANOVA the variances in all the groups should be the same, but when can this assumption be relaxed? a. The samples are large, the same size, and the variances differ by less than tenfold. b. The samples are large, the same size, and the variances differ by less than threefold. c. The samples are small, the same size, and the variances differ by less than tenfold. d. The samples are small, the same size, and the variances differ by less than threefold.

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Chap 15_3e Consider the data table shown with values for five individuals measured in each of four groups (A, B, C, and D). We will conduct an ANOVA analysis of this.

38. Use your calculated F-ratio, the degrees of freedom, and your table of critical F values to make a conclusion for this test? a. P < 0.05, none of the means seem to differ. b. P < 0.05, at least one of the means seems to differ. c. P > 0.05, none of the means seem to differ. d. P > 0.05, at least one of the means seems to differ.

39. What are the means of the groups and overall mean? a. 8, 11, 12, 15, and 12 b. 9, 11, 12, 15, and 12 c. 10, 11, 12, 15, and 11 d. 10, 11, 12, 15, and 12

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Chap 15_3e Consider the data table shown with values for six individuals measured in each of four groups (A, B, C, and D). We will conduct an ANOVA analysis of this.

40. To test the significance of the F-ratio value, what degrees of freedom would we use? a. df = 2 in the numerator, df = 12 in the denominator. b. df = 2 in the numerator, df = 15 in the denominator. c. df = 3 in the numerator, df = 12 in the denominator. d. df = 3 in the numerator, df = 15 in the denominator.

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Chap 15_3e Consider the data table shown with values for five individuals measured in each of four groups (A, B, C, and D). We will conduct an ANOVA analysis of this.

41. What is the error mean square? a. 8 b. 9 c. 10 d. 11 42. When using the Tukey-Kramer method, the P-value is exact when the sample sizes in all groups are the same. a. True b. False 43. The repeatability measures the overall similarity of repeat measurements made on the same group. a. True b. False 44. An experimental mistake is always equivalent to either a Type I or Type II error. a. True b. False

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Chap 15_3e Consider the data table shown with values for five individuals measured in each of four groups (A, B, C, and D). We will conduct an ANOVA analysis of this.

45. What is the value of the R2 value we obtain from the analysis? a. 0.222 b. 0.333 c. 0.444 d. 0.555

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Chap 15_3e Consider the data table shown with values for six individuals measured in each of four groups (A, B, C, and D). We will conduct an ANOVA analysis of this.

46. What are the means of the groups and overall mean? a. 12, 13, 13, 19, and 15 b. 13, 13, 14, 19, and 15 c. 13, 14, 14, 19, and 15 d. 14, 14, 15, 19, and 15

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Chap 15_3e 47. Consider a study involving six populations from which we draw samples of 12 values each in which the group mean square is 426 and the error mean square is 1416.

(a) Complete the ANOVA table. (b) Does it appear that any of the population the samples are drawn from have means that differ from one another?

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Chap 15_3e 48. Consider a study involving seven populations from which we draw samples of 13 values each in which the group mean square is 315 and the error mean square is 2020.

(a) Complete the ANOVA table. (b) Does it appear that any of the population the samples are drawn from have means that differ from one another?

49. If the data intended for an ANOVA does not meet the assumptions, there are three options. Describe each of these options and what you would do to pursue each of them.

50. Describe the difference between ANOVA analyses examined fixed and random effects. Describe how the interpretation of the same numerical values is done differently.

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Chap 15_3e 51. Using the data set shown, calculate all the values you need to complete an ANOVA table.

52. Describe the difference between ANOVA analyses using planned and unplanned comparisons. Describe how the analysis is done differently.

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Chap 15_3e 53. Using the data set shown, calculate all the values you need to complete the ANOVA table.

54. Describe the reason we need a technique like the ANOVA. Illustrate the problem with an example using ttests to study several groups. Make reference to the appropriate type of statistical error and use an example calculation to show the problem the ANOVA addresses.

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Chap 15_3e Answer Key 1. d 2. b 3. b 4. a 5. b 6. a 7. b 8. b 9. a 10. b 11. d 12. c 13. b 14. a 15. b 16. a 17. c 18. c 19. d 20. b 21. a 22. d 23. a 24. d 25. a 26. b Copyright Macmillan Learning. Powered by Cognero.

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Chap 15_3e 27. b 28. b 29. c 30. d 31. c 32. d 33. a 34. c 35. b 36. d 37. a 38. c 39. d 40. c 41. a 42. a 43. a 44. b 45. b 46. c 47.

48.

49.

50.

51.

52.

53.

54.

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Chap 15_3e

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Chap 16_3e Indicate the answer choice that best completes the statement or answers the question.

1. Attenuation is the term that describes how measurement error tends to move the correlation coefficient closer to zero than its true value. a. True b. False Consider the data set shown. The mean X value is 6 and the mean Y value is 5.

2. What would the correlation coefficient be for this data set? a. –0.333 b. –0.300 c. –0.267 d. –0.233

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Chap 16_3e Consider the data set shown. The mean X value is 6 and the mean Y value is 6.

3. What is the 95% confidence interval for ρ? a. 0.033 to 0.993 b. –0.023 to 0.983 c. 0.013 to 0.973 d. 0.277 to 0.987

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Chap 16_3e Consider the data set shown. The mean X value is 6 and the mean Y value is 5.

4. What would the Spearman's rank correlation coefficient be for this data set? a. –0.333 b. –0.300 c. –0.267 d. –0.233 5. If measurement error in our variables is high when attempting to calculate correlation coefficients, which of the following three approaches is not a good way to deal with this? a. Find a different measuring method that yields more precise measurements. b. Measure each individual multiple times and use the average value. c. Remeasure individuals with the most extreme values to eliminate outliers. d. Use repeat measurements to calculate a corrected correlation, r*.

6. The value of the correlation coefficient increases as the difference between the largest and smallest X values increases. a. True b. False

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Chap 16_3e Consider the data set shown. The mean X value is 6 and the mean Y value is 5.

7. What would the t-value be for a t-test of the Spearman's rank correlation coefficient for this data set? a. 2.973 b. 3.073 c. 3.175 d. 3.335 8. Spearman's rank correlation measures the strength and direction of the linear association between the ranks of two variables. a. True b. False

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Chap 16_3e Consider the data set shown. The mean X value is 6 and the mean Y value is 6.

9. What is the t-value for a significance test of ρ? a. 3.268 b. 3.899 c. 3.468 d. 3.568 10. We use the standard error of the correlation coefficient to calculate confidence intervals for the correlation coefficient. a. True b. False 11. Research studies with many test results where P > 0.05 are often easier to publish than those in which most of the tests result in P < 0.05. a. True b. False

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Chap 16_3e Consider the data set shown. The mean X value is 6 and the mean Y value is 5.

12. What would the t-value be for a t-test of the Spearman's rank correlation coefficient for this data set? a. –0.545 b. –0.585 c. –0.625 d. –0.665

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Chap 16_3e Consider the data set shown. The mean X value is 6 and the mean Y value is 5.

13. What is the 95% confidence interval for ζ? a. –1.88 to 1.31 b. –1.77 to 1.21 c. –1.66 to 1.11 d. –1.55 to 1.01 14. This value measures the strength and direction of the association between two numerical variables. a. Correlation coefficient. b. Correlation factor. c. Correlation measurement. d. Correlation value.

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Chap 16_3e Consider the data set shown. The mean X value is 6 and the mean Y value is 6.

15. What would the correlation coefficient be for this data set? a. 0.799 b. 0.829 c. 0.859 d. 0.889 16. Measurement error will tend to decrease the absolute value of the correlation coefficient. a. True b. False 17. A funnel plot is a graphical method to examine the relationship between the sample size of an experiment and the estimated effect size from that experiment. a. True b. False

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Chap 16_3e Consider the data set shown. The mean X value is 6 and the mean Y value is 6.

18. What is the t-value for a significance test of r? a. –0.479 b. –0.979 c. –1.479 d. –1.979 19. Calculated values for the Spearman's rank correlation can be treated like regular correlation coefficients with respect to determining the t-value when the sample size exceeds 20. a. True b. False

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Chap 16_3e Consider the data set shown. The mean X value is 6 and the mean Y value is 5.

20. What would the Spearman's rank correlation coefficient be for this data set? a. 0.797 b. 0.827 c. 0.857 d. 0.887

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Chap 16_3e Consider the data set shown. The mean X value is 6 and the mean Y value is 5.

21. What is the 95% confidence interval for ρ? a. –0.810 to 0.665 b. –0.850 to 0.725 c. –0.890 to 0.765 d. –0.930 to 0.805 22. A bivariate distribution has all of the following features except which one? a. The X and Y values each have their own separate normal distributions. b. The X and Y values have a linear relationship with one another. c. The X and Y values have symmetric distributions and the same range of values. d. We see a circular or elliptical cloud of points when we make a scatter plot of the X and Y values.

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Chap 16_3e Consider the data set shown. The mean X value is 6 and the mean Y value is 5.

23. What would the sum of the products be for this data set? a. –8 b. –6 c. 4 d. 20 24. The correlation coefficient measures the strength, but not the direction, of the association between two numerical variables. a. True b. False

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Chap 16_3e Consider the data set shown. The mean X value is 6 and the mean Y value is 5.

25. What would the standard error of the correlation coefficient be for this data set? a. 0.071 b. 0.462 c. 0.556 d. 0.650 26. What is the general pattern seen in funnel plots used to examine publication bias? a. As the effect size on the X-axis increases, the range of effect sizes on the Y-axis tightens around the likely true value. b. As the effect size on the X-axis increases, the range of P-values on the Y-axis tightens around the likely true value. c. As the sample size on the X-axis increases, the range of effect sizes on the Y-axis tightens around the likely true value. d. As the sample size on the X-axis increases, the range of P-values on the Y-axis tightens around the likely true value.

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Chap 16_3e Consider the data set shown. The mean X value is 6 and the mean Y value is 6.

27. What would the standard error of the correlation coefficient be for this data set? a. 0.244 b. 0.228 c. 0.284 d. 0.304 28. What would the z-transformation of the correlation coefficient be? a. 1.379 b. –1.399 c. 1.419 d. 1.439 29. When two numerical variables are correlated, then the relationship between them is linear. a. True b. False

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Chap 16_3e Consider the data set shown. The mean X value is 6 and the mean Y value is 5.

30. What would the z-transformation of the correlation coefficient be? a. –0.273 b. –0.233 c. –0.193 d. –0.153 31. The absolute value of the correlation coefficient is between zero and one. a. True b. False 32. When can you use a subset of the range of values to estimate the correlation coefficient for the whole range? a. When the data have been transformed using the natural log transformation. b. When the data have been transformed using the square root transformation. c. When the range of X values is at least 50% of the range of the total data set. d. You cannot ever do this.

33. When transforming variables in a correlation analysis, both the X and Y values must be transformed. a. True b. False 34. A statistically significant correlation coefficient indicates a linear relationship between the two variables. a. True b. False

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Chap 16_3e 35. The technique that measures the strength and direction of the linear association between the ranks of two variables is called which of the following? a. Fisher's magnitude correlation. b. Fisher's rank correlation. c. Spearman's magnitude correlation. d. Spearman's rank correlation.

Consider the data set shown. The mean X value is 6 and the mean Y value is 6.

36. What would the sum of the products be for this data set? a. 20 b. 22 c. 24 d. 26

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Chap 16_3e Consider the data set shown. The mean X value is 6 and the mean Y value is 5.

37. What would the standard error of the Spearman's rank correlation coefficient be for this data set? a. 0.247 b. 0.257 c. 0.281 d. 0.301 38. The term ____ is used to describe the phenomenon by which measurement error reduces the absolute value of r. a. Attenuation b. Minimization c. Shrinkage d. Stochasticity

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Chap 16_3e Consider the data set shown. The mean X value is 6 and the mean Y value is 5.

39. What would the standard error of the Spearman's rank correlation coefficient be for this data set? a. 0.491 b. 0.511 c. 0.531 d. 0.551 40. Correlation coefficients for studies using different ranges of values can be compared as long as 50% of the range overlaps. a. True b. False 41. When we determine that two variables are correlated, which of the following is the best way to think about our observation? a. Correlation alone does not tell us anything. b. One of them is causing the other, but we don't know which is which c. Something interesting is going on, but we need more information. d. The relationship between the two factors is linear, not curved.

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Chap 16_3e Consider the data set shown. The mean X value is 6 and the mean Y value is 6.

42. What is the 95% confidence interval for ζ? a. 0.123 to 2.954 b. –0.093 to 2.904 c. 0.063 to 2.854 d. 0.286 to 2.548 43. Which of the following is not a factor that can adversely influence the accuracy of a correlation analysis? a. The width of the set of points is wider at one end than the other. b. There are more points toward the center of the axes than at the ends. c. There are outliers. d. There is a curved relationship between the X and Y values.

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Chap 16_3e 44. Consider the data set shown. Convert these values into ranks and conduct a Spearman's rank correlation analysis.

(a) Calculate the Spearman's rank correlation coefficient and standard error. (b) Calculate the t-value for the Spearman's rank correlation coefficient. (c) Using your results from (a) and (b), make a statement about the significance of the association between the X and Y values.

45. Consider two different kinds of publication bias: one arising from the behaviors of journal reviewers and the other arising from the economic interests of companies that fund the research. Both are sources of publication bias, but the reasons differ. Describe how the biases are caused and contrast the morality of the scientists submitting the papers in these two situations.

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Chap 16_3e 46. Consider the data set shown. Convert these values into ranks and conduct a Spearman's rank correlation analysis.

(a) Calculate the Spearman's rank correlation coefficient and standard error. (b) Calculate the t-value for the Spearman's rank correlation coefficient. (c) Using your results from (a) and (b), make a statement about the significance of the association between the X and Y values.

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Chap 16_3e 47. Consider the data set shown. Conduct a full correlation analysis on these values.

(a) Make a graph of the data points. (b) Calculate the correlation coefficient with 95% confidence interval. (c) Calculate the t-value for the correlation coefficient. (d) Using your results from (b) and (c), make a statement about the significance of the association between the X and Y values.

48. When might we prefer to use rank data even if we have quantitative values for our variables?

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Chap 16_3e 49. Consider the data set shown. Conduct a full correlation analysis on these values.

(a) Make a graph of the data points. (b) Calculate the correlation coefficient with 95% confidence interval. (c) Calculate the t-value for the correlation coefficient. (d) Using your results from (b) and (c), make a statement about the significance of the association between the X and Y values.

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Chap 16_3e Answer Key 1. a 2. c 3. d 4. b 5. c 6. b 7. d 8. a 9. b 10. b 11. b 12. a 13. c 14. a 15. d 16. a 17. a 18. a 19. b 20. c 21. d 22. c 23. a 24. b 25. c 26. c Copyright Macmillan Learning. Powered by Cognero.

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Chap 16_3e 27. b 28. c 29. b 30. a 31. a 32. d 33. b 34. b 35. d 36. b 37. b 38. a 39. d 40. b 41. c 42. d 43. b 44.

45.

46.

47.

48.

49.

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Chap 17_3e Indicate the answer choice that best completes the statement or answers the question.

1. The Michaelis-Menten equation models exponential growth. a. True b. False 2. Which of the following was not listed as a suggestion for creating data sets that can be used in subsequent meta-analyses? a. Clearly describe conflicts of interest. b. Provide standard errors and effect size. c. Provide test statistics and degrees of freedom. d. Upload data sets to an established online archive.

3. The method in which quantitative statements about effect sizes from all known scientific studies are combined to generate an overall estimate is called which of the following? a. Combo-analysis b. Meta-analysis c. Uber-analysis d. Ultra-analysis 4. If the linear least squares equation for a data set is Y = 12 – (0.7)X, what is the residual corresponding to a data point with a value of (8, 8)? a. –1.6 b. 0 c. 1.6 d. 3.5 5. Residuals can have either positive or negative values. a. True b. False 6. What is a weakness of the ANOVA method compared to the t-test method when performing a significance test on the slope of a regression? a. The ANOVA method can't test against null hypothesis slopes different from 0. b. The ANOVA method can't use data that has outliers. c. The ANOVA method is more prone to Type I error for data with high variance. d. The ANOVA method is more prone to Type I error for small sample sizes.

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Chap 17_3e Consider the partially completed ANOVA table showing the results of a regression analysis shown.

7. What is the R2 value? a. 0.197 b. 0.245 c. 0.755 d. 0.803 8. Which of the following equations describes a line that passes through the point (15,51)? a. Y = 2 + 5X b. Y = 4 + 4X c. Y = 6 + 3X d. Y = 7 + 2X 9. If the slope is –1.64, the residual mean square is 3.6, the sum of squares for X is 2.5, and the sample size is 16, based on the t-test statistic using a hypothesized slope of 1.0, and using your table of critical t-values, which of the following P-value ranges matches the one for the t-value? a. P > 0.05 b. 0.02 < P < 0.05 c. 0.01 < P < 0.02 d. P < 0.01 10. The Michaelis-Menten equation is used to model what kind of nonlinear pattern in a data set? a. Asymptotic increase. b. Cyclical fluctuations. c. Exponential growth. d. Power law declines.

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Chap 17_3e 11. The Michaelis-Menten equation takes the form of which of the following? a. Y = aX / bX b. Y = aX / (b + X) c. Y = (a + X) / bX d. Y = (a + X) / (b + X) 12. If the slope is –1.64, the residual mean square is 3.6, the sum of squares for X is 2.5, and the sample size is 16, what is the 95% confidence interval of the slope? a. –4.214 to 0.934 b. –3.562 to 0.282 c. –2.840 to –0.440 d. –2.133 to –1.115 13. Measurement error reduces the R2 . a. True b. False 14. Which of the following is true for 95% confidence bands? a. 95% of the population data will be bracketed by the 95% confidence bands. b. 95% of the sample data will be bracketed by the 95% confidence bands. c. The 95% confidence bands from 95% of samples will bracket the true population regression line. d. There is a 95% chance that the sample regression will match the true population regression line.

15. If the linear least squares equation for a data set is Y = 2 + (0.4)X, what is the residual corresponding to a data point with a value of (9, 4)? a. –0.4 b. 0.4 c. 0.8 d. –1.6 16. The effects of measurement error in the X-values and the Y-values are identical with regard to the slope of the linear regression line. a. True b. False 17. Confidence bands allow us to predict the region within which 95% of the data points used in a regression will be. a. True b. False

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Chap 17_3e 18. The quadratic curve is specified by an equation like which following? a. Y = aXb b. Y = abx c. Y = a + bX + cX 2 d. Y = (a + bX) / cX2 19. Which of the following equations describes a line that passes through the point (4,12)? a. Y = 20 – 2X b. Y = 25 – 3X c. Y = 30 – 4X d. Y = 35 – 5X 20. Thee null hypothesis of a logistic regression is that the probability of the occurrence of the binary variable is unrelated to the values of proposed explanatory numerical variable. a. True b. False 21. Which of the following equation defines the line with the largest slope and Y-intercept? a. Y = 12 + 9X b. Y = 12 + 6X c. Y = 15 + 9X d. Y = 15 + 6X 22. The linear least squares line always goes through the point corresponding to the mean values of X and Y. a. True b. False 23. The log transformation often works well to resolve problems of unequal variance for count data. a. True b. False 24. Regression toward the mean will occur for data sets that exhibit R 2 < 1.0. a. True b. False 25. The regression fallacy describes the process by which subsequent measurements will result in the slope of a relationship attenuating. a. True b. False

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Chap 17_3e 26. The quadratic curve is used to model parabolic patterns. a. True b. False 27. If the null hypothesis of an ANOVA test of the slope of a regression line is true, then there is no association between the X and Y values. a. True b. False 28. What criterion do we use to decide on the "least squares regression" line through data? a. It is the line for which the sum of all the deviations between the points and the line (in the X direction) is minimized. b. It is the line for which the sum of all the deviations between the points and the line (in the Y direction) is minimized. c. It is the line for which the sum of all the squared deviations between the points and the line (in the X direction) is minimized. d. It is the line for which the sum of all the squared deviations between the points and the line (in the Y direction) is minimized.

29. If the slope is –1.64, the residual mean square is 3.6, the sum of squares for X is 2.5, and the sample size is 16, what is the t-value we obtain when doing a t-test using a hypothesized slope of 1.0? a. –2.000 b. –2.200 c. –2.400 d. –2.600 30. If the slope is –1.64, the residual mean square is 3.6, the sum of squares for X is 2.5, and the sample size is 16, based on the t-test statistic using a hypothesized slope of zero, and using your table of critical t-values, which of the following P-value ranges matches the one for the t-value? a. P > 0.05 b. 0.02 < P < 0.05 c. 0.01 < P < 0.02 d. P < 0.01 31. If the slope is –1.64, the residual mean square is 3.6, the sum of squares for X is 2.5, and the sample size is 16, what is the t-value we obtain when doing a t-test using a hypothesized slope of zero? a. –0.867 b. –1.367 c. –1.867 d. –2.367 Copyright Macmillan Learning. Powered by Cognero.

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Chap 17_3e 32. Using extrapolation to predict Y values outside the range of X values studied is not recommended. a. True b. False 33. Formula-free curve fitting includes methods called "kernel," "spline," and "loess," which collectively are called ______. a. basing b. linearizing c. modeling d. smoothing 34. Meta-analysis studies can often provide more-precise estimates of effect sizes than individual studies can. a. True b. False 35. Regression analyses require that the X and Y values follow a bivariate distribution. a. True b. False 36. If the slope is –1.64, the residual mean square is 3.6, the sum of squares for X is 2.5, and the sample size is 16, what is the standard error of the slope? a. 0.215 b. 0.310 c. 0.833 d. 1.200 37. To calculate the residual mean square, we use n–3 instead of n–1 as we would for a usual variance. a. True b. False 38. Logistic regression predicts the ____ of occurrence of a(n) ____ variable as a function of a continuous variable? a. distribution; integer b. number; qualitative c. probability; binary d. rate; quantitative

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Chap 17_3e Consider the partially completed ANOVA table showing the results of a regression analysis shown.

39. What is the F-ratio? a. 1.245 b. 4.088 c. 5.088 d. 5.871 40. Single outliers can have a dramatic effect on the slope obtained in a regression analysis. a. True b. False 41. For a logistic regression analysis of doses of a drug (measured in mg of drug/kg body mass) in which a = – 0.66 and b = 2.8, what would the LD50 be? a. 0.118 mg/kg b. 0.236 mg/kg c. 2.121 mg/kg d. 4.242 mg/kg 42. Reporting the P-values of statistical tests is sufficient detail for most subsequent meta-analysis studies. a. True b. False 43. If the null hypothesis of a t-test for the slope of a regression line is true, then there is no association between the X and Y values. a. True b. False

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Chap 17_3e 44. What is the effect of measurement error in the Y-values? a. Both the slope and the variance of the residuals are changed. b. Neither the slope or the variance of the residuals is changed. c. The slope is changed, but the variance of the residuals is not. d. The variance of the residuals is changed, but the slope is not.

45. Which of the following is not an assumption of linear regression? a. Across the entire range of the X-values, the distribution of Y-values is normally distributed around the regression line. b. Across the entire range of the X-values, the mean of the Y-values lies on a straight line. c. Across the entire range of the X-values, the number of Y-values is constant. d. Across the entire range of the X-values, the variance of the Y-values is the same.

46. If the assumptions of linear regression are met, then a residual plot will have all of the following features except which one? a. The cloud of points above and below the zero line will be roughly symmetric. b. The cloud of points above and below the zero line will have roughly the same variance. c. The distribution of X-values will be roughly symmetric. d. There will be no clear signs of a curved pattern throughout the range of X-values.

47. The log transformation works well to linearize exponential relationships but not power relationships. a. True b. False 48. In your own words, describe what a logistic regression is. What is the goal of a logistic regression and what do the axes in the plot represents conceptually?

49. Draw a graph showing the data points (1, 1), (2,4), (3,9), (4,16) and then transform the data with a square root transformation on the Y-values and show those points using different symbols. Indicate which type of curve would be most appropriate to model each data set and describe what you would do if you wanted to know if the relationship between X and Y was statistically significant.

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Chap 17_3e 50. When and why would we transform data during a linear regression procedure?

51. Using a very simplified diagram, illustrate the phenomenon of regression to the mean. Do this by drawing a set of data and then showing how it would likely change from that first measurement to the second and how this influences the slope. Annotate your diagram to make it clear what is happening.

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Chap 17_3e 52. Consider the data set shown in the table.

(a) Make a graph of the data points. (b) Calculate the slope and Y-intercept. (c) Plot the linear least squares line on your graph. (d) Make a second graph showing the residuals. (e) Calculate the t-value for a significance test of the slope of your linear least squares line. (f) Using your results from (e), make a statement about the significance of the relationship between the X and Y values.

53. Describe when would we prefer to use the t-test procedure to test the significance of our linear least squares slope and when would we prefer the ANOVA approach.

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Chap 17_3e 54. Consider the data set shown in the table.

(a) Make a graph of the data points. (b) Calculate the slope and Y-intercept. (c) Plot the linear least squares line on your graph. (d) Make a second graph showing the residuals. (e) Calculate the t-value for a significance test of the slope of your linear least squares line. (f) Using your results from (e) make a statement about the significance of the relationship between the X and Y values.

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Chap 17_3e Answer Key 1. b 2. a 3. b 4. c 5. a 6. a 7. a 8. c 9. b 10. a 11. b 12. a 13. a 14. c 15. d 16. b 17. b 18. c 19. a 20. a 21. c 22. a 23. a 24. a 25. b 26. a Copyright Macmillan Learning. Powered by Cognero.

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Chap 17_3e 27. a 28. d 29. b 30. a 31. b 32. a 33. d 34. a 35. b 36. d 37. b 38. c 39. d 40. a 41. b 42. b 43. a 44. d 45. c 46. c 47. b 48.

49.

50.

51.

52.

53.

54.

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Chap 17_3e

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Chap 18_3e Indicate the answer choice that best completes the statement or answers the question.

1. In the linear model RESPONSE = CONSTANT + A + B + A*B, what does the A*B represent? a. The interaction between factors A and B b. The mean of factor A multiplied by the mean of factor B c. The mean of factor A raised to the power of factor B d. The product of factors A and B 2. When the assumptions of the linear model are met, a plot of the residuals will show a slope different from zero if the numerical factor is significant. a. True b. False 3. If we fail to appreciate the fact that species may be similar due to relatedness and instead examine their traits and relationships between traits as independent data points, what kind of error are we likely to be prone to making? a. Getting a P-value larger than 0.05 when we shouldn't, making a Type I error. b. Getting a P-value larger than 0.05 when we shouldn't, making a Type II error. c. Getting a P-value less than 0.05 when we shouldn't, making a Type I error. d. Getting a P-value less than 0.05 when we shouldn't, making a Type II error.

4. When linear models include more than one explanatory variable, there will always be an interaction between them. a. True b. False 5. What is the purpose of adding a blocking variable to a randomized block design ANOVA experiment? a. To factor out the effects of the block on the means of the groups b. To increase the overall sample size and reduce the standard errors c. To investigate the effects of the block on the means of the groups d. To reduce the variation and observed differences between groups 6. If the value of one explanatory variable modifies the effects of the values of the other explanatory variable, the variables are said to ____. a. balance b. combine c. influence d. interact

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Chap 18_3e 7. When the interaction term is not significant in an ANCOVA analysis, we can conclude that there is no influence of the confounding variable on the values measured. a. True b. False 8. Blocking factors are considered explanatory factors in factorial designs. a. True b. False 9. In a randomized block design with each treatment replicated once per block, the null model of the data can be visualized via which of the following equations? a. RESPONSE = CONSTANT + BLOCK b. RESPONSE = CONSTANT + TREATMENT c. RESPONSE = CONSTANT + BLOCK + TREATMENT d. RESPONSE = CONSTANT + BLOCK + TREATMENT + INTERACTION 10. The interaction plot shown most likely represents which of the following?

a. Effect of diet treatment, no effect of vitamin treatment, with an interaction b. Effect of diet treatment, no effect of vitamin treatment, with no interaction c. Effect of vitamin treatment, no effect of diet treatment, with an interaction d. Effect of vitamin treatment, no effect of diet treatment, with no interaction Copyright Macmillan Learning. Powered by Cognero.

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Chap 18_3e 11. Adding blocks to a design is usually with the goal of estimating how important the blocks are for influencing the value of the response variable. a. True b. False 12. Adding blocks to a design will always improve the fit of the model to the data. a. True b. False 13. Consider an experiment using birds in which we will use a simple ANCOVA to examine the effects of seed type (low calorie vs. high calorie) and amount of salt eaten (measured by changes in the mass of a salt stick) on feather stiffness. Which of the following is a representation of the model we will use to analyze the data? a. Feather = constant + seed + salt b. Feather = constant + seed + salt + seed*salt c. Salt = constant + seed + feather + seed*feather d. Seed = constant + salt + feather + salt*feather 14. The analysis method called a two-way, fixed-effect ANOVA is used in which of the following study designs? a. Dose-response b. Factorial experiment c. Observational study d. Randomized block 15. When the assumptions of the linear model are met, which of the following is not a property of the residuals in a residual plot? a. They appear to cluster around the value of zero. b. They appear to have a curved pattern. c. They are fairly equally variable above and below zero. d. They are fairly symmetric above and below zero.

16. An ANCOVA analysis typically uses two categorical variables and one numerical one. a. True b. False 17. Closely related species are more similar on average than randomly chosen species. a. True b. False

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Chap 18_3e 18. The interaction plot shown most likely represents which of the following?

a. Effects of diet treatment and an interaction, but no effect of temperature b. Effects of vitamin treatment and an interaction, but no effect of temperature c. Effects of diet and vitamin treatments, and an interaction d. Effects of diet and vitamin treatments, but no interaction 19. Which of the following is not an assumption for analyzing data with linear models? a. For every combination of explanatory variables, the population has a normal distribution. b. For every combination of explanatory variables, the variance of the response variables is equal. c. The sample represents a random sample from the population of explanatory variables. d. The sample represents a random sample from the population of response variables.

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Chap 18_3e 20. The interaction plot shown most likely represents which of the following?

a. Associations with diet and bird age/sex, and an interaction b. Associations with diet and bird age/sex treatment, but no interaction c. An association with diet, but no effect of bird age/sex or any interaction d. An association with fertilizer treatment, but no effect of diet or any interaction 21. Analyses with linear models assume that the measurements of every combination of explanatory variable have a normal distribution in their population. a. True b. False

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Chap 18_3e 22. The interaction plot shown most likely represents which of the following?

a. Associations with diet and bird age/sex, and an interaction b. Associations with diet and bird age/sex treatment, but no interaction c. An association with diet and an interaction, but no effect of bird age/sex d. An association with bird age/sex and an interaction, but no effect of diet 23. Consider an experiment using birds in which we create a full factorial design to examine the effects of seed type (low calorie vs. high calorie) and availability of a salt stick (present vs. absent) on feather stiffness. Which of the following is a representation of the model we will use to analyze the data? a. Feather = seed + salt + seed*error b. Feather = constant + seed + salt + seed*salt c. Seed = salt + feather + salt*feather d. Seed = constant + salt + feather + salt*feather

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Chap 18_3e 24. The interaction plot shown most likely represents which of the following?

a. An association with environment, but no effect of fertilizer treatment or any interaction b. An association with fertilizer treatment, but no association with environment or any interaction c. Associations with environment and fertilizer treatment, and an interaction d. Associations with environment and fertilizer treatment, but no interaction 25. A two-factor ANOVA analysis using a factorial design would typically calculate how many P-values of interest? a. 1 b. 2 c. 3 d. 4

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Chap 18_3e 26. The interaction plot shown most likely represents which of the following?

a. Associations with diet and bird age/sex, and an interaction b. Associations with diet and bird age/sex treatment, but no interaction c. An association with diet, but no effect of bird age/sex or any interaction d. An association with fertilizer treatment, but no effect of diet or any interaction

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Chap 18_3e 27. The interaction plot shown most likely represents which of the following?

a. Effects of diet and vitamin treatments, and an interaction b. Effects of diet and vitamin treatments, but no interaction c. Effect of diet treatment, but no effect of vitamin treatment or any interaction d. Effect of vitamin treatment, but no effect of diet treatment or any interaction

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Chap 18_3e 28. For the figure shown, which of the four plots most likely shows a situation where one factor has a significant effect while the other does not?

a. Plot A b. Plot B c. Plot C d. Plot D 29. If the null hypothesis for a linear regression is true, then the regression line will not fit the data better than a line of constant value. a. True b. False 30. The best definition of a mathematical mode is which of the following? a. A simplified mathematical expression that separates out the true pattern and the bias. b. A simplified mathematical expression that separates out the true pattern and the noise. c. A mathematical representation of the relationship between an explanatory variable and one or more response variables. d. A mathematical representation of the relationship between a response variable and one or more explanatory variables.

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Chap 18_3e 31. For the figure shown, which of the four plots most likely shows a situation where both factors have a significant association with the response variable?

a. Plot A b. Plot B c. Plot C d. Plot D 32. Most ANCOVA analyses do not include a term for the interaction between the categorical variable and the numerical one. a. True b. False 33. Analyses with linear models assume that the variances of values for every combination of explanatory variable are equal. a. True b. False 34. In an interaction plot, the two factors don't interact unless the lines connecting the means of the groups cross. a. True b. False

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Chap 18_3e 35. The interaction plot shown most likely represents which of the following?

a. Associations with environment and fertilizer treatment, and an interaction b. Associations with environment and fertilizer treatment, but no interaction c. An association with environment, but no effect of fertilizer treatment or any interaction d. An association with fertilizer treatment, but no effect of environment or any interaction 36. In a randomized block design with each treatment replicated once per block, the full linear model of the data can be visualized via which of the following equations? a. RESPONSE = CONSTANT + BLOCK b. RESPONSE = CONSTANT + TREATMENT. c. RESPONSE = CONSTANT + BLOCK + TREATMENT d. RESPONSE = CONSTANT + BLOCK + TREATMENT + INTERACTION 37. The calculation of the F-value for a possible explanatory variable measures the improvement in the fit of a linear model when the variable is included versus when it is not. a. True b. False 38. Data points for various species are generally independent of one another. a. True b. False Copyright Macmillan Learning. Powered by Cognero.

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Chap 18_3e 39. In the preliminary stages of an ANCOVA analysis, if the test for the presence of an interaction returns a Pvalue larger than 0.05, what does this mean? a. The slopes of the regression lines are not significantly different for the groups of the categorical variable. b. The slopes of the regression lines are significantly different for some of the groups of the categorical variable. c. The Y-intercepts of the regression lines are not significantly different for the groups of the categorical variable. d. The Y-intercepts of the regression lines are significantly different for some of the groups of the categorical variable.

40. The interaction plot shown most likely represents which of the following?

a. Associations with environment and fertilizer treatment, and an interaction b. Associations with environment and fertilizer treatment, but no interaction c. An association with environment and an interaction, but no association with fertilizer treatment d. An association with fertilizer treatment and an interaction, but no association with environment

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Chap 18_3e 41. Draw a flowchart showing the decisions you make leading to the technique you will use when examining the relationship of two explanatory variables (one categorical and one numerical) on a single response variable.

42. Imagine a factorial ANOVA design experiment with two categorical variables that have three values each.

Sketch a plot showing data that would show a pattern consistent with the F-tests for both of the categorical variables being significant. Be sure to use three visually distinct symbols for the data values in the three categories.

43. Imagine an ANCOVA with one numerical explanatory variable and three values for a categorical variable.

Sketch a plot showing data that would show a pattern consistent with an F-test of the numerical variable being significant, but the F-test of the categorical variable is not. Be sure to use three visually distinct symbols for the data values in the three categories.

44. Imagine a factorial ANOVA design experiment with two categorical variables that have three values each.

Sketch a plot showing data that would show a pattern consistent with an F-test of one of the categorical variables being significant, but the F-test of the second categorical variable is not. Be sure to use three visually distinct symbols for the data values in the three categories.

45. Imagine an ANCOVA with one numerical explanatory variable and three values for a categorical variable.

Sketch a plot showing data that would show a pattern consistent with an F-test of the categorical variable being significant, but the F-test of the numerical variable is not. Be sure to use three visually distinct symbols for the data values in the three categories.

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Chap 18_3e 46. Imagine we wish to perform an ANCOVA on a data set with one numerical explanatory variable and three values for a categorical variable. Sketch a plot with data showing a pattern that would not satisfy the assumptions required for the ANCOVA and therefore require us to transform the data or use another technique to examine the data.

47. Compare and contrast ANOVAs that use blocking and factorial designs. Specifically, explain the similar values calculated and the difference in our focus and the goal of these values.

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Chap 18_3e Answer Key 1. a 2. b 3. c 4. b 5. a 6. d 7. b 8. b 9. a 10. a 11. b 12. a 13. a 14. b 15. b 16. b 17. a 18. c 19. d 20. a 21. a 22. d 23. b 24. d 25. c 26. b Copyright Macmillan Learning. Powered by Cognero.

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Chap 18_3e 27. b 28. d 29. b 30. d 31. a 32. a 33. a 34. b 35. a 36. c 37. a 38. b 39. a 40. d 41.

42.

43.

44.

45.

46.

47.

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Chap 19_3e Indicate the answer choice that best completes the statement or answers the question.

1. To generate a bootstrap standard error of an estimate, there are four steps. Which of these is not one of them? a. First, obtain a random sample from the original data using a computer. b. Second, using the values in the first step, calculate the variance of the estimate. c. Third, perform the first and second steps over and over again. d. Fourth, calculate the standard deviation of all the values from step three; this is the bootstrap standard error.

2. When we do a simulation, we typically sample from the population many times and calculate the test statistic each time. a. True b. False 3. To generate a bootstrap standard error of an estimate, there are four steps. Which of these is not one of them? a. First, obtain a random sample from the original data using a computer. b. Second, using the values in the first step, calculate the estimate. c. Third, perform the first two steps over and over again until the cumulative value no longer changes. d. Fourth, calculate the standard deviation of all the values from step three; this is the bootstrap standard error.

4. The bootstrap standard error tends to be smaller than the standard deviation. a. True b. False 5. When doing a simulation study, if any of our test statistic values are more extreme than the original value, then we would not reject the null hypothesis. a. True b. False 6. Bootstrapping involves sampling the original population many times to create new data sets that are analyzed. a. True b. False 7. The bootstrapping procedure is used to approximate which of the following distributions based on the data in the sample? a. Normal distribution of the mean b. Poisson distribution of the median c. Sampling distribution of an estimate d. Distribution of values for a statistical test

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Chap 19_3e 8. What is the common situation in which we would use simulation methods to analyze our data? a. For normally distributed data values b. For small sample sizes c. When the data violates the assumptions of all the standard tests d. When the estimated population parameter differs greatly from the sample statistic 9. Bootstrapping involves sampling the original data set without replacement to create new data sets that are analyzed. a. True b. False 10. Simulation involves sampling the original data set with replacement to create new data sets that are analyzed. a. True b. False 11. Bootstrapping is most commonly used to estimate the mean of a population. a. True b. False 12. The first step in a simulation analysis is to create a theoretical population with values matching a null hypothesis. a. True b. False 13. To generate a bootstrap standard error of an estimate, there are four steps. Which of these is not one of them? a. First, use a computer to randomly sample the original data, without replacement, to make a new data set. b. Second, calculate the estimate using the sampled values in the first step. c. Third, repeat the first two steps a large number of times. d. Fourth, the bootstrap standard error is the standard deviation of the set of values from step three.

14. In general, simulations are used to create an approximation of which of the following? a. The distribution of parameter values when the null hypothesis is false b. The distribution of parameter values when the null hypothesis is true c. The distribution of test statistic values when the null hypothesis is false d. The distribution of test statistic values when the null hypothesis is true 15. Bootstrapping can be used to calculate the standard error of almost any estimate. a. True b. False

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Chap 19_3e 16. The null distribution is best described as which of the following? a. The test statistic's mean value b. The test statistic's distribution c. The test statistic's sum of squares d. The test statistic's variance 17. When doing a simulation, after you assume the null hypothesis is true, what is the key value that you calculate over and over? a. The probability of getting the original sample statistic b. The probability of getting the original test statistic c. The value of the sample statistic d. The value of the test statistic 18. Bootstrapping involves sampling the original data set without replacement to create new data sets that are analyzed under which conditions? a. When the mean of the estimated value is unknown b. When the sampling distribution of the estimated value is unknown c. When the standard deviation of the estimated value is unknown d. When the variance of the estimated value is unknown 19. When performing a bootstrap, some values from the original data set may get chosen far more than others in a replicate. a. True b. False 20. When doing a simulation study, we calculate a test statistic over and over to create a distribution of values for comparison to our original test statistic value. a. True b. False 21. When we do a simulation, the distribution of test statistic values is used to calculate a P-value for our original value. a. True b. False 22. When deciding if we can use the bootstrapping procedure, which of the following is a requirement of our data? a. The sample distribution must be normal b. The sample distribution must be symmetric c. The sample must have a large sample size d. The sample must have a small sample bias Copyright Macmillan Learning. Powered by Cognero.

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Chap 19_3e 23. When doing a bootstrap, if we use a sample size that is too small, how does this bias our results? a. The confidence intervals are too narrow and the standard errors are too large. b. The confidence intervals are too narrow and the standard errors are too small. c. The confidence intervals are too wide and the standard errors are too large. d. The confidence intervals are too wide and the standard errors are too small.

24. The bootstrap standard error is the standard deviation of the bootstrap replicates divided by the square root of the number of replicates. a. True b. False

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Chap 19_3e 25. Consider the two data sets shown. Imagine that we are interested if the mean of the second population is larger than the mean of the first population and we wish to test this using the bootstrap procedure. We will use a one-tailed approach with the alternative hypothesis being a situation in which the mean of the second population exceeds the first.

a. Calculate the difference in means between the two data sets. Is this consistent with the null hypothesis or the alternative hypothesis? b. Perform a single bootstrap and calculate the difference between the means of the two groups. Use the first set of digits from π below as a method to generate the appropriate random numbers for each group (treat zeroes as a 10) and then sequentially choose the appropriate number of bootstrap values from each sample, starting with the first sample. Clearly show which values you use and how (i.e., show your work). c. Is the difference in means from part (b) consistent with the null or alternative hypothesis? d. What would our conclusion be if we performed 99 more replicates and they showed the same general pattern (i.e., the sign of the difference) as in part (c)? π = 31415926535897932384626433

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Chap 19_3e 26. Consider the two data sets shown. Imagine that we are interested if the mean of the second population is larger than the mean of the first population and we wish to test this using the bootstrap procedure. We will use a one-tailed approach with the alternative hypothesis being a situation in which the mean of the second population exceeds the first.

a. Calculate the difference in means between the two data sets. Is this consistent with the null hypothesis or the alternative hypothesis? b. Perform a single bootstrap and calculate the difference between the means of the two groups. Use the first set of digits from π below as a method to generate the appropriate random numbers for each group (treat zeroes as a 10) and then sequentially choose the appropriate number of bootstrap values from each sample, starting with the first sample. Clearly show which values you use and how (i.e., show your work). c. Is the difference in means from part (b) consistent with the null or alternative hypothesis? d. What would our conclusion be if we performed 99 more replicates and they showed the same general pattern (i.e., the sign of the difference) as in part (c)? π = 31415926535897932384626433

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Chap 19_3e Answer Key 1. b 2. b 3. c 4. a 5. b 6. b 7. c 8. c 9. b 10. b 11. b 12. a 13. a 14. d 15. a 16. b 17. d 18. b 19. a 20. a 21. a 22. c 23. b 24. b 25.

26.

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Chap 20_3e Indicate the answer choice that best completes the statement or answers the question.

1. Likelihood measures the probability that the null hypothesis is true. a. True b. False 2. Which of the following is the correct test statistic for a likelihood ratio test? a. b. c. d.

3. The bias in maximum likelihood estimation is usually small compared to the magnitude of the confidence interval. a. True b. False 4. When we use the maximum likelihood method in complicated scenarios, the likelihood value corresponding to the maximum likelihood estimate is often quite small. a. True b. False 5. Which of the following equations correctly shows the relationship between likelihoods and probabilities? a. pr [ data | parameter = value ] = L [ data | value ] b. pr [ data | parameter = value ] = L [ value | data ] c. pr [ parameter = value | data ] = L [ data | value ] d. pr [ parameter = value | data ] = L [ value | data ] 6. When using maximum likelihood to determine the locations of genes that influence traits, the ratio of two different probabilities was calculated for each marker location. a. True b. False 7. If the null hypothesis is true, then log-likelihood ratio values based on large sample sizes will be chi-squared distributed. a. True b. False

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Chap 20_3e 8. The maximum likelihood estimate (MLE) can be determined by doing which of the following? a. Across the whole range of possible parameter values, we calculate the likelihood and the MLE is the largest probability value. b. Across the whole range of possible parameter values, we calculate the likelihood and the MLE is the smallest probability value. c. Across the whole range of possible parameter values, we calculate the log-likelihood and the MLE is the parameter that gives the largest value. d. Across the whole range of possible parameter values, we calculate the log-likelihood and the MLE is the parameter that gives the smallest value.

9. When using likelihood to find the locations of genes that cause disease, which best describes the process? a. The likelihood that a gene located at each marker site causes the disease was compared to 0.05 b. The likelihood that a gene located at each marker site causes the disease was compared to the null hypothesis. c. The likelihood that a gene located at each marker site causes the disease was compared to the likelihood that a gene located at each marker site is unrelated to the disease. d. The likelihood that a gene located at each marker site causes the disease was compared to the likelihood that a gene located at each marker site prevents the disease.

10. For a likelihood ratio test in which the null hypothesis requires the estimation of four parameters and the alternative requires the estimation of one parameter, the degrees of freedom will be which of the following? a. 1 b. 2 c. 3 d. 4 11. To determine the maximum likelihood estimate, we can calculate the likelihood for a range of parameter values and choose the parameter that gives the smallest value. a. True b. False 12. Which of the following best describes the maximum likelihood estimate? a. The likelihood value with the highest probability b. The likelihood value with the highest value c. The parameter closest to the sample likelihood d. The parameter that results in the highest likelihood

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Chap 20_3e 13. When comparing alternative phylogenies to decide on the most probable one, which best describes the process? a. The likelihood of each phylogeny, based on the gene sequence data, is calculated and the one with the highest likelihood is deemed most likely. b. The likelihood of each phylogeny, based on the gene sequence data, is calculated and the one with the lowest likelihood is deemed most likely. c. The likelihood of each phylogeny, based on the gene sequence data, is calculated and the one with P < 0.05 is deemed most likely. d. The likelihood of each phylogeny, based on the gene sequence data, is calculated and the one with P > 0.05 is deemed most likely.

14. To find the 95% confidence interval for the maximum likelihood estimate (MLE), we can do which of the following? a. Finding the range of parameter values with log-likelihood estimates within 0.05 of the MLE b. Finding the range of parameter values with log-likelihood estimates within 0.95 of the MLE c. Finding the range of parameter values with log-likelihood estimates within 1.92 of the of the MLE d. Finding the range of parameter values with log-likelihood estimates within 1.96 of the log of the MLE 15. The maximum likelihood estimate will always give the highest log-likelihood value. a. True b. False 16. Larger sample sizes reduce the bias often seen in maximum likelihood estimation. a. True b. False 17. The maximum likelihood estimate is the parameter value that results in the highest likelihood value. a. True b. False 18. Likelihood measures which of the following? a. How probable it is that the null hypothesis is false b. How probable it is that the parameter equals a certain value c. The probability of obtaining the sample values if the alternative hypothesis is true d. The probability of obtaining the sample values if the parameter equals a certain value 19. The maximum likelihood approach is very powerful for small and moderate data sets, but it is very limited in the types of scenario it can be used for. a. True b. False

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Chap 20_3e 20. In the log-likelihood figure shown, which of the following ranges best matches the 95% confidence interval for the values on the X-axis?

a. 25 to 70 b. 30 to 65 c. 35 to 60 d. 40 to 55

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Chap 20_3e 21. In the log-likelihood figure shown, which of the following ranges best matches the 95% confidence interval for the values on the X-axis?

a. 58 to 78 b. 60 to 76 c. 62 to 74 d. 64 to 72 22. Which of the following is the correct test statistic for a likelihood ratio test? a. b. c. d.

23. The maximum likelihood estimate of a parameter is the value that results in the highest log-likelihood, given the data. a. True b. False

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Chap 20_3e 24. The maximum likelihood estimate is the highest probability value we calculate when calculating probabilities of occurrence in our data set. a. True b. False 25. Likelihood measures the probability we would get the data we did if a hypothesis is true. a. True b. False 26. When using maximum likelihood to choose the most probably phylogeny, the probabilities of getting the data if each phylogeny is true were compared. a. True b. False 27. A good rule of thumb for the 95% confidence interval for the maximum likelihood estimate is the range of values that lie within 1.92 log-likelihood values of the maximum likelihood estimate. a. True b. False 28. When doing a log-likelihood ratio test, the degrees of freedom for the test statistic is the sum of the number of parameters estimated in each hypothesis minus two. a. True b. False

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Chap 20_3e 29. Consider a situation in which we plot the log-likelihood values for a range of parameter values as shown in the figure. What is the MLE and 95% confidence interval of the MLE based on this figure?

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Chap 20_3e 30. Consider a situation in which we plot the log-likelihood values for a range of parameter values as shown in the figure. What is the MLE and 95% confidence interval of the MLE based on this figure?

31. Describe how and why we can use likelihood to conclude that an extremely unlikely situation is probably true.

32. Describe the logic of the log-likelihood ratio test. What does it compare and what conclusions does it make?

33. In your own words describe what likelihood is and what a maximum likelihood estimate is for a data set.

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Chap 20_3e

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Chap 20_3e Answer Key 1. b 2. d 3. a 4. a 5. b 6. a 7. a 8. c 9. c 10. c 11. b 12. d 13. a 14. c 15. a 16. a 17. a 18. d 19. b 20. b 21. c 22. d 23. a 24. b 25. a 26. a Copyright Macmillan Learning. Powered by Cognero.

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Chap 20_3e 27. a 28. b 29.

30.

31.

32.

33.

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Chap 21_3e Indicate the answer choice that best completes the statement or answers the question.

1. A hazard ratio can be less than 1.0. a. True b. False 2. Survival analysis allows _____ data to be included when estimating and testing times until various events. a. incomplete b. non-normal c. outlier d. variable 3. Data from individuals who leave the study before it ends are said to "right censored." a. True b. False Consider the data table showing epidemiology data for 25 individuals with a disease and 25 healthy comparison individuals. Their deaths are recorded over a period of 12 months.

4. What proportion of individuals died during the interval between 6 and 8 months after starting the trial? a. 0.128 b. 0.152 c. 0.170 d. 0.197

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Chap 21_3e 5. The term for the instantaneous rate of death of subjects who have survived up to a certain point is called which of the following? a. The hazard rate b. The mortality rate c. The risk rate d. The survival rate Consider the data table showing patients in a trial in which 30 are given a placebo and 20 are given an experimental drug and the deaths are recorded over a period of 24 months.

6. What are the total number of expected deaths for the control and drug treatment groups respectively? a. 19 and 7 b. 12.50 and 13.50 c. 13.50 and 12.50 d. 14.50 and 11.50 7. A key assumption of the Kaplan-Meier method for calculating survival curves is which of the following? a. All individuals eventually experience the event of interest. b. All subjects, including censored ones, have the same probabilities of experiencing events in each time period. c. Fewer than 5% of individuals are censored. d. Probabilities of experiencing events are constant across all time periods.

8. The value that measures the hazard rate in a group, relative to that in the other group at a particular time, is called which of the following? a. The hazard fraction b. The hazard ratio c. The hazard proportion d. The hazard value Copyright Macmillan Learning. Powered by Cognero.

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Chap 21_3e Consider the data table showing epidemiology data for 25 individuals with a disease and 25 healthy comparison individuals. Their deaths are recorded over a period of 12 months.

9. One individual dropped out of the study. Which of the following is a possible month during which they withdrew? a. Month 3 b. Month 5 c. Month 7 d. Month 9

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Chap 21_3e Consider the data table showing patients in a trial in which 30 are given a placebo and 20 are given an experimental drug and the deaths are recorded over a period of 24 months.

10. What is the standard error of the natural log of the hazard ratio for the control group relative to the drug treatment group? a. 0.196 b. 0.395 c. 0.442 d. 0.503 11. What proportion of patients died during the interval between 6 and 9 months after starting the trial? a. 0.080 b. 0.142 c. 0.114 d. 0.161 12. The 95% confidence intervals in a survival curve become wider for later time periods because there are fewer individual remaining and the estimate is therefore less precise. a. True b. False 13. Survival curves displays what value on the Y-axis? a. The probability of an individual experiencing an event in that time period b. The probability of an individual surviving to the next time period c. The proportion of individuals remaining from the initial sample d. The proportion of individuals that have not experienced an event

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Chap 21_3e 14. The median survival time cannot be calculated for studies in which the survival proportion fails to reach 0.050. a. True b. False Consider the data table showing epidemiology data for 25 individuals with a disease and 25 healthy comparison individuals. Their deaths are recorded over a period of 12 months.

15. What is the hazard ratio for the disease group relative to the healthy group? a. 0.373. b. 0.594. c. 1.683. d. 2.683.

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Chap 21_3e Consider the data table showing patients in a trial in which 30 are given a placebo and 20 are given an experimental drug and the deaths are recorded over a period of 24 months.

16. One patient dropped out of the study. Which of the following is a possible month during which they withdrew? a. Month 5 b. Month 8 c. Month 11 d. Month 23 17. How many deaths were expected for the control group in the interval between 9 and 12 months after starting the trial? a. 2.171 b. 2.419 c. 2.581 d. 3.349

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Chap 21_3e Consider the data table showing epidemiology data for 25 individuals with a disease and 25 healthy comparison individuals. Their deaths are recorded over a period of 12 months.

18. What are the total number of expected deaths for the diseased and healthy groups, respectively? a. 24 and 10 b. 13.95 and 11.05 c. 14.95 and 10.05 d. 15.95 and 9.05 19. What is the χ2 value we obtain from a χ2 test of the hazard ratio for the disease group relative to the healthy group? a. 3.850 b. 5.526 c. 5.743 d. 7.134 20. How many deaths were expected for the disease group in the interval between 4 and 6 months after starting the trial? a. 2.692 b. 3.030 c. 3.471 d. 4.085.

21. Censored data combine individuals who experience the event and those who leave the study before it ends. a. True b. False

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Chap 21_3e 22. If D1 and D2 are the observed deaths in the two groups while E1 and E2 are the expected number of deaths for the two groups, which of the following is the correct equation for the hazard ratio? a. HR = ( D1/D2 ) / ( E1/E2 ) b. HR = ( D1/D2 ) / ( E2/E1 ) c. HR = ( D2/D1 ) / ( E1/E2 ) d. HR = ( D2/D1 ) / ( E2/E1 ) 23. The Kaplan-Meier method assumes the probabilities of survival for censored subjects are the same as those who remain in the study. a. True b. False Consider the data table showing epidemiology data for 25 individuals with a disease and 25 healthy comparison individuals. Their deaths are recorded over a period of 12 months.

24. What is the 95% confidence interval of the hazard ratio for the disease group relative to the healthy group? a. From 0.169 to 0.821 b. From 0.212 to 1.110 c. From 0.256 to 1.377 d. From 0.270 to 1.308 25. Based on the χ2 value from a test of the hazard ratio for the disease group relative to the healthy group, what is our conclusion? a. P < 0.05, the survival curves are the same. b. P < 0.05, the survival curves differ from each other. c. P > 0.05, the survival curves are the same. d. P > 0.05, the survival curves differ from each other.

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Chap 21_3e 26. What is the standard error of the natural log of the hazard ratio for the disease group relative to the healthy group? a. 0.200 b. 0.302 c. 0.403 d. 0.429 27. The assumption of proportional hazards when using the Kaplan-Meier method states which of the following? a. The hazard ratio between the two groups must be normally distributed. b. The hazard ratio between the two groups stays constant over time. c. The hazard ratio is in direct proportion to the sample sizes in each group. d. The hazard ratio is the same as the overall number of deaths in each group.

28. To test the proportional hazards assumption, we plot the logs of the proportions surviving in each group over time, and if the lines are parallel, then the assumption is met. a. True b. False Consider the data table showing patients in a trial in which 30 are given a placebo and 20 are given an experimental drug and the deaths are recorded over a period of 24 months.

29. What is the hazard ratio for the control group relative to the drug treatment group? a. 2.152 b. 2.768 c. 3.424 d. 3.783

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Chap 21_3e 30. Based on the χ2 value from a test of the hazard ratio for the control group relative to the drug treatment group, what is our conclusion? a. P < 0.05, the survival curves are the same. b. P < 0.05, the survival curves differ from each other. c. P > 0.05, the survival curves are the same. d. P > 0.05, the survival curves differ from each other.

31. What is the χ2 value we obtain from a χ2 test of the hazard ratio for the control group relative to the drug treatment group? a. 3.153 b. 5.090 c. 6.145 d. 8.202 32. The proportional hazards assumption states that the probabilities of survival for individuals in each group are proportional to one another. a. True b. False Consider the data table showing patients in a trial in which 30 are given a placebo and 20 are given an experimental drug and the deaths are recorded over a period of 24 months.

33. What is the 95% confidence interval of the hazard ratio for the control group relative to the drug treatment group? a. From 0.905 to 5.118 b. From 0.992 to 4.665 c. From 1.439 to 8.145 d. From 1.579 to 7.425

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Chap 21_3e 34. Consider the data table showing patients in a trial in which 40 are given a placebo and 40 are given an experimental drug and the deaths are recorded over a period of 24 months.

a. Calculate the hazard ratio and 95% confidence interval for the hazard ratio. b. Perform a χ2 test on the hazard ratio. Present the χ2 value, a range for the P-value it corresponds to, and the interpretation of your test.

35. Describe a real-world situation in which a survival analysis would not be feasible because the proportional hazards assumption is violated.

36. Draw a hypothetical survival curve and illustrate how you would find the median time to survival using this figure.

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Chap 21_3e 37. Consider the data table showing epidemiology data for 36 individuals with a disease and 38 healthy comparison individuals. Their deaths are recorded over a period of 16 months.

a. Calculate the hazard ratio and 95% confidence interval for the hazard ratio. b. Perform a χ2 test on the hazard ratio. Present the χ2 value, a range for the P-value it corresponds to, and the interpretation of your test.

38. Explain conceptually why we can use censored data in survival analyses, but we are unable to use censored data in other techniques.

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Chap 21_3e Answer Key 1. a 2. a 3. a 4. b 5. a 6. d 7. b 8. b 9. c 10. b 11. c 12. a 13. d 14. a 15. a 16. a 17. c 18. b 19. c 20. a 21. b 22. a 23. a 24. a 25. b 26. c Copyright Macmillan Learning. Powered by Cognero.

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Chap 21_3e 27. b 28. a 29. a 30. c 31. a 32. b 33. b 34.

35.

36.

37.

38.

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