TEST BANK FOR Analyzing Data and Making Decisions Statistics for Business Microsoft Excel 2010 Updat

Analyzing Data and Making Decisions Statistics for Business Microsoft Excel 2010 Updated 2e Judith Skuce (Test Bank All Chapters, 100% Original Verified, A+ Grade) Answers At The End Of Each Chapter Chapter 1 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1) In a city of 50,000 households, 200 were randomly sampled and the heating bill for January was recorded. The standard deviation of these 100 values was then computed. The standard deviation is a: A) parameter B) interquartile range C) range D) statistic

1)

2) A scientist is testing the hardness of a new type of ceramic and controls the contents of the mixture as well as the oven temperature. This is an example of: A) a longitudinal study B) an experimental study C) an observational study D) a cross-sectional study

2)

3) A scientific team collects water samples from a fresh-water lake to measure levels of a certain pollutant. For the team, this constitutes: A) tertiary data B) primary data C) population data D) secondary data

3)

4) You have a population of 500 numbers from which you wish to randomly sample 50 of them. The best approach is: A) sort the data from lowest to highest and pick the first 50 B) add the digits in each number, sort by the sum and pick the first 50 C) put the data in a spreadsheet column, generate random numbers in the next column, sort by the random numbers and pick the first 50 D) sort by the number of threes in each number and pick the first 50

4)

5) A polling firm conducts a survey for a political party to determine the level of support for the party's policies. If a third party then observes the poll results, for this third party this constitutes: A) population data B) tertiary data C) secondary data D) primary data

5)

6) A survey has a convoluted question in which the respondent might answer incorrectly in spite of not clearly understanding the question. This is an example of: A) coverage error B) sampling error C) processing error D) response error

6)

7) A secretary does data entry for a survey conducted by paper. If a value is entered incorrectly, this is an example of: A) sampling error B) nonresponse error C) coverage error D) processing error

7)

8) You interview people coming out of a store to see how much they spent. The data type is: A) secondary B) six-sigma C) primary D) tertiary

8)

1

9) Restaurants have survey cards that people can fill out. The people who fill out the cards are an example of: A) self-selected sample B) stratified sample C) convenience sample D) simple random sample

9)

10) You ask all the residents of an apartment building how many times a month they eat out and then compute the average for all the residents. This average is a: A) median B) parameter C) statistic D) mode

10)

11) You have a list of people to call for a survey. However, the list is 5 years old. This is an example of: A) coverage error B) processing error C) nonresponse error D) sampling error

11)

12) A class of 60 students writes a test out of which you randomly sample 10. The difference between the average of this sample and that of the entire class is an example of: A) sampling error B) processing error C) nonresponse error D) coverage error

12)

13) In a city of 100,000 people, you survey 100 of them to ask how much they spend per month on gasoline. You then compute the average for this sample of 100 people This average is a: A) statistic B) mode C) parameter D) median

13)

14) A computer was used to calculate certain statistics from data. However, one of the formulas was set up incorrectly. This is an example of: A) sampling error B) processing error C) estimation error D) response error

14)

15) You mail a survey to 500 people, but receive back only 67. This is an example of: A) processing error B) nonresponse error C) coverage error D) sampling error

15)

16) You consult a Stats Canada publication to find out the populations of a number of cities. The data type is: A) tertiary B) six-sigma C) primary D) secondary

16)

17) While standing outside a store, you record the gender of a person coming out of the store. This is an example of: A) a longitudinal study B) an observational study C) a cross-sectional study D) an experimental study

17)

18) A poll was conducted of executives in a certain industry. However, not all of them could be contacted in the time frame of the survey. This is an example of: A) nonresponse error B) estimation error C) processing error D) sampling error

18)

19) Polling firms can sample telephone numbers for any city in Canada from a CD. If a polling firm samples 1,000 numbers for a city of 500,000 from a CD with no regard for what part of the city the number is from, this is an example of: A) stratified sample B) convenience sample C) self-selected sample D) simple random sample

19)

2

20) A store, upon opening, handed out a survey to the first 10 customers that came in. This is an example of: A) convenience sample B) self-selected sample C) cluster sample D) simple random sample

20)

21) In a survey of 1,000 Canadian households, a polling firm asked the respondents how much they spend per month on entertainment. The firm then calculated the standard deviation of the 1,000 values. The difference between the standard deviation of this sample and that of the entire population is an example of: A) coverage error B) sampling error C) processing error D) nonresponse error

21)

22) You post a poll on a website in which a maximum of 100 respondents is allowed. This is an example of: A) cluster sample B) self-selected sample C) simple random sample D) stratified sample

22)

23) A researcher in a grocery store takes note of whether a customer goes to a regular checkout or the express checkout. This is an example of: A) an experimental study B) a longitudinal study C) an observational study D) a cross-sectional study

23)

24) In a factory with 100 workers, management computed the total number of sick days in the previous year for each worker. They then computed the standard deviation of the number of sick days for all the workers. The standard deviation is a: A) range B) interquartile range C) parameter D) statistic

24)

25) A researcher is comparing twins on the length of time to complete a test. The researcher designed the test and uses an accurate watch to time the results. This is an example of: A) an observational study B) a cross-sectional study C) an experimental study D) a longitudinal study

25)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

26) A person is doing data entry from a paper survey. If the person makes a mistake entering a value, in a word, what type of error is this?

26)

27) You are sitting outside a store, counting how many people per hour enter it. In a word, what type of study is this?

27)

28) You conduct a one-question survey with the first 5 students entering a classroom. In a word, what type of sample is this?

28)

29) You are trying to phone IT executives to conduct a survey. However, most of them have voice mail set up to capture incoming calls; consequently you never reach them. In a word, what type of error is this?

29)

3

30) A scientist designs a study to measure the amount of impurities removed from oil samples, carefully controlling the factors which may impact the results. In a word, what type of study is this?

30)

31) You conduct a door-to-door survey to see if the residents own or rent. In a word, what type of data is this?

31)

32) An interviewer inflects his/her voice in such a way that it may influence the answer given by the respondent. In a word, what type of error is this?

32)

33) In a company with 12 employees, you ask all 12 of them how many hours a week they work. If you compute the average of all 12 data points, in a word, what is this an example of?

33)

34) In a city of 500,000 people, 500 were surveyed to determine how many times per month they take public transit. If the mean of this sample is computed, in a word, what type of error is the difference between this mean and the population mean?

34)

35) In a company with 500 employees, you sample 50 and examine how many sick days they took last year. If you compute the standard deviation of these 50 data points, in a word, what is this an example of?

35)

36) You read the results of a research study in a journal. The data is listed in an appendix. If you use this data, what type of data is it, in a word?

36)

37) You have a list of people to call for a survey but you are not sure how old the list is. If you call a number of this list and find it is out of service, in a word, what type of error is this?

37)

38) This Section Intentionally Left Blank

38)

39) You examine the results of a survey conducted in 1999 asking companies which of them were Y2K ready. In a word, what type of data is this?

39)

40) You conduct an experiment in which you measure the amount of methane produced by a certain chemical reaction. In a word, what type of data is this?

40)

41) In a survey, people are willing to answer the main questions, but reluctant to answer demographic questions such as income. If a person does not answer the income question, in a word, what type of error is this?

41)

TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.

42) A question in a survey is phrased in such a way so as to elicit a certain response. This is an example of response error.

42)

43) A frame is essentially a database of a population.

43)

44) In 1995, a group of researchers interviewed people to find out which of them used email. If you look up the results of this research, this would be an example of secondary data.

44)

4

45) In a simple random sample of students at a university, some students are more likely to be chosen than others because some faculties are larger than others.

45)

46) A spreadsheet is used to calculate a certain formula. If the formula is incorrect, this is an example of a processing error.

46)

47) A class of 50 students wrote a test. Afterward, the teacher computed the standard deviation for all 50 students. This standard deviation is a parameter.

47)

48) A newspaper put a poll on its website and then published the results. The people who did the poll is an example of a self-selected sample.

48)

49) A mall conducted a survey with the first 10 people who walked through the door. Since we don't know who would come through the door, this is an example of a simple random sample.

49)

50) If you conduct a survey to determine the average amount per month that companies spend on office supplies, the difference between the mean calculated from the survey and the population mean is known as sampling error.

50)

51) A city examined each household in the city to determine the average number of people per household. This average is a statistic.

51)

52) Descriptive statistics are used to summarize raw data.

52)

53) A market research firm will call potential respondents up to 6 times in an attempt to reach them before giving up. If these respondents are not reached, this is an example of response error.

53)

54) A scientist sets up an experiment to measure the boiling point of a certain liquid under various barometric pressures. This is an example of an observational study.

54)

55) A company sets up 2 displays in a store of the same product to see if women are more likely to stop at one display than the other. This is an example of an experimental study.

55)

56) This is an appropriate statement to put in a report aimed at a non-technical audience: We reject the null hypothesis if the test statistic is greater than 1.645.

56)

57) A survey of 1,000 people in a province was conducted to see which of them would vote for a certain party in the next election. The percentage of these people who would do so is a statistic.

57)

58) You are calling people for a survey using a frame purchased from a sampling firm. However, some listings occur more than once in the frame. This would be an example of coverage error.

58)

59) You survey a group of people to find out how far they drive to work. This is an example of primary data.

59)

60) A researcher mailed out a consumer survey, but not everyone replied. This is an example of sampling error.

60)

5

61) You survey a group of people to find out whether or not they recycle at least once a month. This is an example of secondary data.

6

61)

Answer Key Testname: CHAPTER 1 1) D 2) B 3) B 4) C 5) C 6) D 7) D 8) C 9) A 10) B 11) A 12) A 13) A 14) C 15) B 16) D 17) B 18) A 19) D 20) A 21) B 22) B 23) C 24) C 25) C 26) processing 27) observational 28) convenience 29) nonresponse 30) experimental 31) primary 32) response 33) parameter 34) sampling 35) statistic 36) secondary 37) coverage 38) 39) secondary 40) primary 41) response 42) TRUE 43) TRUE 44) TRUE 45) FALSE 46) FALSE 47) TRUE 48) TRUE 49) FALSE 50) TRUE 7

Answer Key Testname: CHAPTER 1 51) FALSE 52) TRUE 53) FALSE 54) FALSE 55) FALSE 56) FALSE 57) TRUE 58) TRUE 59) TRUE 60) FALSE 61) FALSE

8

Chapter 2 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1) A frequency table has the following classes: 24 to under 36, 36 to under 48, 48 to under 60, etc. The class width is: A) 12 B) 11.99 C) 12.01 D) 24

1)

2) The following table summarizes respondents' agreement with a certain statement: Strongly disagree Somewhat disagree Somewhat agree Strongly agree 132 264 302 169 In creating a bar chart, the appropriate starting point for the y-axis is: A) 130 B) 100 C) 0 D) 50

2)

3) The number of times per week a person eats out can be categorized as: A) nominal data B) discrete data C) continuous data D) ordinal data

3)

4) The following frequency table is provided to explain the number of home sales in the West Side of Vancouver by price category:, and the number of unit sold: Class { price range] Frequency [# of homes sold] 250-279.9 162 280-309.9 128 310-349.9 96 350-389.9 66 390-469.9 43 470-549.9 11

4)

Compute the relative frequency of [470-549.9] class A) 162/506 B) 11/506

C) 43/506

5) You are given the following frequency table: Class Frequency 0 to under 5 2 5 to under 10 8 10 to under 15 6 15 to under 20 9 The percentage of values that are less than 10 is: A) 40% B) 32%

D) 66/506 5)

C) 25%

D) 44%

6) A university professors lists a number of high income earning companies on the NASDAQ Stock Exchange, by the name of the company. This is an example of: A) ordinal scale B) nominal scale C) interval scale D) quantitative variable

1

6)

7) The following table summarizes annual charitable contributions: 0 to under $20 5% $20 to under $40 16% $40 to under $60 79% The data may be characterized as: A) continuous data B) ordinal data C) discrete data D) nominal data

7)

8) A scatterplot's origin is at (100,50). An appropriate lowest value for the x-axis is: A) 324 B) 205 C) 105 D) 184

8)

9) A pie chart has the following labels: Poor 12%, Average 54%, Good 25%, Excellent 9%. If the pie chart is based on a survey of 800 people, how many chose good or excellent?

A) 280 B) 264 C) 256 D) 272

9)

10) The following frequency table is provided to explain the number of home sales in the West Side of Vancouver by price category:, and the number of unit sold: Class { price range] Frequency [# of homes sold] 250-279.9 162 280-309.9 128 310-349.9 96 350-389.9 66 390-469.9 43 470-549.9 11

10)

What is the cumulative frequency of [390-469.9] class: A) 506 B) 495 C) 452

11) The data from a sample is provided: Class Frequency 10-24 10 25-49 30 50-74 50 75-99 40 100-114 20 115-124 10 What is the lower limit of the third class?

A) 100 B) 50

D) 162 11)

C) 10

D) 25

12) You are creating a frequency table in which the smallest data value is $2.36 and the largest is $114.62. If you are using a class width of $25, the number of classes in the table is: A) 4 B) 7 C) 6 D) 5

12)

13) A company had a table of its gross annual income (thousands) by year: Year 2000 2001 2002 2003 2004 Income 13.2 25.4 20.6 29.6 34.7 If you wished to examine a linear trend from year to year, the appropriate graph is: A) scatter diagram B) bar chart C) histogram D) pie chart

13)

2

14) You are given the following table of how people voted in the last election: Party A 24% Party B 38% Party C 32% Party D 6% The appropriate graph is: A) time series graph B) histogram C) bar chart D) scatter diagram

14)

15) A certain stem and leaf plot has the stem unit = 10 and the leaf unit = 1. The stem value of 154.3 would be: A) 3 B) 1 C) 15 D) 4

15)

16) A researcher had the following table summarizing the number of employees at a company and gross annual revenues (millions): Employees 62 89 162 208 312 Revenue 1.3 2.8 5.6 7.9 10.4 When creating a scatterplot of this data, an appropriate origin would be: A) (25,0) B) (60,1) C) (70,2) D) (0,0)

16)

17) One thousand consumers rank a financial product in a bank, with the following scale. poor fair good very good excellent What will be the difficulty of using such a ranking to find the median response?

A) nonnumeric data is difficult to tabulate B) it is difficult to rank data in an increasing order C) large data sets make it difficult to set up frequency tables D) data needs to be converted to a numeric (quantitative) scale

17)

18) Consider the following table of how people rate the service at a store on a scale from 1 to 5, 1 = poor, 5 = excellent: Rating 1 2 3 4 5 Frequency 24 68 132 267 192 In creating a pie chart, what percentage of the pie would the combined ratings of 1 and 2 occupy?

A) 13.47% B) 13.58% C) 13.4% D) 13.52%

18)

19) According to Globe and Mail newspaper, the following Canadian companies fewer than five thousand employees , had the following average sales per each employee Size of Average sales company per employee [number of [Thousands of employees] Dollars] 1-4 112 5-19 128 20-99 127 100-499 118 500-4999 120 Estimate the average sales per employee for all the firms having fewer then five thousand employees A) $120,000 B) $125,000 C) $112,000 D) $121,000

19)

3

20) You are given the following contingency table of income by gender: Under $25K $25K to under $50K $50K to under $75K Male 62 78 92 Female 56 84 98 The appropriate graph in which gender runs along the x-axis is: A) histogram B) scatter diagram C) pie chart

20) $75K or over 24 18

D) bar chart

21) A trucking company had a table of travel distances (im) and the average number of hours estimated to travel that distance: Distance 100 250 400 500 800 Time 1.2 3.1 4.8 6.25 10.2 The appropriate graph is: A) scatter diagram B) pie chart C) histogram D) bar chart

21)

22) Statistics Canada recently collected average gas prices posted at the gas stations in Vancouver over the last five years. This type of data can be considered as: A) nominal scale data B) cross-sectional data C) ratio scale data D) time series data

22)

23) In a survey, people were asked to name their favourite pet. The spreadsheet labelled dog = 1, cat = 2, budgie = 3, etc. This data can be categorized as: A) nominal data B) continuous data C) ordinal data D) discrete data

23)

24) A frequency table has the following rows: 0 to under 10 8 10 to under 20 16 etc. The appropriate graph is: A) histogram B) pie chart

24)

C) scatter diagram

D) bar chart

25) A bar chart of people's agreement with a statement had the following heights for their respective categories: Strongly disagree Somewhat disagree Somewhat agree Strongly agree 12 74 198 62 If this were remade into a pie chart, what percentage of the pie would be occupied by those who disagree with the statement, either strongly or somewhat?

A) 21.39% B) 24% C) 25% D) 24.86%

25)

26) You want to create a frequency table on Excel using the class 0 to under $50, $50 to under $100, $100 to under $150, etc. The bin value for the second class is: A) 100 B) 99.99 C) 100.01 D) 149.99

26)

27) You are given the following partial frequency table: 0 to under 2.5 17 2.5 to under 5.0 26 5 to under 7.5 42 What is the upper class limit of the fifth class?

A) 10.0 B) 15.0

27)

C) 17.5

4

D) 12.5

28) A certain stem and leaf plot has the stem unit = 1 and the leaf unit = 0.1. The leaf value of 1.243 would be: A) 243 B) 1 C) 2 D) 0.2

28)

29) In a survey, people were asked to rate their agreement with a statement on a scale from 1 to 5, 1 = strongly disagree, 5 = strongly agree. This data can be categorized as: A) discrete data B) continuous data C) ordinal data D) nominal data

29)

30) You are given the following frequency table of daily sales at a store for the month of March: Class Frequency 0 to under $2000 6 $2000 to under $4000 11 $4000 to under $6000 8 $6000 to under $8000 6 The percentage of days in which the store had at least $4000 in sales is: A) 74.19% B) 45.16% C) 54.84% D) 25.81%

30)

31) The price of a car can be categorized as: A) nominal data C) continuous data

31)

B) discrete data D) ordinal data

32) You are creating a frequency table on Excel showing the distribution of how many times a year people recycle. The classes are 0 to 1, 2 to 3, 4 to 5, etc. The bin value for the first class is: A) 3 B) 2 C) 0 D) 1 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

33) You are using a 7-point scale to rate people's satisfaction with a service where 1 = extremely dissatisfied and 7 = extremely satisfied. What would be the numeric value of neither satisfied nor dissatisfied?

33)

34) Transport Canada [TC] is concerned about the rising jet fuel costs and its negative impact on the Canadian airlines. TC recently conducted a survey of the number passengers flown into Vancouver with particular airline to assess if the passenger load capacity is declining over time. Data is provided: Passengers in Airline (thousands) Air Canada 277 West Jet 350 Continental 200 Alaska 150 What would be the best non-tabular form of analyzing this data set ?

34)

35) You have a frequency table with the following classes: $70 to under $105, $105 to under $140, $140 to under $175, etc. What is the class width?

35)

36) You are creating a frequency table using Excel. The first 2 classes are 0 to under $30 and $30 to under $60. What is the bin value of the second class?

36)

5

32)

37) A statistics professor decides to create a data set of student achievement in his class. He creates the following frequency table Degree of Relative achievement Frequency frequency (%) High achiever 55 26.6 Medium achiever 67 32.4 Low achiever 77 37.2 Poor performer 8 3.9 Total 207 100 The professor is is does not find this table to useful for distribution of student performance.

He would rather see the results in a non-tabular form. What type of graph would be the best way of presenting this data?

37)

38) You have a scatter plot in which two of the points are (2,3) and (3,7). If you draw a straight line through these points, for an x value of 4, what is the y value of the point that lies on this line?

38)

39) You are creating a stem and leaf plot with the stem unit = 10 and leaf unit = 1. What is the stem value of 262.9?

39)

40) You are computing a class width by hand. The smallest value is 2.5, the largest is 60.2 and there are 25 data points. What is the class width, round to the nearest whole number?

40)

41) You have a time series graph of a company's gross annual sales in thousands of dollars.

Two of the points are (1910,4.1) and (1911,3.6). If you draw a straight line through these 2 points, what would be the gross sales value on the line for the year 1913?

41)

42) A contingency table was created from a survey in which upper management, middle management and non-management staff were asked to rate a courier on a scale from 1 to 10. Suppose the ratings are grouped 1-3, 4-6, 7-9, and 10 in the contingency table. If a bar chart is created from the table and the staff positions occupy the x-axis, how many categories are in the legend?

42)

43) A frequency table has the following classes: 0 to under $9, $9 to under $18, $18 to under $27, etc. What is the lower class limit of the sixth class?

43)

44) The following table is from a survey in which people were asked how many times per week they eat out: Class Frequency 0 68 1 192 2 98 3 42 What percentage of the respondents eat out no more than once a week. Express your answer as a decimal number.

44)

45) You have a scatter plot in which the smallest data point is (1432.7, 680.6). If the origin should be a multiple of 30, what should be the y value of the origin?

45)

6

46) A firm's annual sales, in thousands of dollars, for the past 10 years are as follows: 105,210,322,330,362,368,420,425,435,440 The analyst wishes to represent this data in a graphical form. What would the type of graph that is best suited for such a data set ?

46)

47) You have the following stem and leaf plot in which the stem unit = 1 and leaf unit = 0.1: 0 12334 1 0112556 2 003446889 3 1455568 If you create a frequency table with the first class being 0 to under 2, what is the frequency of that class?

47)

48) A survey asked people how interested they would be in a new type of cell phone: Not at all Not very Somewhat Very 142 57 24 13 What percentage of the respondents are at least somewhat interested? Express your answer as a decimal number accurate to 4 decimals.

48)

49) You are using the following table to create a pie chart: Poor Fair Good Excellent 25 89 163 272 In the pie chart, what percentage of the pie is occupied by those giving either a good or excellent rating? Express your answer as a decimal number accurate to 4 decimals.

49)

50) You are creating a histogram from a frequency table in which the first class is 0 to under 25 and the last class is 175 to under 200. If each class has the same width, how many bars will the histogram have?

50)

TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.

51) In a survey, people were asked which party they would likely vote for in the next election. A number representing a party was entered into a spreadsheet. This data would be considered nominal.

51)

52) A scatter diagram plots number of monthly sales along the x-axis and gross income along the y-axis. The fewest number of sales is 1 while the highest is 10. The lowest gross income is $8.50 while the highest is $64.50. An appropriate origin for this graph would be (0,0).

52)

53) A frequency table summarized annual gross sales for a set of 100 companies. This data would be classified as continuous.

53)

54) A certain stem and leaf plot has a stem unit of 1 and leaf unit of 0.1. The leaf value of 2.03 would be 3.

54)

55) You are creating a frequency table in which the first 2 classes are 0 to under $4.50 and $4.50 to under $9.00. The upper class limit of the fifth class would be $22.50.

55)

7

56) Consider the following table: Office Workers Doctors Income < $100K 1800 20 Income at least $100K 200 180 Total 2000 200 In creating a bar graph from this data, the scale along the y-axis should be a frequency scale to get a sense of the number of people in each occupation group earning at least $100,000 per year.

56)

57) In creating a scatter diagram, another name for the response variable is the dependent variable and is plotted along the y-axis.

57)

58) The following data is based on a recent daily product sales in a grocery store Number of Price $ sales $18-20.99 2 21-23.99 7 24-26.99 7 27-29.99 5 30-32.99 4 Total 25 The store manager wishes to expand this data set into a full frequency table. The next two columns in this table will be "relative frequency" and "probability of cumulative frequency."

58)

59) In creating a scatter diagram, the data for the y-axis does not necessarily have to be quantitative.

59)

60) You have a table with sales dates and the number of units sold on those dates. If you wish to track a linear trend from one date to the next, the appropriate graph is a histogram.

60)

61) If you were creating a frequency table using Excel and the first class was 0 to under $25, the bin value for this class would be $24.99.

61)

62) The title of a chart is not important, so long as the actual chart coveys the necessary information.

62)

63) If people rate an ad on a scale from 1 to 5, 1 = poor and 5 = excellent, the data is classified as ordinal.

63)

64) In plotting simultaneous histograms to compare data from different sources, it is not important to use the same x-axis for the histograms.

64)

65) We may depict the information contained in frequency distributions as bar graphs known as frequency tables.

65)

66) The primary difference in the x-axis between a histogram and a bar chart is that, for a histogram, the data is qualitative while that of a bar chart is quantitative.

66)

67) The cumulative frequency of a class is the sum of the frequency of the class and all preceding classes.

67)

8

68) You have a contingency table consisting of 4 income categories and 3 job descriptions. If the job descriptions are used as the x-axis of a bar graph, the legend would have 3 categories.

68)

69) A store conducted a survey and grouped people by their overall satisfaction with the service: Neither Very Somewhat satisfied nor Somewhat Very dissatisfied dissatisfied dissatisfied satisfied satisfied 2 12 98 164 132 If this data were plotted in a bar chart, it would appear to be skewed left.

69)

70) In a survey, people were asked how many times a month they order out for pizza. This data would be classified as discrete.

70)

71) When creating a bar graph or histogram, the appropriate starting point for the y-axis is zero.

71)

72) The annual household incomes of people in a city were summarized as follows: Class Frequency Under $25K 1624 $25K to under $50K 5609 $50K to under $75K 8284 $75K to under $100K 2098 The appropriate graph for this data is a bar chart.

72)

73) A 3-D pie chart is more informative than a 2-D pie chart.

73)

9

Answer Key Testname: CHAPTER 2 1) A 2) C 3) B 4) B 5) A 6) B 7) A 8) C 9) D 10) B 11) B 12) D 13) A 14) C 15) C 16) B 17) B 18) A 19) D 20) D 21) A 22) D 23) A 24) A 25) D 26) B 27) D 28) C 29) C 30) B 31) C 32) D 33) 4

10

Answer Key Testname: CHAPTER 2 34) Pie chart would be the best option with the data labels. A historical data base may also be required to see if there is indeed a decline with the passenger loads over time.

35) 35 36) 59.99

11

Answer Key Testname: CHAPTER 2 37) A pie chart, as displayed below

38) 11 39) 26 40) 12 41) 2.6 42) 4 43) 45 44) 0.65 45) 660

12

Answer Key Testname: CHAPTER 2 46) A time series line will be the best graphical representation, as sales trend can best be depicted over time. The linearity of the line can be further tested

47) 12 48) 0.1568 49) 0.7923 50) 8 51) TRUE 52) TRUE 53) TRUE 54) FALSE 55) TRUE 56) FALSE 57) TRUE 58) FALSE 59) FALSE 60) FALSE 61) TRUE 62) FALSE 63) TRUE 64) FALSE 65) FALSE 66) FALSE 67) TRUE 68) FALSE 69) TRUE 70) TRUE 71) TRUE 72) FALSE 73) FALSE

13

Chapter 3 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1) For a set of data of x and y, you are told that r = -0.002. If you plot the data, what would you expect?

A) The data appears somewhat linear, sloping upward to the left B) The data appears slightly linear, sloping upward to the left C) The data will have no discernable pattern D) The data appears somewhat linear, sloping upward to the right

1)

2) A researcher sampled 6 households to determine the correlation of annual household income (thousands of dollars) to the amount spent monthly on entertainment: Income 25.2 30.6 42.7 49.8 57.8 62.9 Entertainment 100 135 162 198 207 508 It is determined that the last data point has an adverse impact on the linear relationship of the two variables. If it is removed, what is the ratio of the new correlation coefficient to the original one?

A) 0.75 B) 0.8 C) 1.25 D) 1.33

2)

3) The Construction Association of BC reports the following data on the average construction completion time, in months: Average Construction Year time [months] 1980 46 1981 50 1982 55 1983 50 1984 40 1985 76 1986 82 1987 89 1988 90 Find the Pearson correlation coefficient for construction completion time as a function of time.

A) 0.86 B) 0.75 C) 0.80 D) 0.90

3)

4) Given this set {2, 8, 15, 20, 350}, it would appear that 350 is an extreme value. If it is removed, how much does the mean reduce by?

A) 70 B) 67.75 C) 72 D) 62.25

4)

5) You have a sample of 5 numbers representing the number of times per week that people eat out.

The mean of this sample is 2.4. You interview a sixth person and find this person eats out twice a week. What is the mean now?

A) 2.33 B) 2.4 C) 2.5 D) 2.0

5)

6) Find the covariance coefficient for the given data set 20, 36, 29, 42, 37, 48 21, 22, 29, 35, 39, 42 A) 59 B) 54

6)

1

C) 57

D) 58

7) A researcher asked 50 people how many times a week they watch TV; the average was 6.2.

However, the next 2 people told the researchers they do not watch TV at all. What is the average now, accurate to 2 decimals?

A) 5.96 B) 5.87 C) 5.98 D) 6.2

7)

8) Given x = {1, 7, 9, 16}, what is x2 ?

A) 804 B) 625

8)

C) 1,089

D) 387

9) A researcher asked a sample of 9 people how much per week they spend on groceries. The values are $100, $120, $90, $135, $250, $75, $160, $180 and $120. If we remove the largest value, how much does the IQR change by if the needed percentiles are computed by hand?

A) 12.5 B) 15 C) 13.75 D) 0.5

9)

10) Find the range of the following data 18,6,14,27,12,44,38,33 A) 38 B) 38.5

10) C) 39

D) 37

11) For a set of 12 numbers, the seventy-fifth percentile is 111.75. If the ninth value in the data set is 108, what is the tenth value?

A) 110.5 B) 113 C) 109.25 D) 114.75

11)

12) Given this data set {12, 62, 135, 457, 609, 834, 937, 1,024, 1,368, 1,567}, what is the numerical difference between the median and the twenty-fifth percentile if they are computed by hand?

A) 615.25 B) 575.25 C) 604.75 D) 510.5

12)

13) Compute the first quartile (QR 1) of the following data set 5, 5,10,12, 14, 15, 17, 17, 18, 19, 19 , 20 A) 12 B) 19 C) 5

13) D) 11

14) A clothing store had 9 sales on a certain day in which the average sale was $150. Before the store closed, it had a customer who spent $875. How much did the average increase by?

A) 77.50 B) 67.50 C) 72.50 D) 82.50

14)

15) For this set of numbers {12, 17, 21, 29, 33, 37, 46, 55, 64, 78}, what is the sixty-second percentile if it is computed by hand?

A) 44.38 B) 38.8 C) 40.52 D) 39.78

15)

16) You have a set of 8 numbers, of which 5 are 1, 5, 9, 16 and 18. The remaining 3 numbers are the mode. If the mean of these 8 numbers is 7.25, what is the mode?

A) 9 B) 2 C) 3 D) 5

16)

17) A researcher investigated the relation between annual gross revenues (in thousands of dollars) and annual technology expenditures in (thousands of dollars): Revenue 56 62 78 98 105 150 Technology 0.62 1.3 1.67 2.98 4.06 5.78 When a seventh company was surveyed, its annual gross revenues were $75,000 but its technology expenditures were $9,230. If this data point is included, what is the ratio of the original correlation coefficient to the new one?

A) 2.06 B) 0.67 C) 0.41 D) 2.42

17)

2

18) Suppose the amount that people spend per week on groceries follows a bell curve with an average of $150 and standard deviation of $42. What is the most that people spend on groceries 95% of the time?

A) $276 B) $22 C) $228 D) $234

18)

19) The hours wages of employees at Extra Company were recorded as follows Hourly Wages Number of [$] Employees $5-5.99 20 $6-6.99 35 $7-7.99 48 $8-8.99 167 $9-9.99 55 $10-10.99 25 Estimate the mean, variance and standard deviation of hourly wages A) $1.205, $1.455 and $1.287 B) $8.332, $1.552 and$1.201 C) $8.286, $1.211 and $1.541 D) $8.286, $1.451 and $1.205

19)

20) For a set of 8 numbers, the mean is 58.625. The sum of the 7 lowest numbers is 377. The lowest value is 11. What is the range?

A) 81 B) 85 C) 83 D) 75

20)

21) Given this sample of numbers {6, 12, 21, 29, 31, 39, 42}, what is the interquartile range if the values are computed by hand?

A) 19 B) 17 C) 27 D) 4

21)

22) For the past six years, Esta Company's annual sales, in millions of dollars, have been: 46.2,48.8,55.7,59.3,62.4,66.0 Find Esta's mean and median annual sales.

A) $56.4, $54.5 B) $55.3, $54.5 C) $57.5, $56.0 D) $56.4, $57.5

22)

23) Given this data set {15, 18, 23, 28, 32, 39, 41, 48, 55, 162}, it is assumed that 162 is an extreme value.

If it removed, how much does the IQR change if the appropriate percentiles are computed by hand?

A) 6 B) 2 C) 4 D) 0

23)

24) The average sale at a discount store is $47.75 with a standard deviation of $7.45. Find the smallest interval such that 90% of the store's sales are within the interval.

A) [$25.15, $77.43] B) [$24.00, $70.00] C) [$24.19 , $71.31] D) [$24.19, $72.45]

24)

25) Given {5, 15, 20, 30}, what is (x-18)2 ?

A) 4 B) 326

25)

C) 1,550

3

D) 180

26) A store takes a sample of one hundred customers' charge accounts and finds the following: Balance Outstanding Number of ($) accounts 10,000 10 15,555 12 17,000 18 19,999 21 25,999 37 Compute the standard deviation of the balance outstanding variable.

A) $5,885 B) $6,500 C) $2,631

26)

D) $6,100

27) For a sample of 9 numbers, you are told the standard deviation is 6.4 and that x2 = 580.49. What is the mean?

A) 5.30 B) 5.02 C) 5.34 D) 4.85

27)

28) A sample of 5 number is taken. The mean of this sample is 25. Four of the numbers are 17, 19, 30 and 35. What is the fifth number?

A) -1 B) 24 C) 25 D) 18

28)

29) Given this sample data set {9.2, 6.8, 10.6, 13.2, 13, 14.3, 4.5, 9.4, 12.7, 7.3, 8.7}, if it can be assumed the data is symmetric, what percentage lies within 1 standard deviation of the mean?

A) 81.82% B) 72.73% C) 54.55% D) 63.64%

29)

4

30) A store takes a sample of one hundred customers' charge accounts and finds the following: Balance Outstanding Number of ($) accounts 10,000 10 15,555 12 17,000 18 19,999 21 25,999 37 Determine if there is a significant degree of association between the balance outstanding on the charge accounts and the number of accounts. Estimate the Pearson Correlation Coefficient and comment on your findings A) Correlation Coefficient ($) No of Accounts ($) Balance 1 Number of accts 0.877777 1 There is a positive correlationary relationship between the two variables B) Correlation Coefficient ($) No of Accounts ($) Balance 1 Number of 0.94949236 1 accounts There is very strong positive correlationary relationship between the account balances and the number of accounts. Coefficient value = 94.9% C) There is no visible relationship between these variables thus no need to run the correlation application D) Account balances and the number of accounts can not be related as the level of account balances is a function of sales and not the number of accounts, thus no need to run the correlation application

30)

31) Given this sample of numbers {5, 12, 18, 36, 269}, it would appear that 269 is an extreme value. If it is removed, what is the ratio of the larger standard deviation to the smaller one?

A) 8.51 B) 8.65 C) 8.79 D) 8.62

31)

32) A data set is skewed right if the mean is greater than the median. For a set of 6 numbers, the first 5 are 3, 14, 24, 36 and 63. The sum of the 6 numbers is 240. What is the difference between the mean and the median?

A) 16 B) 10 C) 4 D) 12

32)

33) The percentage of gross income that people give to charity follows a bell curve with an average of 2.3% and standard deviation of 0.72%. What is the largest percentage of gross income that people would be expected to give based on this distribution?

A) 4.52% B) 3.74% C) 3.02% D) 4.46%

33)

34) You have a set of 5 numbers and find the mean to be 9.4. Four of the numbers are 3, 7, 13 and 15.

What is the median of this data set?

A) 8.7 B) 12.3 C) 9 D) 10.2

34)

5

35) A store takes a sample of one hundred customers' charge accounts and finds the following: Balance Outstanding Number of ($) accounts 10,000 10 15,555 12 17,000 18 19,999 21 25,999 37 Compute the variance of the balance outstanding variable.

A) $33634816.3 B) $36634816.3 C) $34634816.3

35)

D) $37634816.3

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

36) A researcher asked 10 people how much they typically spend per month on movie entertainment.This table summarizes the results: 5.00 15.50 25.00 25.00 25.50 30.00 40.00 40.00 50.00 60.00 If we remove the low value of $5.00, how much does the median move by?

36)

37) Given this set of numbers x = {3, 7, 11, 13, 17, 19}, what is (x-5)2 ?

37)

38) For this data set {0.25, 0.762, 0.903, 1.254, 2.043, 3.162, 4.739, 10.162}, if the value of 10.162 is removed, how much does the mean reduce by? Round to 2 decimals.

38)

39) For a sample of 10 numbers, s2 = 29.16 and x2 = 1,015.2. What is the mean, rounding to 2 decimals.

39)

40) A researcher conducted a survey asking people how many times per year they recycle bottles. For the first 12 people, the average was 2.5 times per year. However, the thirteenth person said he recycles bottles every month. How much does the mean increase by? Round to 2 decimals.

40)

41) For a sample of 8 people visiting a store, they were asked to rate the store on a scale from 1 to 10, 1 = poor, 10 = excellent, as well as how much they spent on that visit: Rating 3 5 6 6 7 7 8 9 Spending 17.50 20.62 19.50 22.65 20.40 35.62 29.62 35.02 Using the Spearman rank correlation coefficient, what is the association between the two variables? Round to 2 decimals.

41)

42) Given this sample of data {6, 12, 17, 24, 27, 36, 102}, it would appear that 102 is an extreme value. If we remove it, what is the ratio of the original standard deviation to the new one?

Round to 2 decimals.

42)

43) In a set of 10 numbers, 6 of them are 10, 16, 22, 28, 35 and 43. The remaining 4 values is the mode. If the mean of the 10 values is 25.4, what is the value of the mode?

43)

6

44) The coefficient of variation is defined as the ratio of the standard deviation to the mean for a set of data. For this sample of data {10.3, 12.7, 13.4, 16.6, 18.4, 19.2, 20.9, 25.4}, what is the coefficient of variation? Round to 2 decimals.

44)

45) A clothing store observed that its sales follow a bell curve with a mean of $185.62 and standard deviation of $24.50. What is the lowest sale they should expect about all the time?

45)

46) The Construction Association of BC reports the following data on the average construction completion time, in months: Average Construction Year time [months] 1980 46 1981 50 1982 55 1983 50 1984 40 1985 76 1986 82 1987 89 1988 90

46)

Compute the mean, mode, median and the standard deviation of the average construction completion time.

47) A class of 16 students had an average of 76% on a test. The lowest student mark was 6% and the highest was 100%. The trimmed mean is defined as the mean once the lowest and highest values are removed. For this test, what is the trimmed mean in percent? Round to 2 decimals.

47)

48) Given this data set {3.75, 6.42, 8.67, 10.903, 15.262, 17.606, 21.622, 29.005}, what is the eighty-second percentile if it is computed by hand? Round to 2 decimals.

48)

49) For a certain bell-curved distribution, the mean is 10.2 and the standard deviation is 25.6.

For approximately 95% of the distribution, what is the highest value?

49)

50) The annual number of sick days taken by 15 employee is provided . Compute the mode of this data set.

12, 19, 21, 22, 23, 28, 6, 25, 13, 30 , 14, 30, 33, 26, 46

50)

51) A researcher wanted to measure the correlation between annual household income (in thousands of dollars) and weekly amount spent on groceries. For a sample of 7 households, these were the results: Income 25.2 36.7 45.5 58.2 69.6 72.8 84.7 Groceries 120 129 138 156 182 212 249 What is the correlation coefficient? Round to 2 decimals.

51)

52) Given this data set {5, 9, 14, 22, 35, 43, 54, 69}, what is the interquartile range if you compute the necessary percentiles by hand?

52)

7

TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.

53) If the correlation coefficient for a set of x and y data is 0.925, this indicates a strong cause-and-effect relationship between the variables.

53)

54) For a set of data, the standard deviation would be smaller if the data set were a sample than if it were a population.

54)

55) You have a set of 10 numbers ranging from 5 to 60 with a median of 42.5 and mean of 30.6. If you add 46.7 to the data set, both the mean and standard deviation will increase.

55)

56) Suppose you had to assign ranks to this data set: {1, 3, 3, 3, 4, 4, 5, 6, 10}. The value of 4 would be assigned a rank of 5.

56)

57) In a data set with 16 numbers, if the average is 12.4 and you added 15.8 to the data set, the average would increase by 0.2.

57)

58) In a distribution that is bell curved, almost all the data is within 2 standard deviations of the mean.

58)

59) In a data set with 15 values, the IQR would be the difference between the twelfth and fourth values.

59)

60) If there is concern of extreme values in a set of x and y data, the Spearman rank correlation coefficient may be superior to the normal correlation coefficient.

60)

61) The standard deviation is the square root of the variance.

61)

62) The range is one measure of the degree of dispersion in a data set.

62)

63) An instructor collected the following data concerning students' performance on the final exam: Student A B C D Final exam mark 91 86 85 73 The instructor can assume the distribution of the final exam marks fits the normal distribution criteria, with a small degree of variance.The standard deviation of the final exam marks will be greater than 20.

63)

64) The coefficient of variation is the ratio of the standard deviation to the mean. If you have a data set and multiply all the values by 5, the coefficient of variation will also increase.

64)

65) You have a set of x and y data with r = 0.623. You remove one pair of data and now r = 0.895. This would indicate that the removed data pair were outliers.

65)

66) The correlation coefficient can be greatly affected by extreme values in the data.

66)

67) The Spearman rank correlation coefficient should only be used for linear data.

67)

8

68) An instructor collected the following data concerning students' performance on the final exam: Student A B C D Final exam mark 91 86 85 73 The instructor can assume the distribution of the final exam marks fits the normal distribution criteria, with a small degree of variance

68)

69) You have a data set in which the standard deviation is 8.3. If you add 10 to all the values in the set, the standard deviation increases to 18.3.

69)

70) If you have a data set ranging from 2 to 26 and you add -50 to the data set, the standard deviation will increase.

70)

71) If you have a data set of 10 numbers ranging from 10 to 52 and you add 26 to the data set, the standard deviation will increase.

71)

72) If you have a data set of 15 numbers ranging from 10 to 62 and you add 5 and 169 to the data set, the median would increase.

72)

73) In a data set, the average is affected more by extreme values than the median.

73)

74) You have a data set in which the standard deviation is 2.75. If all the values are multiplied by 8, the standard deviation increases to 22.

74)

75) In computing the standard deviation of either a population or a sample, the denominators in the formulas are the same.

75)

76) You have a set of 17 numbers in which the median is 18.3. If you remove the lowest and highest values, the median remains the same.

76)

9

Answer Key Testname: CHAPTER 3 1) C 2) C 3) A 4) B 5) A 6) C 7) A 8) D 9) C 10) A 11) B 12) C 13) D 14) C 15) A 16) C 17) D 18) D 19) D 20) A 21) C 22) D 23) C 24) C 25) B 26) A 27) A 28) B 29) D 30) B 31) A 32) B 33) D 34) C 35) C 36) 2.25 37) 448 38) 1.04 39) 8.68 40) 0.73 41) 0.72 42) 2.99 43) 25 44) 0.29 45) 112.12 46) 64.2, 50, 55, 19.8 47) 79.29 48) 24.43 49) 61.4 50) 30 10

Answer Key Testname: CHAPTER 3 51) 0.95 52) 41 53) FALSE 54) FALSE 55) FALSE 56) FALSE 57) TRUE 58) FALSE 59) TRUE 60) TRUE 61) TRUE 62) TRUE 63) FALSE 64) FALSE 65) TRUE 66) TRUE 67) FALSE 68) FALSE 69) FALSE 70) TRUE 71) FALSE 72) FALSE 73) TRUE 74) TRUE 75) FALSE 76) TRUE

11

Chapter 4 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1) Given the following data: <500 Hours lasted Number of bulbs tested in the experiment 5

1) 500-699

700-899

=>900

50

600

400

Find the probability that a light bulb will last fewer than 500 hours.

A) 5/400 B) 5/1055 C) 5/500

D) 10/100

2) Fifty-eight percent of the members of a fitness club are under the age of 25. Forty-five percent of the members under the age of 25 come to the club at least 3 times per week. What percentage of the club's members are under the age of 25 and come to the club less than 3 times per week?

A) 45.4% B) 31.9% C) 42% D) 55%

2)

3) 20.2% of car batteries last longer than 5 years. However, 90.6% of car batteries costing at least $120 last longer than 5 years. Currently, 20% of batteries cost at least $120. What percentage of batteries lasting longer than 5 years cost at least $120?

A) 18.12% B) 90.6% C) 89.7% D) 22.08%

3)

4) A real estate agent has 500 customers on her database; 123 of these customers have annual household incomes of $75,000 or more. What percentage have annual household incomes under $75,000?

A) 76% B) 25% C) 24.6% D) 75.4%

4)

5) A cable company offers 3 tiers of service; 60,000 customers use tier A while 25,400 use tier C. If the company has 200,000 customers in total and a customer can use only one tier, what percentage of its customers use tier B? A) 41% B) 57.3% C) 42.7% D) 58%

5)

6) Executives at Apple Canada are discussing the new iPhone's market success. The marketing manager is certain that the new product will be very successful, with no chance of failure. What probability factor can be assigned to product failure?

A) P (failure) = 0.1 B) P (failure) = 0 C) P (failure) = 1-.1 D) P (failure) = unknown, can not be estimated

6)

7) Executives at Apple Canada are discussing the new iPhone's market success. The marketing manager is certain that the new product will be very successful, with no chance of failure. What probability factor can be applied to this assumption?

A) P (Success) = 0 B) P (success) = 1-.5 C) P (success) = 1-.95 D) P (success) = 1

7)

1

8) Forty-two percent of companies have at least 10 employees. Eighty-six of companies have annual gross earnings under $100,000. If 30% of companies that have annual gross earnings of at least $100,000 have fewer than 10 employees, what percentage of companies overall have at least 10 employees and annual gross earnings of at least $100,000?

A) 14% B) 23.33% C) 9.8% D) 70%

8)

9) In testing the new H1N1 flue shots. 725 out of 1050 patients treated with the drug experienced improvement in their health condition. Find the probability that a patient treated with this new vaccination will not experience improvement in their health condition?

A) 69% B) 32% C) 31% D) 25%

9)

10) In a certain region, the probability it is sunny is 76%, the probability the daytime high temperature is above 15 degrees is 68% and the probability of both happening is 51%. What is the probability that on any given day it is not sunny and the temperature is not higher than 15 degrees?

A) 93% B) 7% C) 49% D) 7.68%

10)

11) In a baseball stadium, the number of hamburgers sold is shown as follows: Dozens of hamburgers sold 1 2 3 4 5 6 Number of days this occurred 2 5 8 20 30 5 Find the probability that the merchant will sell one dozen hamburgers on a given day?

A) 1/7 B) 2/70 C) 1/2 D) 1/70

11)

12) If the probability of rain is 0.4, what are the odds against rain?

A) 6 to 4 B) 10 to 1 C) 4 to 10

12)

D) 4 to 6

13) Thirty-two percent of students take fewer than 4 courses per term. Seventy-five percent of students taking fewer than 4 courses per term work full-time. Thirty-five percent of students work full-time. What percentage of students take at least 4 courses and do not work full-time?

A) 24% B) 57% C) 68.57% D) 83.82%

13)

14) A theatre company divided people by gender and whether or not they have seen live theatre in the past 5 years; 10% are males who have seen live theatre in the past 5 years while the corresponding percentage for females is 24%. If we assume a 50/50 gender split, what percentage of those who have not seen live theatre in the past 5 years are male?

A) 66% B) 60.61% C) 80% D) 40%

14)

15) A meteorologist examined records for a period of 180 days from the previous year. On 25 of the days, the temperature at least 30 degrees and there was a smog alert. On 17 of the days, the temperature was under 30 degrees and there was a smog alert. On 9 of the days, the temperature was at least 30 degrees and there was no smog alert. On what percentage of the days was the temperature under 30 degrees and there was no smog alert?

A) 37.81% B) 71.67% C) 28.33% D) 62.19%

15)

2

16) Forty percent of a store's customers are male. Fifty-two percent of the store's customers spend less than $25 per purchase. Thirty-two percent of the store's customers are female who spend at least $25 per purchase. What percentage of the store's customers are male who spend less than $25 per purchase?

A) 24% B) 16% C) 12% D) 8%

16)

17) In a baseball stadium, the number of hamburgers sold is shown as follows: Dozens of hamburgers sold 1 2 3 4 5 6 Number of days this occurred 2 5 8 20 30 5 What is the probability that the merchant will sell more than four dozen hamburgers?

A) 4% B) 20% C) 5% D) 50%

17)

18) BC Insurance Corporation claims that 8 out of 100 new vehicles will be involved in an accident within the first year of purchase. What is probability that new vehicle purchased will be in an accident within the first year?

A) 8% B) 92% C) 90% D) 10%

18)

19) 62.4% of an office supply firm's customers have fewer than 5 employees. 17.4% of the customers have fewer than 5 employees and have annual gross earnings of $100,000 or more. 21.3% of the customers have fewer than 5 employees and have annual gross earnings of at least $50,000 but under $100,000. What percentage of the customers have fewer than 5 employees and annual gross earnings of under $50,000?

A) 23.7% B) 37.98% C) 26.8% D) 37.6%

19)

20) Sixty percent of passenger vehicles are domestic brands. Twenty-five percent of vehicles are domestic brands that cost less than $20,000. What percentage of domestic vehicles cost less than $20,000?

A) 35% B) 40% C) 41.67% D) 58.33%

20)

21) Twenty-five percent of a store's customers pay by debit while 54% pay by credit. If the percentage of the store's customers who pay by either method is 68%, what percentage of the store's customers pay by both methods (sometimes using one method, sometimes the other)?

A) 56% B) 44% C) 0% D) 11%

21)

22) A marketing firm plans to mail marketing pieces to those who are either 55 or older or have annual gross incomes of at least $100,000. They have a database of 5 million names. If 10% of the database has annual gross income of at least $100,000, 25% is 55 or older and 7% is 5 or older and have annual gross income of at least $100,000, how many pieces will they be mailing?

A) 0.35 million B) 1.75 million C) 4.65 million D) 1.4 million

22)

23) Fifty-two percent of people watch new episodes of a certain TV show. Eighteen percent of people watch reruns of the show while 3% watch both new episodes and reruns of the show. What percentage of people watch either new episodes or reruns of the show?

A) 33% B) 67% C) 73% D) 70%

23)

3

24) Statistics Canada claims that 70% of all the small businesses opened in Canada fail within the first two years. What is the probability that newly opened business will fail in Canada?

A) 70% B) =1-.7 C) 100% D) 30%

24)

25) The probability Joe is at work is 49%. The probability Joe is at home is 25%. What is the probability Joe is neither at work nor at home?

A) 74% B) 52% C) 26% D) 39%

25)

26) The probability of an earthquake in a certain region in any given year is 2.5%. The probability of a dry summer in the same region in a given year is 20.4%. If the two events are unrelated, what is the probability of neither event happening in any given year?

A) 22.9% B) 22.39% C) 77.61% D) 77.1%

26)

27) Sixty-two percent of people listen to radio station A. Forty-eight percent of people listen to radio station B. If 17% of people do not listen to either station, what percentage of people listen to station A but not station B? A) 35% B) 19% C) 47% D) 45%

27)

28) Companies are divided into small, medium and large as well as these income groups: under $100,000, $100,000 to under $500,000, $500,000 to under $1 million, $1 million or more. If the sample space were set up as a tree, how many branches would it have?

A) 9 B) 7 C) 12 D) 10

28)

29) Ninety-two percent of office workers do text messaging on their computer while at work.

Eighty-two percent do text message on their cell phones while at work. Three percent don't do text message on either their computer or cell phone while at work. What percentage of office workers do text messaging on either device while at work?

A) 97% B) 15% C) 77% D) 68%

29)

30) 80.6% of households own either a mid-size sedan or an SUV. If 16.7% of households own both a mid-size sedan and an SUV, what percentage of households own only a mid-size sedan or an SUV? A) 63.9% B) 19.4% C) 97.3% D) 41.6%

30)

31) The probability that one stock index rises on any given day is 45%. The probability that another stock index rises is 52%. It can be assumed that the activities of one index are not affected by the other. What is the probability both stock indexes rise on the same day?

A) 23.4% B) 97% C) 7% D) 41.4%

31)

32) The probability a certain store's daily sales is above $5,000 on a given day is 72%. The probability a certain taxi driver's gross daily income is above $200 on a given day is 54%. What is the probability of both events happening on any given day?

A) 75% B) 38.88% C) 61.12% D) 18%

32)

4

33) Given this table of gender and income for 500 people: Under $25K $25K to under $50K $50K or more Male 37 158 42 Female 69 158 36 Total 106 316 78 What percentage of those earning less than $50,000 are female?

A) 38.8% B) 53.79% C) 46.15%

33) Total 237 263 500

D) 73.76%

34) It is estimated that 70 of 950 common stocks listed on the Toronto Stock Exchange ( TSX) decline in market value, in a typical day. What is the probability that a newly listed company on the TSX will not decline in value in a day ?

A) 100% B) 7.4% C) 7% D) 93?

34)

35) Eighty percent of males flip channels while watching TV; the corresponding percentage for females is 5%. Assume the gender split of people watching TV is 50/50. If a person is flipping channels while watching TV, what is the probability the person is male?

A) 94.12% B) 80% C) 40% D) 42.5%

35)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

36) The Accounting Department of the Insurance Corporation collected the following data on its accounts receivables: Balance of On time paid Never pay account (OT) Late ( LT) (DEL) less than $100 30 6 1 $100 to $500 22 12 2 More than $500 16 7 4 Totals 48 25 7

36)

Find the probability that the account is paid, given that it is less than $100 balance?

37) A study segregated people by age and whether they own a driver's licence or not. 1.6% are under the age of 25 and have a licence. 28.6% are under the age of 25 and do not have a licence. 58.5% are 25 or older and have a licence. What percentage of people are 25 or older and do not have a driver's licence? Express it as a decimal number.

37)

38) The Accounting Department of the Insurance Corporation collected the following data on its accounts receivables: Balance of On time paid Never pay account (OT) Late ( LT) (DEL) less than $100 30 6 1 $100 to $500 22 12 2 More than $500 16 7 4 Totals 48 25 7

38)

Find the probability that the account is more than $500, given that it will be paid?

5

39) 36.7% of people own a vehicle that is at least 5 years old. 72% of those who own a vehicle at least 5 years old spend at least $500 per year on servicing and repairs. Overall, 70.4% of people spend less than $500 per year on servicing and repairs. What percentage of those who spend less than $500 per year on servicing and repairs own vehicles less than 5 years old? Express it as a decimal number accurate to 3 decimals.

39)

40) 72.5% of those whose annual income is at least $75,000 contribute to RRSP while the corresponding percentage for those whose annual income is under $75,000 is 10.5%. 82.6% of people have an annual income under $75,000. What percentage of those who contribute to RRSP have annual income of $75,000 or more? Express it as a decimal number accurate to 4 decimals.

40)

41) Thirty percent of people shop at store A, 64% shop at store B while 8.5% shop at both stores. What percentage of those who shop at store A do not shop at store B? Express it as a decimal number accurate to 4 decimals.

41)

42) A study classified people into 5 income categories and 8 ethnic background categories. If a tree were build to classify people by both their income and ethnic backgrounds, what would be the number of branches?

42)

43) 12.4% of companies have short-term debt, 2.7% have long-term debt while 0.86% have both. What percentage of companies that have long-term debt also have short-term debt?

Express it as a decimal number accurate to 4 decimals.

43)

44) Consider this contingency table of people divided by annual income and number of books purchased per year: $25K to $50K to Under $25K under $50K under $75K $75K or more Total 0 to 1 74 89 138 31 332 2 to 3 32 74 240 73 419 4 or more 19 43 129 58 249 Total 125 206 507 162 1000 What percentage of those who buy fewer than 4 books per year have annual incomes under $50,000? Express it as a decimal number accurate to 4 decimals.

44)

45) 23.4% of people have a graduate degree. 74.8% of people in general earn less than $50,000 per year, but only 10.5% of those with a graduate degree earn less than $50,000 per year.

What percentage of those who earn at least $50,000 per year do not have a graduate degree? Express it as a decimal number accurate to 4 decimals.

45)

46) 16.2% of people own savings bonds while 8.4% own GICs. However, 72.4% of people own neither savings bonds nor GICs. What percentage of people own either savings bonds or GICs? Express it as a decimal number.

46)

6

47) The Accounting Department of the Insurance Corporation collected the following data on its accounts receivables: Balance of On time paid Never pay account (OT) Late ( LT) (DEL) less than $100 30 6 1 $100 to $500 22 12 2 More than $500 16 7 4 Totals 48 25 7

47)

Find the probability P (LT) that the account paid will be late given that it is less than $100?

48) 59.4% of new vehicles cost under $30,000. 76.4% of vehicles purchased by females cost under $30,000. If we assume a 50/50 gender split, what percentage of vehicles purchased by males cost at least $30,000? Express it as a decimal number.

48)

49) The Accounting Department of the Insurance Corporation collected the following data on its accounts receivables: Balance of On time paid Never pay account (OT) Late ( LT) (DEL) less than $100 30 6 1 $100 to $500 22 12 2 More than $500 16 7 4 Totals 48 25 7

49)

Find the probability that the account is never paid, given that it is less than $100 balance?

50) The probability that a person uses coupon A at a grocery store is 2.7%, while that for coupon B is 6.4%. If the acceptable date for the two coupons never coincide, what is the probability a person checking out at a grocery store uses either coupon? Express it as a decimal number.

50)

51) A survey of 500 corporations segregated them by gross annual incomes and annual expenditures on technology: $100K to $500K to $1 million Tech | Income Under $100K under $500K under $1 million or more Under $10K 22 63 82 8 $10K to under $50K 2 29 112 32 $50K or more 0 10 53 87 What percentage of companies with gross annual incomes of $500,000 or more spend at least $10,000 per year on technology? Express it as a decimal number accurate to 4 decimals.

51)

52) Suppose 80.2% of people recycle at least once a year. You are given the following partial table of the breakdown: 4 or # times 1 2 3 more % x 0.204 0.103 0.012 What is the value of x? Express it as a decimal number.

52)

7

53) The probability it is sunny is a particular region is 58.2%. The probability there is a full-blown blizzard in the same region is 0.6%. What is the probability of either event happening in the region? Express it as a decimal number.

53)

54) The probability that a person under the age of 25 listens to a certain radio station is 50.4%.

The probability that a person aged 55 or older listens to this station is 1.4%. If two people, one from each of the above age groups, are randomly selected, what is the probability that both of them listen to this station. Express it as a decimal number accurate to 4 decimals.

54)

TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.

55) If A and B are independent, then P(A and B) = 0.

55)

56) The set consisting of all possible outcomes of an experiment is called an event.

56)

57) Suppose 70% of people vacation once a year. If we assume a 50/50 gender split, then we can conclude that 35% of those who vacation are male.

57)

58) In a contingency table of gross annual income and gross annual profit for a sample of 1000 companies, one income category is Under $50,000 while one profit category is $50,000 or more. The value of the cell for the intersection of these two categories must be zero.

58)

59) If A and B are independent, then P(A and B) = P(A)*P(B).

59)

60) The percentage of people with annual incomes above $50,000 is 12.4%. The percentage of people whose annual income is above $50,000 that own their own home is 75%. We can conclude the percentage of people with annual income above $50,000 and do not own their own home is 3.1%.

60)

61) If A and B are mutually exclusive, then P(A or B) = P(A) + P(B).

61)

62) A deck of cards has 40 cards; 28 are numbered seven while 12 are yellow. If 5 of the cards are yellow sevens, this means that 5 of the cards are neither yellow nor seven.

62)

63) Suppose 2.5% of people subscribe to both newspaper A and newspaper B. If 28.7% of people do not subscribe to either paper, then the percentage who subscribe to only one of the newspapers is 68.8%

63)

64) The probability it is raining where I live is 15.4%. The probability I am watching TV if it is raining is 60%. Then, the probability that it is raining and I am not watching TV is 40%.

64)

65) 62.5% of executives own a PDA device. However, 92% of executives who own a PDA device work 50 hours per week or more while the corresponding percentage for those who do not own a PDA device is 84%. From this, we can conclude that 5% of those who work less than 50 hours per week own a PDA device.

65)

66) If P(A) = 0.6 and P(A and B) = 0.06, then P(Bc | A) = 0.9.

66)

67) You have two variables A and B. If you know P(A and B) and P(Ac and Bc), this is sufficient information to complete a contingency table.

67)

8

68) The percentage of people who surf the Internet at least once a week is 70.4%. The corresponding percentage for those under 18 is 98%. This means the percentage of those 18 or older who surf the Internet less than once a week is 29.2%.

68)

69) Surveys of business school graduates show that the 85% of the graduates obtain full time employment immediately earning at least $65,000 per year. From this data, we can assume that a new graduate will have the probability of not obtaining a job that pays more than $65, 000 to be 85%.

69)

70) If P(A) = 0.4 and P(A | B) = 0.2, then we can conclude that P(A and B) = 0.08.

70)

71) 20.4% of companies have monthly revenues of $30,000 or more. 16.8% of companies spend at least $500 per month on staff training. 8.3% of companies have monthly revenues of $30,000 or more and spend at least $500 per month on staff training. We can conclude the percentage of companies with monthly revenues under $30,000 and spending less than $500 per month on staff training is 71.1%.

71)

72) If P(A) = 0.54, P(B) = 0.62 and P(A or B) = 0.89, then P(A and B) = 0.27.

72)

73) If P(B | A) = 0.7 and A and B are independent, we can conclude that P(A) = 0.7.

73)

74) The sample space of an experiment contains all possible outcomes.

74)

75) If A and B are mutually exclusive, this means that Ac and Bc are also mutually exclusive.

75)

76) Suppose 24% of people own a flat-screen TV. If we assume a 50/50 gender split and 40% of men own a flat-screen TV, then 4% of women own a flat-screen TV.

76)

77) Suppose people are divided into low, medium and high income. If we know the percentage of low and high income groups, we can compute the percentage of the medium income group.

77)

9

Answer Key Testname: CHAPTER 4 1) B 2) B 3) C 4) D 5) B 6) B 7) D 8) C 9) C 10) B 11) B 12) A 13) B 14) B 15) B 16) A 17) D 18) A 19) A 20) C 21) D 22) D 23) B 24) A 25) C 26) C 27) A 28) C 29) A 30) A 31) A 32) B 33) B 34) D 35) A 36) P (paid | balance < $100) = 36/37= 97.3% 37) 0.113 38) P (more than $500 balance | paid)= 23/73= 31.5% 39) 0.854 40) 0.5926 41) 0.7167 42) 40 43) 0.3185 44) 0.3582 45) 0.1689 46) 0.276 47) P (paid|LT)=16.2% 48) 0.576 49) P (not paid | balance < $100) = 1/37= 2.70% 50) 0.091 10

Answer Key Testname: CHAPTER 4 51) 0.7594 52) 0.483 53) 0.588 54) 0.0071 55) FALSE 56) FALSE 57) FALSE 58) TRUE 59) TRUE 60) TRUE 61) TRUE 62) TRUE 63) TRUE 64) FALSE 65) FALSE 66) TRUE 67) FALSE 68) FALSE 69) FALSE 70) FALSE 71) TRUE 72) TRUE 73) FALSE 74) TRUE 75) FALSE 76) FALSE 77) TRUE

11

Exam

Chapter 5

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1) For a certain distribution, p(x) = (3x + 5)/80, x = 2, 4, 6, 8. What is the value of µ + 3 ?

A) 11.3196 B) 12.0696 C) 11.3595 D) 12.1095

1)

2) The amount of sleep that people get is normally distributed with a mean of 7.25 hours and standard deviation of 45 minutes. Below how many hours of sleep do 1% of people get?

A) 8.9945 B) 5.5025 C) 9.182 D) 5.318

2)

3) Joe invested $5,000 in a portfolio of common stocks on the Toronto Stock Exchange. He estimates that the annual percent returns on his investment is normally distributed with a mean of 25% and standard deviation of 5%. Joe's marginal tax rate is 40%. Calculate the probability that Joe will need to pay the Canada Revenue Agency at least $500 of income tax.

A) 0.55 B) 1-.55 C) 0.45 D) 0.50

3)

4) The standard deviation of a probability distribution can be computed as: A) positive square root of the variance B) square root of expected value C) cube of the variance D) square root of the variance

4)

5) Customers at QuakX Drug Store spend varying amounts of cosmetics. Data collected on customer spending in 2009, per customer, is normally distributed with mean of $125 and standard deviation of $10. Calculate the probability that customers at this store spend at least $110.

A) 0.945 B) 0.067 C) 0.922 D) 0.933

5)

6) The percentage of people who weigh more than 75 kg is 60%. If a random sample of 8 people is selected, what is the probability that at least 2 but no more than 4 of them weigh more than 75 kg?

A) 0.3974 B) 0.3561 C) 0.3867 D) 0.1652

6)

7) The amount of milk in a carton is normally distributed with a mean of 1 L and standard deviation of 2.5 ml. What is the probability a carton has between 998 ml and 1002 ml?

A) 0.5762 B) 0.4238 C) 0.7119 D) 0.2881

7)

1

8)

Number of vehicles crossing the US border point at Point Roberts is given by the following, along with the number of days tracked Number of cars passing Number of Days 0 10 1 20 2 45 3 59 Total 134 What is the probability that in a certain day, there will be no more than 2 cars that will pass the border point?

A) 0.335 B) 0.440 C) 0.559 D) 0.500

8)

9) For a certain distribution, p(x) = (81/130)(2/3)x , x = 1, 2, 3, 4. What is the mean?

A) 1.9066 B) 1.6308 C) 1.8423 D) 2.0154

9)

10) The distance that people travel to work is normally distributed with a mean of 10.2 km and standard deviation of 1.6 km. What is the farthest that 95% of people travel to work?

A) 7.064 km B) 13.336 km C) 7.568 km D) 12.832 km

10)

11) The amount that people spend at a clothing store is normally distributed with a mean of $125 and standard deviations of $60. What is the least amount that 95% of people spend at a clothing store?

A) $26.30 B) $223.70 C) $242.60 D) $7.40

11)

12) For a certain distribution, p(x) = (32/31)(1/2)x where x = 1, 2, 3, 4, 5. What is P(X 2)?

A) 0.5161 B) 0.7741 C) 0.2581 D) 0.4839

12)

13) For a certain distribution, p(x) = x/40 for a set of 5 values. Four of the values are 1, 2, 9 and 16. What is the fifth value?

A) 28 B) 18 C) 12 D) 10

13)

14) The percentage of people who recycle milk jugs is 16.4% on average. If a sample of 20 people is randomly selected, what is the probability that no more than 2 of them recycle milk jugs?

A) 0.2033 B) 0.3402 C) 0.1369 D) 0.3124

14)

15) The time it takes a student to do a certain IQ test is normally distributed with a mean of 40 minutes and standard deviation of 8 minutes. What is the probability a student will take between half an hour and an hour to do the test?

A) 0.0994 B) 0.9006 C) 0.8885 D) 0.1118

15)

16) A random variable that can only take on finite number of data values is referred as: A) infinite sequence B) unfinite sequence C) discrete random variable D) finite sequencing

16)

2

17) In a certain region, the percentage of time that it rains on a given day is 15.5%. If a random sample of 5 days is chosen, what is the probability it rains on less than half of those days?

A) 0.0775 B) 0.9709 C) 0.8259 D) 0.0291

17)

18) In a binomial experiment the probability of success is 0.10. What is the probability of two successes in 10 trials?

A) 0.193 B) 1-.193 C) 0.192 D) 0.199

18)

19) Hot Ovens Company sells kitchen stoves. Company is currently forecasting customer demand to be normally distributed with mean of 100 stoves for the year and standard deviation of 25 units.

What is the probability that the Company will sell at least 50 kitchen stoves this year?

A) 0.22 B) 0.55 C) 0.50 D) 0.98

19)

20) For a certain probability distribution, p(x) = 1/5 where x = 1, 3, 5, 7, 9. What is the standard deviation of this distribution?

A) 5 B) 3.1623 C) 8 D) 2.8284

20)

21) The starting annual salaries of students employed at the Vancouver 2010 Winter Olympics is normally distributed with a mean of $6,000 and a standard deviation of $450.What is the probability that a randomly selected student will get a starting salary of at least $5,000?

A) 0.130 B) 0.495 C) 0.500 D) 0.987

21)

22) The percentage of people who travel overseas on vacation is 8.4% on average. If a sample of 500 people is randomly selected, what is the value of [µ - 3 ] , rounding to the nearest whole number?

A) 23 B) 20 C) 22 D) 24

22)

23)

23)

Number of vehicles crossing the US border point at Point Roberts is given by the following, along with the number of days tracked Number of cars passing 0 1 2 3 Total

A) 0.925

What is the probability that in a given day at least 1 car will pass the border point.

Number of Days 10 20 45 59 134

B) 0.07

C) 0.924

D) 0.999

24) For a certain distribution, x2 p(x) = 250.6 and the mean is 10.4. What is the standard deviation?

A) 142.44 B) 240.2 C) 11.9348 D) 15.4984

24)

25) In a certain factory, the probability of an accident on any given day is 0.55% on average. In a sample of 1,000 days, what is the probability of at least 1 accident?

A) 0.9777 B) 0.004 C) 0.9960 D) 0.0223

25)

3

26) For a certain distribution, p(x) = (9x - 2)/323 for a set of 5 numbers. Four of the numbers are 1, 3, 7 and 15. What is the mean of this distribution?

A) 10.9208 B) 11.2848 C) 11.0557 D) 11.3706

26)

27) Sam is a telemarketer. The probability that Sam makes a sale is 20% on average. If Sam makes 250 sales calls, what is the standard deviation of the number of sales made?

A) 6.3246 B) 40 C) 50 D) 7.0711

27)

28) In a certain region, the daily high temperature is normally distributed with a mean of 18 degrees and standard deviation of 2.5 degrees. What is the probability the high temperature on any given day is below 15 degrees?

A) 0.1151 B) 0.3849 C) 0.8849 D) 0.6151

28)

29) X is a normally distributed random variable with a mean of 35 and a standard deviation of 10. The probability that X is less than 9 is: A) 0.9865 B) 0.00125 C) 0.0047 D) 0.0135

29)

30) The distance travelled by transport trucks per day is normally distributed with a mean of 540 km and standard deviation of 80 km. What is the probability a truck travels between 600 km and 640 km in a day?

A) 0.121 B) 0.5 C) 0.812 D) 0.6678

30)

31) Joe invested $5,000 in a portfolio of common stocks on the Toronto Stock Exchange. He estimates that the annual percent returns on his investment is normally distributed with a mean of 25% and standard deviation of 5%. Joe's marginal tax rate is 40%. Calculate the probability that Joe will need to pay the Canada Revenue Agency at least $500 of income tax. What is the probability that Joe's income tax liability will be less than $500 ?

A) 0.45 B) None of the above C) 0.50 D) 0.55

31)

32) For a normal distribution with a mean of 10 and a standard deviation of 2, calculate the probability of P ( X 12) A) 0.166 B) 0.841 C) 0.159 D) 0.160

32)

33) The percentage of people whose annual income exceeds $100,000 is 1.2%. If 10 people are randomly selected, what is the probability that at least one of them has an annual income of more than $100,000?

A) 0.012 B) 0.1137 C) 0.0061 D) 0.1076

33)

34) The percentage of people who watch a certain TV show is 56%. If a sample of 12 people is randomly selected, what is the probability that exactly 7 of them watch the show?

A) 0.2256 B) 0.1393 C) 0.9607 D) 0.7744

34)

35) For a certain normal distribution, the mean is 20 and the standard deviation is 9.5. What percentage of the distribution lies within 2 standard deviations of the mean?

A) 0.475 B) 0.95 C) 0.9545 D) 0.4773

35)

4

36) The size of a house is normally distributed with a mean of 1640 square feet and standard deviation of 308 square feet. What is the probability a house has more than 2157.44 square feet?

A) 0.0465 B) 0.9535 C) 0.9475 D) 0.0525

36)

37) For a certain distribution, p(x) = x/15, x = 1, 2, 3, 4, 5. What is the mean?

A) 3.0 B) 2.67 C) 3.7

37)

38) For the following binomial distribution, compute P (x=2): n = 10, p=.12 A) 9.73 B) 0.129 C) 0.212

D) 3.67

38) D) 0.233

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

39) The amount that people spend per week on groceries follows a normal distribution with a mean of $175 and standard deviation of $40. What is the probability that a person spends less than $149.80 per week on groceries? Express it as a decimal number accurate to 4 decimals.

39)

40) The amount of TV that people watch per week is normally distributed with a mean of 16.4 hours and standard deviation of 3.2 hours. Above how many hours per week do 95% of people watch TV? Do not round the answer.

40)

41) Suppose the number of times per week that people eat out follows this distribution: X 0 1 2 3 P(x) 0.08 0.52 0.38 0.02 What is the average number of times per week that people eat out? Do not round your answer.

41)

42) A baseball player hits the ball 30% of the time on average. Suppose µ + 3 is a reasonable upper limit on the number of hits the player can expect in a season. If the player bats 600 times in a season, what is the most number of hits he can reasonably expect to get? Round to the nearest whole number.

42)

43) Suppose that in a certain region, the number of thunderstorms per week in the summer follows this distribution: X 0 1 2 3 P(x) 0.03 0.25 0.63 0.09 What is the standard deviation of the number of thunderstorms per week. Round to 4 decimals.

43)

44) Let X represent the number of times per year a certain power generator will break down, x = 0, 1, 2, 3, etc. If P(x) = (1/16)(15/16)x, what is the probability the generator will break

44)

45) The amount that people spend per visit at a certain hotel is normally distribute with a mean of $1,250 and standard deviation of $348. Below what amount do 99% of the hotel's visitors spend per visit? Round to the nearest cent.

45)

down no more than once a year? Express it as a decimal number accurate to 4 decimals.

5

46) For a bolt manufacturing machine, the bolt length is normally distributed with a mean of 2.5 cm and standard deviation of 0.04 cm. What is the probability a bolt's length is between 2.51 cm and 2.54 cm? Express it as a decimal number accurate to 4 decimals.

46)

47) The time needed or a transport truck to travel a certain route is normally distributed with a mean of 10.5 hours and standard deviation of 30 minutes. What is the probability a certain trip will take between 9 hours and 11 hours? Express it as a decimal number accurate to 2 decimals.

47)

48) Suppose the percentage of companies that send a courier package on any given day is 18% on average. For a sample of 10 companies, what is the probability that at least one of them send a courier package on any given day. Express it as a decimal number accurate to 4 decimals.

48)

49) Suppose a bus is late 2% of the time at a certain bus stop on average. In a sample of 9 trips to this stop, what is the probability it is late no more than twice? Express it as a decimal number accurate to 4 decimals.

49)

50) Let X represent the number of times you flip a fair coin until you get a head, X = 1, 2, 3, etc.

If P(x) = (1/2)x, what is the probability you must flip a coin at least 3 times before getting

50)

51) Suppose the percentage of people who subscribe to at least one newspaper is 65% on average. In a sample of 20 people, what is the probability that at least 15 but no more than 17 of them subscribe to at least 1 newspaper? Express it as a decimal number accurate to 4 decimals.

51)

52) The amount that people spend when going out on a weekend is normally distributed with a mean of $54 and standard deviation of $12.50. What is the cutoff for the top 5% of the amount spent? Round to the nearest cent.

52)

53) The percentage of people who buy a lottery ticket at least once a year is 92% on average. If 6 people are randomly selected, what is the probability that at least 5 of them buy a lottery ticket at least once a year? Express it as a decimal number accurate to 4 decimals.

53)

head? Express it as a decimal number but do not round it.

TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.

54) In computing binomial probabilities, it is required that the trials are independent.

54)

55) For a fair die numbered 1 through 6, the standard deviation of the distribution is 1.7078.

55)

56) Given this distribution: X 0 1 p(x) 0.08 0.12 P(X 3) = 0.41

56) 2 0.15

3 0.24

4 0.31

5 0.10

57) If X is normally distributed with a mean of 100.2 and standard deviation of 20.6, then 97.5% of the distribution is below 140.576.

6

57)

58) In a bottle filling plant, the amount of liquid in a bottle is normally distributed with a mean of 540 ml and standard deviation of 0.4 ml. The probability a bottle's contents are within the tolerance limits of 539.2 ml and 540.8 ml is 0.9546.

58)

59) If p(x) = (3x + 5)/50, x = 1, 2, 3, 4, then P(X < 3) = 0.38.

59)

60) In the binomial formula p(x) = (4Cx)(0.2)x(0.8)(4-x), the probability of success is 80%.

60)

61) If X is normally distributed with a mean of 10 and standard deviation of 2.5, then P(X > 12) = 0.8.

61)

62) Suppose the probability of success in a certain binomial trial is 12.5%. In a sample of 50 independent trials, the probability of exactly 7 successes is 0.1528.

62)

63) If p(x) = |x - 3|/15, x = -2, -1, 0, 1 , 2, the mean is 0.

63)

64) Suppose X is normally distributed with a mean of 5 and standard deviation of 2. If X = 3, the corresponding Z value is -1.

64)

65) If X is normally distributed with a mean of 54.6 and standard deviation of 8.4, then 67% of the distribution is above 58.296.

65)

66) For a certain binomial distribution, the probability of success is 0.27. For a sample of 10 independent trials, the probability of at least 1 success is 0.1590.

66)

67) Given x2 p(x) = 209.4 and µ = 10.2, then

= 14.1138.

67)

68) Given this distribution: x 0 2 5 8 p(x) 0.2 0.35 0.18 0.22 the standard deviation is 4.5957.

10 0.05

68)

69) In computing binomial probabilities, P(X 4) = 1 - P(X 4).

69)

70) In computing binomial probabilities, P(X < 3) = P(0) + P(1) + P(2).

70)

71) The 92nd percentile of Z is approximately 1.405.

71)

72) In computing binomial probabilities, the sampling should be done without replacement.

72)

73) If X is normally distributed with a mean of 200.4 and standard deviation of 46.7, then 95% of the distribution is between 123.5785 and 277.2215.

73)

7

Answer Key Testname: CHAPTER 5 1) B 2) B 3) D 4) A 5) D 6) A 7) A 8) C 9) D 10) D 11) B 12) B 13) C 14) B 15) C 16) C 17) B 18) A 19) D 20) D 21) D 22) A 23) A 24) C 25) C 26) C 27) A 28) A 29) C 30) A 31) C 32) C 33) B 34) A 35) C 36) A 37) D 38) D 39) 0.26344 40) 11.136 41) 1.34 42) 214 43) 0.6416 44) 0.1211 45) 2059.45 46) 0.2426 47) 0.84 48) 0.8626 49) 0.9994 50) 0.25 8

Answer Key Testname: CHAPTER 5 51) 0.2333 52) 74.56 53) 0.9227 54) TRUE 55) TRUE 56) FALSE 57) TRUE 58) TRUE 59) TRUE 60) FALSE 61) FALSE 62) TRUE 63) FALSE 64) TRUE 65) FALSE 66) FALSE 67) FALSE 68) FALSE 69) FALSE 70) TRUE 71) TRUE 72) FALSE 73) FALSE

9

Chapter 6 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1) The life span of light bulbs is normally distributed with a mean of 1,000 hours and standard deviation of 56 hours. Bulbs are designed to last a minimum of 994 hours. If a sample of 72 bulbs is randomly chosen, what is the probability the average life span of these bulbs does not meet the minimum standards?

A) 0.1814 B) 0.8186 C) 0.4562 D) 0.9100

1)

2) A simple random sample of 200 observations was taken from a population. The sample mean was determined to be 40, and the population standard deviation was determined to be 18. The standard error of the mean is: A) 2.84 B) 2.28 C) 2.81 D) 1.27

2)

3) The standard deviation of all possible x values is called the: A) standard deviation B) median C) standard error of the mean D) population standard deviation

3)

4) As the sample size increases, the: A) standard error of the mean decreases C) population mean increases

4)

B) standard error of the mean increases D) mean value increases

5) The number of hours per week that people watch TV is normally distributed with a mean of 15.8 hours and standard deviation of 3.3 hours. If a focus group of 8 people is held, what is the probability the amount amount of TV per week they watch is more than 17 hours?

A) 0.3485 B) 0.1515 C) 0.8485 D) 0.0019

5)

6) The percentage of people who buy candy at a grocery store checkout is 8.45% on average. For a sample of 130 people, what is the probability that between 7.92% and 8.68% of them will buy candy?

A) 0.0512 B) 0.1024 C) 0.8770 D) 0.1230

6)

7) The percentage of items returned at a grocery store is 6.4% on average. If a sample of 240 items is randomly chosen, what is the standard error rounded to 4 decimals?

A) 0.0158 B) 0.0163 C) 0.0238 D) 0.0002

7)

8) In a mill, the length of a 2x4 is normally distributed with a mean of 180 cm and standard deviation of 0.12 cm. The board length should be between 179.95 cm and 180.05 cm. For a sample of 24 boards, what is the probability the average length meets the above specifications?

A) 0.9586 B) 0.5207 C) 0.4793 D) 1.0

8)

9) The amount that people spend at a video store is normally distributed with a mean of $12.50 and standard deviation of $3.20. If 256 people are selected at random, what is the standard error?

A) 3.20 B) 0.4 C) 0.0125 D) 0.2

9)

1

10) The amount that goes into a bag of chips has a mean of 50 g and standard deviation of 8.5 g. If 60 bags are randomly chosen, what is the probability the average amount in the bags is between 52 and 53 g?

A) 0.5032 B) 0.5344 C) 0.9624 D) 0.0312

10)

11) The amount of salt in a bag of potato chips is normally distributed with a mean of 1.2 g. You sample 64 bags and the mean is 1.4 g. If the probability that the mean amount of salt for a sample of 64 bags would be this extreme is 0.0548, what is the standard deviation of the parent distribution?

A) 1.125 g B) 0.015625 g C) 1.0 g D) 0.125 g

11)

12) In cutting gears, the tooth angle should be between 1.2 degrees and 1.6 degrees. The tooth angle is normally distributed with a mean of 1.4 degrees and standard deviation of 0.34 degrees. If 6 gears are sampled at a time, what is the probability the average tooth angle of the sample is within the above specifications?

A) 0.8502 B) 0.1498 C) 0.0749 D) 0.8

12)

13) The amount of time that people spend in a grocery aisle follows a right-skewed distribution with a mean of 2.4 minute and standard deviation of 30 seconds. If 100 people are randomly selected, what is the probability the average time they spend in a grocery aisle is less than 2.5 minutes?

A) 0.5120 B) 0.9773 C) 0.0227 D) 0.3707

13)

14) The mean of the all sample means is equal to: A) population standard deviation C) the mean of the original population

14)

B) the mean of the sample D) the distribution of the sample

15) Suppose the level of support for a political candidate is 75%. Fifty people are sampled; the probability their support for the candidate is below a certain point is 0.2061. What is the point, rounding the percentage to the nearest whole number?

A) 80% B) 72% C) 78% D) 70%

15)

16) The probability distribution of all possible values of the sample mean x is:

16)

A) density function of sampling distribution

B) the sampling distribution of x

C) probability density function

D) distribution of sample means

17) The sampling distribution can be approximated normal as long as which of the conditions are met?

A) np 10 and nq 10 B) np 5 and np 5 C) np 5 and nq 10 D) np 10 and pq 10

17)

18) Random samples of size 1025 are taken from a population whose population proportion is 0.7. The standard deviation of the sample proportions is: A) 0.985 B) 0.143 C) 1.44% D) 0.0143

18)

19) For a courier company, the percentage of late deliveries is 0.65% on average. For a sample of 2000 deliveries, what is the probability that fewer than 0.5% of them are late?

A) 0.8348 B) 0.2033 C) 0.1711 D) 0.8289

19)

2

20) The thickness of plastic garbage bags is normally distributed with a mean of 0.5 mm and standard deviation of 0.24 mm. The bags are designed to have a maximum thickness of no more than 0.62 mm. If a sample of 35 bags is randomly chosen, what is the probability the thickness is less than the above specifications?

A) 0.95 B) 0.0015 C) 1.0 D) 0.9985

20)

21) The weight of bananas is normally distributed with a mean of 56 g per banana with a standard deviation of 7.2 g. If a bunch of 6 bananas is randomly chosen, what is the probability the total weight of the bunch is less than 318 g?

A) 0.1539 B) 0.3461 C) 0.8461 D) 0.6539

21)

22) A population has a mean of 85 and a standard deviation of 12. A random sample of 2000 is selected.

22)

The expected value of x is: A) 15

B) 85

C) 0.268

D) 86

23) The percentage of tow trucks used on any given day is 80% on average. Suppose 55 trucks are

23)

^

randomly selected. If P(p > k) = 0.3557, what is the value of k? Round the percentage to the nearest whole number.

A) 82% B) 77% C) 78% D) 81%

24) The percentage of people who buy movie concessions is 55% on average. If 80 people are randomly selected, what is the probability the percentage of these people who bring concessions is between 51% and 58%?

A) 0.0588 B) 0.0304 C) 0.4696 D) 0.9412

24)

25) The average distance travelled by truck drivers is normally distributed with a mean of 402 km per day with a standard deviation of 28 km per day. If a sample of 12 truck drivers is randomly selected, what is the probability the average distance they travel per day is between 410 and 425 km?

A) 0.1633 B) 0.8411 C) 0.8367 D) 0.1589

25)

26) The amount that people spend on vacation is skewed left with a mean of $1,500 and standard deviation of $540. If 120 people are randomly selected, what is the probability the average amount they spend is: between $1,400 and $1,525?

A) 0.6738 B) 0.9050 C) 0.2838 D) 0.5212

26)

27) The percentage of people who watch a particular TV show is 25% on average. If a sample of 100 people is taken, what is the probability the percentage of these people who watch the show is less than 22%?

A) 0.2358 B) 0.6928 C) 0.7242 D) 0.2451

27)

28) A population has a mean of 300 and a standard deviation of 50. A sample of 155 observations will be taken. The probability that the sample mean will be between 200 to 385 is: A) 0.495 B) virtually 1 C) 0.067 D) 0.500

28)

29) The percentage of people who eat a certain brand of cookie is 15% on average. You sample a certain number people. Suppose the probability that fewer than 12% of these people eat this brand is 0.2579. What is the sample size?

A) 60 B) 50 C) 58 D) 62

29)

3

30) The amount of milk going in a carton is normally distributed with a mean of 1 L and standard deviation of 15 ml. For a sample of 100 cartons, what is the probability the mean is greater than 1003 ml?

A) 0.0228 B) 0.9775 C) 0.9545 D) 0.4773

30)

31) The percentage of companies who recycle scrap paper is 32% on average. If 54 companies are randomly selected, what is the probability the percentage of these companies that recycle scrap paper is between 29% and 31%?

A) 81.9% B) 94.0% C) 24.0% D) 11.7%

31)

32) The percentage of people who recycle is 25% on average. A sample of 80 people is taken. What is the probability that the percentage of these people who recycle is more than 20%?

A) 0.1515 B) 0.6970 C) 0.3485 D) 0.8485

32)

33) The percentage of candidates who earn a certain professional designation is 16.2% on average. In a sample of 75 candidates, what is the probability that at least 15% of them will earn the professional designation?

A) 0.3897 B) 0.6217 C) 0.2821 D) 0.6103

33)

34) The percentage of people who return videos on time is 92.4% on average. In a sample of 150 people, what is the probability that more than 95% of them will return the video on time?

A) 0.9279 B) 0.1151 C) 0.4279 D) 0.0721

34)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

35) The amount of time people spend in a clothing store is normally distributed with a mean of 18 minutes and standard deviation of 4 minutes. If a sample of 20 customers is randomly selected, what is the probability they will spend more than 20 minutes on average in a clothing store?

35)

36) The percentage of homes with advanced technology is 7.2% on average. If a sample of 425 homes is randomly selected, what is the probability that between 6.75% and 8.35% of them have advanced technology?

36)

37) The amount of thread on a spool is normally distributed with a mean of 237 cm and standard deviation of 2 mm. If 32 spools are randomly selected, what is the probability the average amount on a spool is between 236.95 and 236.98 cm?

37)

38) The percentage of people who buy additional accessories when they buy a computer is 47.8% on average. For a random sample of 800 people, what is the probability that the percentage who buy additional accessories is between 45.7% and 46.2%.

38)

39) The amount of sleep that people get has a mean of 7.25 hours with a standard deviation of 48 minutes. If a sample of 68 people is randomly selected, what is the probability the average amount of sleep for these people is less than 7 hours?

39)

40) The hardness of steel is uniformly distributed with a mean of 60 units and standard deviation of 5.77 units. If a sample of 65 pieces is randomly selected, what is the probability their average hardness is between 58 and 61 units?

40)

4

41) The average success rate for a telemarketer is 5.2%. In a sample of 200 calls, what is the probability the average success rate is between 5.5% and 6%?

41)

42) The life span of a washing machine is normally distributed with a mean of 15 years and 3 months with a standard deviation of 4 years and 9 months. If a sample of 12 machines is randomly selected, what is the probability their average life span is between 16 and 20 years?

42)

43) The percentage of companies with fewer than 5 employees is 87.3%. If a sample of 400 companies is randomly selected, what is the probability that fewer than 92% of them have fewer than 5 employees?

43)

44) The percentage of people who recycle their old phone books is 15.8% on average. If 240 people are randomly selected, what is the probability that more than 20% of them recycle their phone book?

44)

45) This Section Intentionally Left Blank

45)

46) The percentage of people who buy snacks at a video store is 17% on average. If a sample of 84 people is randomly selected, what is the probability that fewer than 15% of them buy snacks at a video store?

46)

47) The percentage of cars in which the gas gauge is below the quarter mark is 29.8% on average. If a sample of 210 cars is randomly selected, what is the probability that between 25% and 32% have the gas gauge below the quarter mark?

47)

48) The percentage of people with advanced degrees is 16.5% on average. If 1000 people are randomly selected, what is the probability that the percentage of these people with advanced degrees is between 17% and 18.5%?

48)

49) This Section Intentionally Left Blank

49)

50) The average number of pages in a novel is 326 with a standard deviation of 24 pages. If a sample of 50 novels is randomly chosen, what is the probability the average number of pages in these books is between 319 and 331?

50)

51) The amount of carbon dioxide absorbed by a tree follows a normal distribution with a mean of 20 kg per hour with a standard deviation of 6.8 kg per hour. If a sample of 24 trees is randomly selected, what is the probability the average amount of carbon dioxide absorbed by these trees is more than 24.2 kg per hour?

51)

TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.

52) In a print shop, the percentage of flyers that are scrapped is 20.2% on average. If a sample of 150 flyers is randomly chosen, the probability that between 18.2% and 24.5% of them are scrapped is 0.6340.

52)

53) The percentage of trucks on any given day carrying no load is 12.3% on average. If 90 trucks are randomly chosen, the probability that fewer than 10% of them are carrying no load is 0.2546.

53)

5

54) The percentage of magazine returned to printers is 9.7% on average. If a sample of 500 magazines is randomly selected, the probability that fewer than 8.5% of them will be returned is 0.1814.

54)

55) For students taking an IQ test, the IQs are normally distributed with a mean of 108.3 and standard deviation of 5.62. If a sample of 15 students is randomly selected, the probability their average IQ is between 107 and 110 is 0.6949.

55)

56) In a maternity ward, the percentage of underweight babies is 2.75% on average. If 400 babies are randomly selected, the probability that between 2.5% and 3.25% of them are underweight is 0.3379.

56)

57) The percentage of luggage opened for inspection at airports is 11.7% on average. If 110 pieces of luggage are randomly selected, the probability that between 12% and 15% of them will be inspected is 0.3201.

57)

58) The time between customers in a convenience store follows a non-normal continuous distribution with a mean of 3 minutes and standard deviation of 3 minutes. For a sample of 60 customers, the probability the average time between these customers is less than 2.5 minutes is 9.85%.

58)

59) The speed of a fastball is normally distributed with a mean of 95 mph and standard deviation of 1.8 mph. If a sample of 24 fastballs is randomly selected, the probability the average speed of these fastballs is more than 96 mph is 0.4967.

59)

60) The weight of luggage is normally distributed with a mean of 9.75 kg per piece and standard deviation of 2.02 kg. If a person boarding an airplane has 4 pieces of luggage, the probability the total weight of all 4 pieces is less than 38.4 kg is 0.4842.

60)

61) The amount that people spend at fast-food restaurants is normally distributed with a mean of $8.50 and standard deviation of $1.42. If a sample of 8 people is taken, the probability the average amount for these people is between $8.75 and $9.00 is 0.1498.

61)

62) The amount of time people spend per day on the Internet is normally distributed with a mean of 2.4 hours and standard deviation of 15 minutes. A sample of 20 people is chosen. The probability the average time they spend is less than 2.5 hours is 0.9633.

62)

63) The amount of water flowing through a new type of water faucet has a mean of 2.0 L per minute with a standard deviation of 132 ml. If a sample of 70 faucets is randomly selected, the probability the average amount for these faucets is between 1.95 L and 1.98 L is 0.8968.

63)

64) The amount of carbon dioxide emissions per hour from a certain make of automobile is normally distributed with a mean of 9.8 kg and standard deviation of 1.72 kg. A sample of 10 automobiles is randomly selected. If the goal is for the average of these vehicles to be less than 10 kg, the probability of meeting the goal is 0.3677.

64)

65) The percentage of pop cans containing more than 30 ml of syrup is 8.42% on average. If a sample of 20 cans is randomly chosen, the probability that more than 9.23% of them contain more than 30 ml of syrup is 0.3783.

65)

6

66) The amount of time it takes people to drive to work is slightly skewed left with a mean of 50 minutes and standard deviation of 20 minutes. If a sample of 165 people is randomly selected, the probability the average time for these people is less than three-quarters of an hour is 0.9994.

66)

67) The percentage of computers costing less than $800 is 57.3%. If a sample of 84 computers is randomly selected, the probability that more than 64% of them cost less than $800 is 0.1075.

67)

68) The weight of parcels sent by courier has a mean of 10.2 kg with a standard deviation of 1.77 kg. If a truck has 60 parcels, the probability the total weight of them exceeds 252 kg is 0.9951.

68)

69) The percentage of people who travel on vacation is 64% on average. If 50 people are randomly chosen, the probability that more than 68% of them travel on vacation is 0.2709.

69)

70) In a hospital emergency room, 8.5% of patients wait more than 12 hours to see a doctor on average.

If 150 patients are randomly selected, the probability that between 5% and 7.5% of them will wait more than 12 hours is 0.6082.

70)

71) In a computer program, the number of bugs follows a certain discrete distribution with a mean of 1.5876 bugs per 100,000 lines and standard deviation of 1.26. For 150 sets of 100,000 lines, the probability that the average number of bugs exceeds 1.5 is 0.1977.

71)

7

Answer Key Testname: CHAPTER 6 1) A 2) D 3) C 4) A 5) B 6) D 7) A 8) A 9) D 10) D 11) C 12) A 13) B 14) C 15) D 16) B 17) A 18) D 19) B 20) D 21) A 22) B 23) A 24) C 25) D 26) A 27) D 28) B 29) A 30) A 31) D 32) D 33) D 34) B 35) 0.0125 36) 0.4618 37) 0.03 38) 0.0644 39) 0.005 40) 0.9166 41) 0.1196 42) 0.2909 43) 0.9976 44) 0.0375 45) 46) 0.3121 47) 0.6937 48) 0.289 49) 50) 0.9095 8

Answer Key Testname: CHAPTER 6 51) 0.0012 52) TRUE 53) TRUE 54) TRUE 55) TRUE 56) FALSE 57) TRUE 58) TRUE 59) FALSE 60) FALSE 61) TRUE 62) TRUE 63) FALSE 64) FALSE 65) FALSE 66) FALSE 67) TRUE 68) FALSE 69) FALSE 70) FALSE 71) FALSE

9

Chapter 7 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1) In conducting a test to see if the percentage of people who regularly recycle has significantly increased from 12.4% from 2 years ago, the p-value was 0.0329. What is the value of the Z score?

A) 1.84 B) -1.92 C) -1.84 D) 1.92

1)

2) A biologist wanted to determine if the average radiation in a work place was significantly less than 2 Ci after installing new screens. In a series of readings, the mean was 1.8 Ci, the standard deviation was 0.4 Ci and the t score was -1.5. What was the number of readings?

A) 9 B) 3 C) 4 D) 10

2)

3) A bank added one more teller in an effort to significantly reduce average wait times to below 8.5 minutes. In a sample of 60 customers, the standard deviation was 2.48 minutes and the t score was -5.465904. What was the sample mean?

A) 6.75 B) 10.25 C) 7.50 D) 9.75

3)

4) A researcher examined 14 educational institutions to determine if there was a significant increase in average tuition from 2 years ago. If the test is conducted at a 5% level of significance, what is the critical value?

A) 3.012 B) 2.977 C) 1.771 D) 1.761

4)

5) A demographer wanted to determine if the average number of children per household was significantly less than 1.8. A survey of 500 households had a standard deviation of 0.8 and a t score of -5.590170. What is the sample mean?

A) 1.4 B) 2.0 C) 1.6 D) 2.2

5)

6) An educational researcher wanted to determine if the percentage of home-schooled children had significantly dropped from 3.2% in the past 5 years. A survey of 625 households with school-age children indicates that 25 of them do home schooling. What is the p-value of the test?

A) 0.1271 B) 0.8461 C) 0.1539 D) 0.8729

6)

7) The following data was collected as a simple random sample: 12, 35, 42, 74, 65 The point estimate of the population standard deviation is A) 609.3 B) 24.68 C) 26.00

7) D) 11.04

8) In a one-tailed hypothesis test (lower tail) the test statistic is determined to be -3. The p-value for this test is A) 0.0050 B) 0.0027 C) 0.9987 D) 0.0013

8)

9) A marketing research company conducted an online survey on the economic benefits of the 2010 Winter Olympics on the local economy. Sample survey found 288 consumers were optimistic about the results of the Olympics. Assume 545 consumers were surveyed in total. At 95% confidence level, compute the standard error of the sample proportion A) 0.528 B) 0.0412 C) 0.0214 D) -1.96

9)

1

10) An urban planner wanted to determine if the percentage of people taking transit to work had significantly increased from 30% from 5 years ago. In a survey of 600 people, 168 take transit to work. What is the p-value of the test?

A) 0.1379 B) 0.1423 C) 0.8621 D) 0.8577

10)

11) An automobile manufacturer wanted to determine if the average number of years that people own a vehicle has significantly changed from 8.4 years. A focus group of 6 people had the following results: 8, 5, 5, 2, 6, 5. Analysis of the data indicates it is normally distributed. What is the value of the t score?

A) 4.2845 B) -4.2845 C) -4.0808 D) 3.9112

11)

12) An appliance store wanted to determine if the percentage of people owning a certain type of TV was significantly higher than 18%. In a survey of 380 people, 76 do. What is the p-value of the test?

A) 0.8340 B) 0.8437 C) 0.1660 D) 0.1563

12)

13) A clothing store held a focus group of 10 people to determine if the average amount spent per year on clothing was significantly more than $500. If the test is conducted at a 5% level of significance, what is the critical value?

A) 1.833 B) 2.262 C) 2.228 D) 1.812

13)

14) In a two-tailed hypothesis test, the test statistic is computes to be Z = -2.5. The p-value for this test is A) 0.9938 B) 0.0124 C) 0.0062 D) 0.500

14)

15) A medical researcher wants to determine if the percentage of smokers is significantly less than 20% from 5 years ago. In a survey of 500 people, 92 smoke. What is the p-value of the test?

A) 0.8133 B) 0.1788 C) 0.1867 D) 0.8212

15)

16) The manager of a bakery has taken a random sample of 25 customers. The average length of time it takes the customers during the cashier serving time was 5.4 minutes with a standard deviation of 0.25 minutes. The manager wishes to test to determine whether or not the mean cashier serving time of all customers is significantly more than 5 minutes. Test statistic for this sample is 8.

Compute the p value A) close to zero B) 0.999 C) 0.500 D) 0.157

16)

17) In conducting a test to determine if the average heating bill has significantly increased from $137 per month, the critical value used at a 1% level of significance was 2.681. What was the sample size?

A) 12 B) 13 C) 14 D) 11

17)

18) A political party conducted a poll to see if its level of support had significantly changed from 32%.

If the p-value is 1%, what is the magnitude of the test statistic?

A) 2.576 B) 2.0738 C) 2.326 D) 2.173

18)

19) A company instituted new safety measures in an effort to reduce the percentage of weeks with at least 1 safety incidents to below 14%. In a sample of 100 weeks, 9 of them had at least 1 safety incident. What is the value of the Z score?

A) -1.4410 B) 1.7471 C) -1.7471 D) 1.4410

19)

2

20) A TV executive wanted to determine if the percentage of people watching a certain show after running ads for it was significantly higher than 12%. The sample proportion from a survey was 15% and the Z score was 2.145291. What was the sample size?

A) 568 B) 548 C) 540 D) 562

20)

21) A home renovation store wanted to see if the average annual amount that people spend on home renovations has significantly changed from $1,200 from 5 years ago. If the test is conducted at a 5% level of significance, the critical value is 2.101. What is the sample size?

A) 18 B) 20 C) 17 D) 19

21)

22) Weekly average sales data at a retail store captured after an extensive marketing campaign is as follows: $4,666 $6,700 $4,500 $5,550 $4,768 $4,950 $5,225

22)

The average sales at this store before the marketing campaign was $6,000 per week. Does the sample data collected after the marketing campaign indicate that the new marketing campaign had indeed increased the weekly sales? Use a 5% significance level A) The p-value is 0.0615, greater then the level of significance and therefore not evidence for increased sales B) A larger sample size is needed to test this hypothesis C) There is no strong evidence that the weekly average sales increased as a result of the marketing campaign as the the p-value is greater than the level of significance D) The sample size (n=6) is too small to test this hypothesis

23) A travel agency conducted a survey to determine if the percentage of people going overseas for vacation has significantly changed from 4.2%. A survey of people gave a sample proportion of 4.8% and a Z score of 0.813691. What was the sample size?

A) 840 B) 27 C) 740 D) 29

23)

24) A company ran an ad campaign to raise its brand awareness above 6%. After the campaign, the company surveyed 500 people; 36 were aware of the brand name. What is the p-value of the test?

A) 0.8508 B) 0.8708 C) 0.1292 D) 0.1492

24)

25) The manager of a bakery has taken a random sample of 25 customers. The average length of time it takes the customers during the cashier serving time was 5.4 minutes with a standard deviation of 0.25 minutes. The manager wishes to test to determine whether or not the mean cashier serving time of all customers is significantly more than 5 minutes. Test statistic for this sample is A) 7.5 B) 0.4 C) 8 D) 1.6

25)

26) A theatre chain wanted to determine if the percentage of people aged 30-44 going to the movies at least once every other month had significantly dropped from 32% 5 years ago. A survey of 400 people in this age group gave a Z score of -1.714986. What is the sample proportion?

A) 26% B) 36% C) 28% D) 38%

26)

3

27) A researcher wanted to determine if the percentage of manufacturing firms violating environmental standards was significantly less than 10%. In a study of 300 firms, the Z score was -2.545584. What is the value of the sample proportion?

A) 12.7% B) 6.8% C) 5.6% D) 13.2%

27)

28) A researcher wanted to determine if the average amount spent by companies on software was significantly less than $1,500 per year. In a survey of 600 companies, the t store was -2.848244 with a standard deviation of $215. What is the value of the sample mean?

A) 1,538 B) 1,452 C) 1,475 D) 1,525

28)

29) An addictions researcher wanted to determine if the average amount per week that people spend on lottery tickets has significantly changed from $9.42. In a survey of 750 people, the average was $10.52 with a standard deviation of $3.67. What is the value of the t score?

A) 8.2084 B) -7.6284 C) -8.2084 D) 7.6284

29)

30) A researcher wanted to see if the average time for people to get to work is significantly higher than 20 minutes. In a survey of 100 people, the average time was 22.3 minutes with a standard deviation of 8.4 minutes. Analysis of the data indicates that travel times are normally distributed. What is the value of the t score?

A) -2.8409 B) 2.8409 C) -2.7381 D) 2.7381

30)

31) The Department of Commerce (DC) reported that in 2009 the average number of new retail jobs created per each city in British Columbia was 4500. The DC provided the following information regarding a sample of 8 cities in 2009.

4600 4750 3400 4250 4744 4120 5235 6245

31)

What is the sample mean and the standard deviation?

A) 837 and 6245 B) 4668 and 837 C) 296 and 4668

D) 4668 and 296

32) A health club wanted to determine i the percentage of people who exercise regularly has significantly changed from 24% from 2 years ago. In a survey of 450 people, 99 exercise regularly.

What is the p-value of the test?

A) 0.6778 B) 0.1611 C) 0.8389 D) 0.3222

4

32)

33) The Department of Finance provided the following information regarding the new retail jobs created in a sample of 5 cities in 2009. The average number of new jobs created per city estimated to be 3320. We want to determine whether there has been a significant decrease in the average number of jobs created. State the null and the alternative hypotheses 4500 3600 3500 2750 225 A) Ho: µ > 3320 Ha : µ < 3320

B) Ho: µ > 4150

C) Ho: µ 4150

Ha : µ < 4150

Ha : µ < 4150

33)

D) Ho: µ 3320

Ha : µ < 3320

34) A coffee company wanted to determine if the average number of cups of coffee per day that people drink has significantly changed from 5. If the company surveys 15 people and conducts the test at a 1% level of significance, what is the critical value?

A) 2.977 B) 2.602 C) 2.624 D) 2.947

34)

35) The sample statistic, such as x, s, or p, that provides the point estimate of the population parameter is known as A) point estimator B) sample proportion C) population parameter D) population statistic

35)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

36) A marketing research company conducted an online survey on the economic benefits of the 2010 Winter Olympics on the local economy. Sample survey found 288 consumers were optimistic about the results of the Olympics. Assume 545 consumers were surveyed in total. Compute the value of the sample proportion.

36)

37) A researcher wanted to determine if the average price of an online book was significantly less than $20. The summary statistics from the research were a mean of $18.40 and standard deviation of $3.82. The t score was -3.376862. How many online books did the researcher sample?

37)

38) A consumer researcher wanted to determine if the average cost of calculator is less than $30. For a random sample of 6 calculators, these were their prices; $29.99, $32.96, $20.98, $9.99, $15.98, $18.98. Analysis of the data indicates it is normally distributed. What is the value of the t score? Round to 4 decimals.

38)

39) A political party wanted to determine if the percentage of people supporting a certain bill was significantly higher than 50%. In a survey of 900 people, 462 support the bill. What is the value of the Z score? Round to 1 decimal.

39)

40) A social service agency wanted to determine if the percentage of families living below the poverty line was significantly lower than 12.4%. In a study of 850 families, 82 were living below the poverty line. If the p-value is calculate by hand, what is its value? Express it as a decimal number accurate to 4 decimals.

40)

5

41) A phone company wanted to determine if the percentage of people spending more than $20 per month on long distance was significantly higher than 55%. It surveyed 600 people.

The Z test was 3.446562. What was the sample proportion? Express it as a decimal number accurate to 2 decimals.

41)

42) A restaurant wanted to determine if the average bill had significantly changed from $32 since undergoing renovations. If it samples 10 bills and conducts a test at a 1% level of significance, what is the critical value? Round to 2 decimals.

42)

43) A computer firm wanted to determine if the percentage of customers helped on the first call was significantly higher than 90%. In a sample of calls, the sample proportion was 92% and the Z score was 1.914854. What was the sample size?

43)

44) An oil firm held a focus group of 8 people to determine if people spend more than $40 per week for gasoline on average. If the test is conducted at a 5% level of significance, what is the critical value?

44)

45) A researcher conducted a focus group of 12 professionals to determine if the average amount of sleep professionals get is significantly less than 7.5 hours per night. If the test is conducted at a 1% level of significance, what is the critical value?

45)

46) A moving company wanted to determine if the percentage of people moving at least once every 5 years had significantly changed from 38%. In a survey of 1,000 households, 352 had done so. What is the value of the Z score? Round to 4 decimals.

46)

47) A marketing research company conducted an online survey on the economic benefits of the 2010 Winter Olympics on the local economy. Sample survey found 288 consumers were optimistic about the results of the Olympics. Assume 545 consumers were surveyed . At 95% confidence level, compute the z value .

47)

48) A researcher wanted to determine if the average student loan is significantly higher than $20,000 upon graduation. For a sample of 500 graduates, their average was $21,406 with a standard deviation of $5,420. What is the value of the t score? Round to 4 decimals.

48)

49) A school board wanted to determine if the percentage of students achieving a passing grade on provincial achievement exams changed significantly from 87% the previous year.

In a sample of 800 students, 718 passed. If the p-value is calculated by hand, what is its value? Express it as a decimal number accurate to 4 decimals.

49)

50) A bank wanted to determine if the percentage of people who pay their bills online is significantly higher than 18%. In a survey of 500 people with online access, 105 do. If the p-value is calculated by hand, what is its value? Express it as a decimal number accurate to 4 decimals.

50)

51) A researcher wanted to determine if the average time for adults to complete a certain IQ test was significantly longer than half an hour. In a sample of 150 adults, the average was 42 minutes. The t score was 6.123724. What was the standard deviation? Round to the nearest whole number.

51)

6

52) A home manufacturer wanted to determine if the average winter monthly heating cost for homes with upgraded insulation was significantly less than $120. For a sample of 100 such homes, their average was $109 with a standard deviation of $32.50. What is the value of the t score? Round to 4 decimals.

52)

TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.

53) A coffee shop wanted to determine if the average amount that office workers spend per week on coffee would be significantly different than $20. A survey of 10 people had a mean of $22.64 with a standard deviation of $4.05. Analysis of the data indicates it is normally distributed. This indicates the p-value would be between 5% and 10%.

53)

54) You have the hypothesis: Ho: µ 2.4, Ha : µ > 2.4. You have the following statistics: mean = 2.47,

54)

55) A quality control program at a bottling plant ensures the machines will be adjusted if the mean amount filling a bottle is significantly different from 540 ml at a 10% level of significance, based on a sample size of 30 and standard deviation of 0.4 ml. For one such sample, the mean was 539.7 ml.

This indicates the machine does not need to be adjusted.

55)

56) You are conducting a test at a 10% level of significance. If the p-value of the test were 23.8%, you not reject the null hypothesis.

56)

57) In conducting a test for one mean, a histogram is slightly skewed left but has just one mode.

However, the t distribution is appropriate since the t test is robust to non-normality.

57)

58) A city planner wants to determine if the percentage of inner-city dwellers who take more than 15 minutes to get to work is significantly less than 8%. A survey of 250 inner-city dwellers shows that 10 of them take more than 15 minutes to get to work. If this test were conducted at a 2.5% level of significance, you would not reject the null hypothesis.

58)

59) You have the hypothesis Ho: p = 8%, H a : p 8%. The sample proportion is 48/450 based on a

59)

60) You conducted a test at a 5% level of significance and rejected the null hypothesis. This means you would reject the null hypothesis at a 10% level of significance.

60)

61) If you increase the probability of committing a Type I error, you decrease the probability of committing a Type II error.

61)

62) You have the hypothesis: Ho: µ 150, Ha : µ < 150. You have the following statistics: mean = 140.2,

62)

63) You are conducting a test at a 5% level of significance. If the p-value of the test is 2.4%, you would reject the null hypothesis.

63)

standard deviation = 0.092, n = 18. If you were testing at a 1% level of significance, you would reject the null hypothesis.

sample of 450. The p-value is 0.0183.

standard deviation = 21.1, n = 15. You would reject the null hypothesis at a 2.5% level of significance, but not at 5%.

7

64) Widgets Company produces widgets. One of their widgets is a 5 mm thick. To ensure that the thickness of this type of widget meets the 5 mm specification production criterion, random widgets are selected. A random ample of 25 widgets had a mean thickness of 5.6 mm with a standard deviation of 0.2 mm. At 95% confidence using the p value test criterion, we can reject the hypothesis that the mean thickness of the population is significantly more than 5.6 mm.

64)

65) A survey of 600 people is conducted to determine if people spend significantly more than $160 per week on average for groceries. The mean from the survey was $158. This indicates that the p-value would be greater than 50%.

65)

66) An educational researcher wants to determine if grade 5 students spend significantly more than 10 hours per week on homework on average. The following statistics were compiled: mean = 11.2, standard deviation = 2.7, n = 20. If the test were conducted at a 2.5% level of significance, you would reject the null hypothesis.

66)

67) You have the hypothesis Ho: p = 21%, Ha : p 21%. The sample proportion is 18% based on a

67)

68) You have the hypothesis Ho: µ 10, Ha : µ < 10. In conducting the test, you do not reject the null

68)

69) A stock analyst wants to determine if the percentage of middle-upper income earners who invest in mutual funds has significantly changed from 42% from 2 years ago. A survey of 320 people in this income bracket shows that 158 do. The Z score is 2.6388.

69)

70) You have the hypothesis Ho: µ 5, Ha : µ > 5. In conducting the test, you reject the null hypothesis.

70)

71) A researcher wants to determine if the percentage of people who recycle newspapers is significantly different than 14.2%. In a survey of 900 people, 133 do. The p-value of the test is 61.7%.

71)

72) You have the hypothesis Ho: p = 2%, H a : p 2%. If the sample size is 800 and is less than 5% of the

72)

73) A radio station wanted to determine if the percentage of people aged 18-24 listening to it had significantly changed from 65% from the year before. Of 724 people in this age bracket who were surveyed, 506 listen to the station. This indicates the p-value of the test is 0.58%.

73)

sample of 400. You would reject the null hypothesis at a 5% level of significance but not at 10%.

hypothesis. The actual population mean is 12.4. You committed a Type II error.

The actual population mean is 6.2. You committed a Type I error.

population size, the sampling distribution of the sample proportion is approximately normal.

8

Answer Key Testname: CHAPTER 7 1) A 2) A 3) A 4) C 5) C 6) A 7) B 8) D 9) C 10) D 11) C 12) D 13) A 14) B 15) C 16) A 17) B 18) A 19) A 20) C 21) D 22) C 23) C 24) C 25) C 26) C 27) C 28) C 29) A 30) D 31) B 32) D 33) A 34) A 35) A 36) 52.8% 37) 65 38) -2.4163 39) 0.8 40) 0.0073 41) 0.62 42) 3.25 43) 825 44) 1.895 45) -2.718 46) -1.8242 47) -1.96 48) 5.8006 49) 0.0208 50) 0.0401 9

Answer Key Testname: CHAPTER 7 51) 24 52) -3.3846 53) TRUE 54) TRUE 55) FALSE 56) TRUE 57) TRUE 58) FALSE 59) FALSE 60) TRUE 61) TRUE 62) FALSE 63) TRUE 64) TRUE 65) TRUE 66) FALSE 67) FALSE 68) FALSE 69) FALSE 70) FALSE 71) TRUE 72) TRUE 73) TRUE

10

Chapter 8 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1) A survey of 30 executives indicates they spend an average of 32.4 days per year on business travel with a standard deviation of 7.2. A confidence interval of the average number of days executives spend on business travel ranges from 29.163617 to 35.636383. What is the level of confidence?

A) 98% B) 95% C) 90% D) 99%

1)

2) An engineer conducted a series of tests on a new type of engine to determine how far it would go on 40 L of gasoline. The average was 624 km with a standard deviation of 9.75 km. What would be the required sample size for subsequent tests if the researcher wants a 99% level of confidence and to be accurate to within 1.6 km?

A) 196 B) 258 C) 201 D) 247

2)

3) Suppose a printer toner production company wishes to estimate the average number of days a toner will last before the paint impression on paper does not meet the print quality criterion. 10 randomly chosen toner are tested for a number of days to assess toner failure. The sample data is shown below 12 5 6 8 19 12 13 14 15 11 Form a 99% confidence interval for the mean number of days before the toners fail. What is the interval half width.

A) 4.37 B) 3.25 C) 15.87 D) 7.13

3)

4) A restaurant wanted to estimate the percentage of people who eat out at least once a week. A survey of 400 people showed that 56 of them eat out at least once a week. If a 95% confidence interval is built of the actual percentage of people who eat out at least once a week, what is the lower limit of the interval?

A) 0.1178 B) 0.1115 C) 0.0996 D) 0.1060

4)

5) A researcher wants to estimate the percentage of companies that give at least $500 per year to charity. The researcher had no prior information to work with. What would be the required sample size at a 99% level of confidence if the researcher wants to be accurate to within 3.2%?

A) 402 B) 1,626 C) 661 D) 1,321

5)

6) A researcher wants to estimate the hardness of steel produced using a certain process. In a sample of 24 trials, the average was 68.2 units with a standard deviation of 5.04 units. Analysis of the data indicates it is normally distributed. If a 95% confidence interval of the average hardness is constructed, what is the upper limit of the interval?

A) 70.3234 B) 69.9572 C) 69.9603 D) 70.3286

6)

1

7) A survey of 1,000 people indicates that 204 of them have someone else prepare their income tax return for them. If a 90% confidence interval were constructed of the actual percentage of people who have someone else prepare their tax return, what would be the half-width of the interval?

A) 0.0328 B) 0.021 C) 0.025 D) 0.0296

7)

8) A focus group of 8 realtors was asked to estimate how much time per week they spend on paperwork. These are the results in minutes: 86, 75, 93, 105, 104, 111, 64, 87. Analysis of the data indicates the times are normally distributed. If a 90% confidence interval of the average time realtors spend per week is constructed, what is the upper limit of the interval, rounding to the nearest whole number?

A) 98 B) 109 C) 101 D) 116

8)

9) A focus group of 16 companies was asked to estimate the annual amount spent on staff training.

For this group, the average was $1,247 with a standard deviation of $313. If we construct a 99% confidence interval of the average amount spent per year by companies on staff training, what is the upper limit of the confidence interval, rounding to the nearest dollar?

A) $1,384 B) $1,478 C) $1,475 D) $1,426

9)

10) A researcher wants to estimate the percentage of people who make a major purchase at least once every 5 years. However, the researcher does not have any prior data to draw from. What is the required sample size at a 95% level of confidence if the researcher wants to be accurate to within 2.5%?

A) 1,083 B) 2,655 C) 2,165 D) 1,537

10)

11) The manufacturer of cell phones wishes to determine the magnitude of malfunction problems with the new 4 G cell phones. How many 4 G failed phones should the company test given that the estimate of the true proportion is 0.1, with 95% confidence interval and a sampling error of 0.01?

A) 3584 B) 3458 C) 2500 D) 3499

11)

12) A survey of 200 people indicated that 32 of them chew gum. If a 95% confidence interval were constructed of the actual percentage of people who chew gum, what would be the lower limit of the confidence interval?

A) 0.1065 B) 0.1174 C) 0.1184 D) 0.1092

12)

13) A researcher wants to examine the percentage of companies that use the services of a certain courier firm. Based on prior information, 44.6% of companies use this firm. What is the required sample size if the researcher wants a 97.36% level of confidence and to be accurate to within 4.2%?

A) 539 B) 746 C) 691 D) 702

13)

14) A survey of 500 people indicated that 124 of them watch a particular TV show. If we compare the 95% confidence interval to the 99% confidence interval of the actual percentage of people who watch the show, what would be the change in the half-width?

A) 0.0119 B) 0.0242 C) 0.0108 D) 0.0132

14)

2

15) Suppose a printer toner production company wishes to estimate the average number of days a toner will last before the paint impression on paper does not meet the print quality criterion. 10 randomly chosen toner are tested for a number of days to assess toner failure. The sample data is shown below 12 5 6 8 19 12 13 14 15 11 Estimate the interval upper limit value assuming the confidence level is 99% A) 15.87 B) 4.37 C) 7.13 D) 1.34

15)

16) In a survey of 425 farmers, 108 of them spend more than $10,000 per year on fertilizer. If a 93.12% confidence interval is built of the actual percentage of farmers who spend more than $10,000 per year on fertilizer, what is the half-width of the interval?

A) 0.0384 B) 0.0406 C) 0.036 D) 0.0352

16)

17) Visa International credit card estimates that during the 2010 Winter Olympics held in Vancouver 65% of the local Visa card users increased their daily spending on Visa. Assume a sample size of 500. Using 95% confidence level, estimate the standard error of the proportion A) 0.556 B) 0.021 C) 0.743 D) 0.093

17)

18) A survey of 8 shoppers at a grocery store on a Monday afternoon indicated the following amounts they spent: $19.45, $10.64, $15.72, $13.20, $17.48, $9.88, $16.24, $14.32. Analysis of the data indicates it is normally distributed. If a 99% confidence interval were constructed of the average amount spent at a grocery store on a Monday afternoon, what would be the upper limit of the confidence interval?

A) $16.78 B) $18.52 C) $16.82 D) $18.69

18)

19) In a survey of 750 people, 630 indicate that they recycle at least once every 6 months. If a 90% confidence interval is constructed of the actual percentage of people who recycle at least once every 6 months, what is the lower limit of the interval?

A) 0.8180 B) 0.8138 C) 0.8101 D) 0.8228

19)

20) A nutritionist wanted to examine the amount of caffeine in a 500 ml cup of coffee from 6 different coffee shops: 104, 82, 98, 95, 90, 88. Analysis of the data indicates the amount of caffeine is normally distributed. If a 90% confidence interval is constructed, what is the value of the half-width?

A) 6.4231 B) 4.7050 C) 4.5902 D) 6.1936

20)

21) A researcher wanted to estimate the percentage of people who read a certain newspaper. In a survey, the percentage of respondents who read the paper is 28.125%. When constructing a 95% confidence interval of the actual percentage of people who read the newspaper, the half-width is 0.110154255. What was the sample size?

A) 100 B) 49 C) 81 D) 64

21)

3

22) A researcher wants to estimate the average amount people spend per year on over-the-counter medication. Prior data indicates the amount is normally distributed with a mean of $156.42 and standard deviation of $24.08. What would be the required sample size at a 95% level of confidence if the researcher wants to be accurate to within $2.50?

A) 464 B) 357 C) 251 D) 616

22)

23) A researcher wants to estimate the percentage of people who go for an annual checkup. Based on previous data, the percentage was 18.4%. What would be the required sample size if the researcher wants to be accurate to within 1.5% at a 99% level of confidence? Round to nearest ten.

A) 2,560 B) 1,800 C) 3,610 D) 4,430

23)

24) A survey of 300 people showed that 57 of them buy fruit when they buy cereal. If we construct a 98.08% confidence interval of the actual percentage of people who buy fruit with cereal, what is the upper limit of the confidence interval?

A) 0.2427 B) 0.2430 C) 0.2496 D) 0.2483

24)

25) A survey of 20 students on the average amount spent per textbook had a mean of $141.65 and a standard deviation of $9.60. If a confidence interval of the average cost of a textbook ranges from roughly 137.94 to 145.36, what is the level of confidence?

A) 99% B) 97.5% C) 95% D) 90%

25)

26) An entertainment company wants to estimate the average amount that people spend when they go out for dinner and a movie. A survey of 18 people had an average of $75.48 and standard deviation of $10.05. Analysis of the data showed it to be normally distributed. If a 95% confidence interval were constructed of the average amount people spend on dinner and a movie, what is the lower limit of the interval?

A) $72.64 B) $69.12 C) $68.,92 D) $70.48

26)

27) A researcher wants to estimate the average amount of time that people spend to get to work. Based on previous data, the travel times are normally distributed with a mean of 25.2 minutes and standard deviation of 5.4 minutes. What is the required sample size, if the researcher wants to be accurate to within 0.5 minutes at a 95% level of confidence?

A) 774 B) 316 C) 449 D) 632

27)

28) The manufacturer of cell phones wishes to determine the magnitude of malfunction problems with the new 4 G cell phones. Company randomly tests 3458 cell phones. Given that the estimate of the true proportion is 0.1, sampling error 0.01 and the confidence interval of 95%, calculate the z value A) -1.96 B) 2.01 C) 2.25 D) 2.99

28)

29) Visa International credit card estimates that during the 2010 Winter Olympics held in Vancouver 65% of the local Visa card users increased their daily spending on Visa. Using 95% confidence level, estimate the z value.

A) 0.56 B) 0.74 C) -1.96 D) 0.47

29)

30) A sample of 25 students took an average of 65.25 minutes to complete a certain test. The 95% confidence interval of the actual average time to complete the test ranges from 61.86504 to 68.63496.

What is the standard deviation?

A) 8.2159 B) 9.8744 C) 10.4 D) 8.2

30)

4

31) Statistics Canada conducted a survey to assess the economic benefits of 2010 Winter Olympics on Vancouver. Of the 2500 random sample surveyed, 2250 of the respondents were optimistic about the economic benefits. Use a 99% confidence interval, estimate the proportion of all the respondents who were optimistic about the economic benefits. What is the interval value for the lower limit?

A) 0.25 B) 0.888 C) 0.885 D) 0.915

31)

32) A market analyst wants to estimate the average price of stock 6 months after its initial IPO. Based on previous data, these prices are normally distributed with a mean of 85 cents and standard deviation of 14.6 cents. What would be the required sample size at a 99% level of confidence if the analyst wants to be accurate to within 3.5 cents?

A) 67 B) 92 C) 116 D) 48

32)

33) Statistics Canada conducted a survey to assess the economic benefits of 2010 Winter Olympics on Vancouver. Of the 2500 random sample surveyed, 2250 of the respondents were optimistic about the economic benefits. Use a 99% confidence interval, estimate the proportion of all the respondents who were optimistic about the economic benefits. What is the interval value for the upper limit?

A) 0.915 B) 0.950 C) 0.015 D) 2.576

33)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

34) University of the Valley (UV) wishes to determine the current citizens' sentiments on the number of serious crimes committed in the Valley. UV conducts a study with a random sample of 1250 local citizens and finds that 675 have serious concerns with the crime level in the Valley. Use a 90% confidence interval to estimate the standard error of the proportion

34)

35) A movie theatre wants to estimate the average amount people spend on concessions. For a sample of 27 people, the average was $9.50 with a standard deviation of $1.59. Analysis of the data indicates it is normally distributed. What is the lower limit of the 90% confidence interval? Round to the nearest cent.

35)

36) A museum wants to estimate the percentage of people who have visited one in the past 5 years. Based on previous data, the percentage was 4.2%. What would be the required sample size at 99% confidence with a margin of error of 2.5%? Round to nearest ten.

36)

37) A photocopier manufacturer wants to estimate the average annual amount that companies spend on photocopier supplies. Based on prior data, the amount was normally distributed with a mean of $1,260 and standard deviation of $160. What would be the required sample size at 99% confidence with a margin of error of $25?

37)

38) A dentist wants to estimate the percentage of people who floss regularly but has no prior data to work with. What is the required sample size at 95% confidence if the desired margin of error is 2%?

38)

39) NXY Internet security company surveyed 1500 adult males in Canada and asked them if they any concerns about their e-mails. 38% said they had some very serious concerns about Internet security issues. Construct a 99% interval for the population proportion .

What is the interval upper limit value?

39)

5

40) An addictions research agency wants to estimate the average amount spent per month on lotteries and other games of chance. In a survey of 15 people, the average was $20.42 with a standard deviation of $5.94. Analysis of the data indicates it is normally distributed. What would be the half-width of a 95% confidence interval? Round to the nearest cent.

40)

41) A hotel wanted to estimate the percentage of business executives who attend at least 1 convention per year. In a survey of 500 executives, 302 of them attend at least 1 convention per year. If we construct a 95% confidence interval, what is the half-width of the interval?

Express it as a decimal number accurate to 4 decimals.

41)

42) A researcher wants to estimate the average time it takes adults to complete a certain IQ test. For a sample of 18 adults, the average is 20.5 with a standard deviation of 2.25 minutes. Analysis of the data indicates it is normally distributed. What is the upper limit of the 99% confidence interval? Round to the nearest whole number.

42)

43) A scientist wanted to examine the average amount of sleep that college students get. For a sample of 25 students, the 90% confidence interval ranges from 6.23 to 6.57 hours. What is the value of the standard deviation if the mean of the sample is 6.4 hours.

43)

44) University of the Valley (UV) wishes to determine the current citizens' sentiments on the number of serious crimes committed in the Valley. UV conducts a study with a random sample of 1250 local citizens and finds that 675 have serious concerns with the crime level in the Valley. Use a 90% confidence interval to estimate the interval lower level value.

44)

45) A confidence interval of the percentage of companies with annual gross sales under $500,000 was based on a survey of 600 companies and ranges from 0.704 to 0.796. The sample proportion is 75%. What is the level of confidence? Express it as a decimal number accurate to 2 decimals.

45)

46) A researcher wants to estimate the average rent for a one-bedroom apartment. Data from 5 years ago show that rents were normally distributed with a mean of $520 and standard deviation of $65. What would be the required sample size at 95% confidence with a margin of error of $15?

46)

47) A researcher wants to estimate the average amount spent per year on vehicle maintenance.

Data from 5 years ago was normally distributed with a mean of $852 and standard deviation of $172. What would be the required sample size at 99% confidence with a margin of error of $20?

47)

48) NXY Internet security company surveyed 1500 adult males in Canada and asked them if they any concerns about their e-mails. 38% said they had some very serious concerns about Internet security issues. Construct a 99% interval for the population proportion .

What is the standard error of the proportion?

48)

49) A new restaurant wanted to estimate its average bill from a sample of bills: $29.40, $32.64, $35.07, $33.06, $25.40, $40.98, $35.56. Analysis of the data indicates the bills are normally distributed. If we construct a 99% confidence interval of the average bill at this restaurant, what is the upper limit rounded to the nearest cent?

49)

6

50) A health clinic wants to estimate the percentage of seniors who receive an annual flue shot.

In a survey of 200 seniors, 64 do so. if we construct a 95% confidence interval of the percentage of seniors who receive an annual flue shot, what is the lower limit of the interval? Express it as a decimal number accurate to 4 decimals.

50)

51) An auto manufacturer wanted to estimate the percentage of people who service their vehicles on a regular basis. Of 400 people surveyed, 220 service their vehicle regularly. If we construct a 95% confidence interval of the percentage of people who service their vehicles regularly, what is the lower limit of the interval? Express it as a decimal number accurate to 4 decimals.

51)

52) University of the Valley (UV) wishes to determine the current citizens' sentiments on the number of serious crimes committed in the Valley. UV conducts a study with a random sample of 1250 local citizens and finds that 675 have serious concerns with the crime level in the Valley. Use a 90% confidence interval to estimate the interval half width

52)

53) NXY Internet security company surveyed 1500 adult males in Canada and asked them if they any concerns about their e-mails. 38% said they had some very serious concerns about Internet security issues. Construct a 99% interval for the population proportion .

What is the interval lower limit value?

53)

54) A textbook manufacturer wanted to estimate the percentage of students who spend more than $1,000 per year on textbooks. Of 800 students surveyed, 702 did so. If we construct a 99% confidence interval of the percentage of students who spend more than $1,000 per year on textbooks, what is the upper limit of the interval? Express it as a decimal number accurate to 4 decimals.

54)

TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.

55) In constructing a 99% confidence interval of the percentage of companies with fewer than 5 employees, you have a sample proportion of 864 out of 1000. The interval would range from 83.6% to 89.2%.

55)

56) In constructing a 99% confidence interval of the average time needed for trucks to travel a certain route, you have following statistics: n = 12, mean = 7.4, standard deviation = 1.02 hours. The interval would range from 6.87 to 7.93 hours.

56)

57) A 95% confidence interval of the percentage of automobiles having better highway mileage than 7 L / 100 km ranges from 5.42% to 9.58%. If you were testing that the percentage of automobiles achieving this type of mileage was 8%, you would not reject the null hypothesis at a 5% level of significance.

57)

58) You are calculating a sample size to estimate the percentage of people who travel more than 25 km one way to work at a 95% level of confidence. If you have no prior data to work with and you want to be accurate to within 1.5%, the required sample size would be 3,007.

58)

59) In constructing a confidence interval of the average amount of a down payment on a new home, you have the following statistics: n = 18, mean = $15,605, standard deviation = $3,462. If the level of confidence were changed from 95% to 90%, the change in the half-width of the interval would be $332.11.

59)

7

60) In constructing a confidence interval of the percentage of people who eat a certain brand of peanut butter, the sample proportion is 160 out of 400. The interval ranges from 35.9706% to 44.0294%. The level of confidence is 90%.

60)

61) You are calculating a sample size to estimate the percentage of people who would vote for a certain candidate in the next election. The percentage of people who voted for the candidate in the last election was 75%. At a 95% level of confidence, if the margin of error was increased from 2% to 4%, the sample size would decrease by 1,350.

61)

62) In calculating a sample size for a proportion, if you do not have a proportion from a previous study, you use p = 50%.

62)

63) A 95% confidence interval for a mean ranges from 22.6 to 28.4. If we were testing the hypothesis that the population mean is 30, we would reject the null hypothesis at a 5% level of significance.

63)

64) In constructing a 95% confidence interval of the average annual income of those with just a high school education, you have a sample size of 30. The interval ranges from $27,719.86 to $31,080.14.

The value of the standard deviation is $4,506.61.

64)

65) A 99% confidence interval is wider than a 95% confidence interval if the same data is used to construct both intervals.

65)

66) In constructing a confidence interval, if you increase the sample size, the confidence interval becomes wider for the same level of confidence.

66)

67) When calculating a sample size, you round the answer up to the next whole number.

67)

68) If sampling is done without replacement, the size size needs to be less than 5% of the population size.

68)

69) In calculating a sample size at a 95% level of confidence, you have a standard deviation of 5.24 from a previous study. If you want to be accurate to within 0.75, the required sample size would be 133.

69)

70) In estimating the percentage of people who shop at a certain store, the sample proportion is 25/400.

The difference in the half-width between the 90% confidence interval and the 95% confidence interval of the percentage of people who shop at the store would be 0.004394.

70)

71) One of the assumptions in constructing a confidence interval for a mean is that the population is normally distributed.

71)

72) A 95% confidence interval for a mean ranges from 62.4 to 69.8. This means there is a 95% probability the mean is between 62.4 and 69.8.

72)

73) In calculating the average amount of rainfall in a certain region during the summer, you have the following statistics: n = 10, mean = 65.4, standard deviation = 5.52 mm. The 99% confidence interval would range from 59.73 mm to 71.07 mm.

73)

8

74) In calculating a sample size, if you increase the value of the margin of error, the sample size also increases.

9

74)

Answer Key Testname: CHAPTER 8 1) A 2) D 3) A 4) D 5) B 6) D 7) B 8) C 9) B 10) D 11) B 12) D 13) C 14) A 15) A 16) A 17) B 18) D 19) A 20) A 21) D 22) B 23) D 24) B 25) D 26) D 27) C 28) A 29) C 30) D 31) C 32) C 33) A 34) 0.014 35) 8.98 36) 430 37) 272 38) 2401 39) 0.412 40) 3.29 41) 0.0429 42) 22 43) 0.5 44) 0.512 45) 0.99 46) 73 47) 491 48) 0.013 49) 40.05 50) 0.2553 10

Answer Key Testname: CHAPTER 8 51) 0.5013 52) 0.023 53) 0.35 54) 0.9074 55) TRUE 56) FALSE 57) TRUE 58) FALSE 59) FALSE 60) TRUE 61) TRUE 62) TRUE 63) TRUE 64) FALSE 65) TRUE 66) FALSE 67) TRUE 68) TRUE 69) FALSE 70) FALSE 71) TRUE 72) FALSE 73) TRUE 74) FALSE

11

Chapter 9 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1) An office supply store held a focus group with 8 business people to determine if there were any significant difference between what people spend per year at it versus a competitor: Store 150 152 98 95 212 196 124 155 Competitor 87 204 112 78 150 186 152 97 Subtracting the competitor's data from that of the store showed the differences to be normally distributed. Using this procedure, what is the value of the test statistic?

A) 1.06 B) 0.93 C) -0.99 D) -1.06

1)

2) You are conducting a paired t test and have set it up as a left-tail test. You have 12 pairs of data.

What is the critical value if you are testing at a 1% level of significance?

A) -2.65 B) -1.363 C) -2.718 D) -1.356

2)

3) You are conducting a Wilcoxon signed rank sum test and have 17 pairs of data in which there are 2 ties. What is the sum of W+ and W-?

A) 122 B) 120 C) 136 D) 153

3)

4) A weight loss clinic measures clients' weights (kg) when they start the program and six months later. For a sample of 8 clients, these are the results: Before 110 95 102 93 83 120 96 108 After 92 96 98 93 81 118 98 99 What is the mean difference between before and after?

A) 4.57 B) 3.92 C) 4.73 D) 4

4)

5) A survey of 1,000 people was conducted to determine what percentage of Internet users use a certain search engine; 112 indicated they do not use the Internet, 548 use the search engine and the rest do not. What is the value of the sample proportion?

A) 0.548 B) 0.383 C) 0.452 D) 0.617

5)

6) A marketing company company surveyed citizens of Vancouver (n=25) and the Olympic tourists on the level of customer satisfaction with city facilities and matched the responses of these two samples. The mean difference in the scores as 25.56, with a standard deviation of 12.55. Construct a 95% confidence interval estimate for the difference in satisfaction scores.

A) 20.18 to 2.145 B) 20.18 to 27.75 C) 20.38 to 30.74 D) 25.56 to 27.78

6)

7) A focus group of 7 people was held to determine if they preferred brand A coffee over brand B. They were asked to rate each brand on a scale from 1 to 10, 1 = poor, 10 = excellent: A 8 7 8 10 6 4 6 B 8 4 9 8 2 9 4 If we subtract the ratings for brand B from that of brand A, what is W+?

A) 7 B) 13 C) 15 D) 14

7)

1

8) A hotel asked a sample of repeat visitors to rate its decor before and after renovations on a scale from 1 to 7, 1 = poor, 7 = excellent: Person 1 2 3 4 5 6 7 Before 4 2 5 4 6 3 5 After 5 4 4 6 7 7 4 If we were doing the Wilcoxon signed rank sum test, what rank would we assign to person #1?

A) 1 B) 6 C) 2.5 D) 4.5

8)

9) Suppose you are using the Wilcoxon signed rank sum test and the number of non-zero differences is 35. What is the standard deviation used to calculate the Z score?

A) 58.7237 B) 61.0533 C) 17.6246 D) 24.6703

9)

10) The Value Fit center has run a promotional campaign to attract more clients. The center tracked the number of clients who have signed up for the fitness center before and after the promotional campaign, with the following results: Before the campaign 7 8 4 4 After the campaign 2 9 12 9 With the 4 matched pair client numbers, test if there is sufficient evidence that the promotional campaign has been effective ? Compute the t-critical value for one tail test A) -0.800 B) 3.182 C) 2.353 D) 0.481

10)

11) You are doing a Wilcoxon signed rank sum test and the number of non-zero differences is 38. If W = 402, what is the value of the Z score, accurate to 2 decimals?

A) -0.01 B) 0.46 C) 0.01 D) -0.46

11)

12) A group of 90 accountants was interviewed to determine if they preferred brand A tax software to brand B. If 78 preferred A and the rest B, what is the test statistic?

A) -6.96 B) 10.23 C) -10.23 D) 6.96

12)

13) Suppose you are conducting a paired t test on the following data: X 7 6 9 5 2 4 8 7 4 Y 7 8 7 2 8 5 2 3 8 If this were a two-tail test at a 5% level of significance, what would be the critical value?

A) 2.262 B) 2.306 C) 2.447 D) 1.96

13)

14) A sample of gas stations was taken to compare their prices in January to that of the previous July: January 87.7 92.3 80.2 97.9 82.4 85.9 99.5 July 97.6 99.3 87.6 95.2 95.6 103.2 96.2 If we subtract January from June, what is the lower limit of the 95% confidence interval of the average difference in gas prices between these two periods?

A) -0.13 B) 0.11 C) -0.11 D) 0.13

14)

2

15) A trainer introduced a new program to help his runners run farther in a 2 hour period. For a sample of 5 runners, these are the results: Before 30 33 37 27 24 After 32 34 35 27 28 If we examine the differences between after and before, what is the upper limit of the 95% confidence interval of the average difference?

A) 3.483 B) 3.845 C) 3.506 D) 3.776

15)

16) Eight sets of twin aged 8-10 were measured for IQ: Pair 1 2 3 4 5 6 7 8 Twin A 60 70 72 75 80 82 90 92 Twin B 62 70 68 78 75 84 90 94 What rank would we assign for pair #3 if we were doing the Wilcoxon signed rank sum test?

A) 4 B) 3 C) 5 D) 7

16)

17) The final exam scores for a statistics course at two the universities are as follows: University 1 University 2 44 33 45 45 56 43 67 21 78 56 88 67 89 87 56 89 45 65 34 89 Conduct the Wilcoxon Signed Rank Sum Test for a two tail test, estimate the p value. Set level of significance at 0.05 A) p value = 1.96 B) p value= 13.228 C) p value > 0.064 D) p value = 0.113

17)

18) The Value Fit center has run a promotional campaign to attract more clients. The center tracked the number of clients who have signed up for the fitness center before and after the promotional campaign, with the following results: Before the campaign 7 8 4 4 After the campaign 2 9 12 9 With the 4 matched pair client numbers, test if there is sufficient evidence that the promotional campaign has been effective. Use the p -value criterion to decide.

A) There is unsufficient data to test the hypothesis B) p value is 0.4818, fail to reject Ho

18)

C) p value is 0.241, do not reject Ho

D) p value is -0.800, reject Ho

19) A survey of 500 people was conducted to determine if more people preferred Brand A peanut butter over Brand B; 266 people preferred A while the rest preferred B. What is the p-value of the test?

A) 0.9236 B) 0.4236 C) 0.5764 D) 0.0762

3

19)

20) The two methods of training for a final exam provided the following matched exam scores: Method 1 23 33 45 47 49 Method 2 21 34 47 55 53 Use alpha =.05 test criteria . What is the p value for this test of difference between the two methods of exam scores?

A) 0.192 B) 0.0963 C) 2.131 D) 2.776

20)

21) A sample of vehicles was randomly selected to determine if a gasoline additive would improve mileage (L / 100 km): Before 10.3 9.8 9.2 8.6 8.3 8.1 7.9 After 9.8 9.8 9.3 8.8 8.3 7.8 7.6 If we compute the difference between before and after, what would be the half-width for a 95% confidence interval?

A) 0.1604 B) 0.0932 C) 0.1403 D) 0.2354

21)

22) Suppose you are using the Wilcoxon signed rank sum test and the number of non-zero differences is 64. What is the mean used to calculate the Z score?

A) 2,400 B) 2,080 C) 1,040 D) 800

22)

23) An economist measured the unemployment rate of 6 regions of the country for October and then March: October 7.2% 6.9% 5.2% 12.4% 3.8% March 7.8% 6.2% 5.4% 11.8% 3.4% If we construct a 95% confidence interval of the average difference between October and March, what is the half-width of the interval?

A) 0.75% B) 0.35% C) 0.69% D) 0.39%

23)

24) For a sample of 8 students, their math and physics grades were compared: Math 78 90 45 70 65 72 55 60 Physics 62 84 62 85 62 83 53 63 Analysis of the differences indicate they are not normally distributed. If the purpose if to determine if math grades are significantly higher than physics grades, what is the sum of the W- ranks if we subtract physics from math?

A) 21 B) 21.5 C) 22 D) 36

24)

25) A store with two locations examined the daily sales of the stores on a series of dates: June 1 June 4 June 7 June 10 June 13 A 1,403 983 1,158 997 1,517 B 1,123 1,213 877 996 1,173 What rank would we assign for the data on June 7 if we were doing the Wilcoxon signed rank sum test?

A) 4 B) 2 C) 1 D) 3

25)

26) A focus group of 8 women was held to determine which of two brands of hand lotion they preferred: 1 2 3 4 5 6 7 8 A B B A A A A A If the purpose of the test is to determine if more women significantly prefer brand A, what is the p-value of the test?

A) 0.1445 B) 0.2890 C) 0.0704 D) 0.0352

26)

4

27) On a particular night, there were two popular shows on at the same time. Of 800 people surveyed, 385 were watching show A, 306 were watching show B, while 109 were watching neither show. If we are testing to determine if there is any significant difference in the percentage who watch either show, what is the p-value of the test?

A) 0.0026 B) 0.2892 C) 0.1446 D) 0.0026

27)

28) Suppose you are using the Wilcoxon signed rank sum test and the mean used to calculate the Z score is 189. What is the number of non-zero differences?

A) 30 B) 28 C) 25 D) 27

28)

29) A real estate office introduced a new filing system to help the agents reduce the amount of time spent on paperwork. For a sample of 6 agents, these were the results (minutes/day): Before 90 55 126 87 96 110 After 85 65 107 82 90 102 What is the standard deviation of the differences?

A) 4.88 B) 8.47 C) 5.34 D) 9.27

29)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

30) In a survey of 800 working people, 309 travel at least 12 km one way to work while the rest travel less than 12 km. What is the value of the standard deviation used to calculate the Z score? Round to 4 decimals.

30)

31) In constructing a confidence interval for the average difference of paired data, you have 16 pairs and the sample standard deviation of the differences is 5.24. What is the difference in the half-width of the interval between the 99% confidence interval and the 95% confidence interval? Round to 2 decimals.

31)

32) In conducting a Wilcoxon signed rank sum test, there are 25 non-zero differences and W+ = 170.5. What is the value of the test statistic, correct to 4 decimals?

32)

33) In conducting a Wilcoxon signed rank sum test, you find the mean used to calculate the Z score is 451.5. What is the number of non-zero differences?

33)

34) In conducting a Wilcoxon signed rank sum test, you have 18 non-zero differences and W= 86.5. What is the value of W+?

34)

35) A survey company asked its clients (n=1250) to rank the two e-commerce sites for their level of satisfaction with online shopping experience: WXT Links and YXX Online Shopping. 125 respondents rated the two sites to be of same quality. Of the remaining clients, 975 respondents favoured WXT Links. From this sample, determine if there is evidence that clients rate WXT's quality higher then of YXX. Compute the p value and test the hypothesis, Use Alpha =.025

35)

36) A survey of 600 people was conducted to determine if they preferred grocery store A over grocery store B; 308 preferred A, 192 preferred B and the rest do not shop at either store.

What is the value of the sample proportion. Express it as a decimal number accurate to 3 decimals.

36)

5

37) In conducting a Wilcoxon signed rank sum test, the number of non-zero differences is 57.

What is the value of the standard deviation used to calculate the Z score? Round to 3 decimals.

37)

38) The office supply expenses of two departments were compared on a 6-month period: Jan. Feb. Mar. Apr. May June A 152 120 162 137 167 150 B 146 131 150 96 182 152 Analysis of the differences indicate the are normally distributed. If we subtract department B from department A, what is the upper limit of the 95% confidence interval of the average differences? Round to the nearest cent.

38)

39) A random sample of 6 executives was asked to evaluate two accounting software packages on a scale from 1 to 10, 1 = poor, 10 = excellent: A 9 8 10 10 6 4 B 7 8 6 7 8 9 If the ratings for B are subtracted from those of A, what is the value of W+?

39)

40) In a left-tail paired t test, what is the critical value if there are 8 non-zero differences, 2 differences of zero and the level of significance is 10%? Round to 3 decimals.

40)

41) In a sample of 40 days, a certain stock index went up on 26 of them and down on the rest. If the purpose of the test is to determine if the percentage of days the index increases is significantly higher than the days it decreases, what is the value of the test statistic? Round to 4 decimals.

41)

42) A random sample of 7 executive assistants was taken to examine their typing speed (wpm) on two different types of keyboards: A 95 102 87 92 100 89 97 B 97 100 89 92 98 92 97 What is the value of the standard deviation used to compute the test statistic if the differences are normally distributed? Round to 4 decimals.

42)

43) In a survey of 400 people to determine if they preferred movie A over movie B, 210 preferred A, 168 preferred B and the rest had not seen either movie. What is the p-value of the test? Express it as a decimal accurate to 4 decimals.

43)

44) In a two-tail paired t test, there are 16 non-zero differences and 3 differences of zero. If the test is conducted at a 1% level of significance, what is the critical value accurate to 3 decimals?

44)

TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.

45) The Wilcoxon Signed Rank Sum Test can be used whenever the differences in matched data points are symmetric about their mean.

45)

46) You are conducting a right-tail sign test to determine the percentage in favour of a new law. Of 800 people polled, 200 are against, 450 are in favour and the remainder are neutral. The value of the Z score is 3.5355.

46)

6

47) You are conducting a right-tail sign test. The sample proportion is 45/80. The p-value is 13.14%.

47)

48) The sample mean and sample standard deviation for 16 differences are 0.2 and 1.64 respectively.

The lower limit of the 99% confidence interval of the differences is -0.5187.

48)

49) The Wilcoxon Signed Rank Sum Test is called a distribution-free technique

49)

50) If the test statistic for a small-sample Wilcoxon signed rank sum test falls between two critical values in the table, you use the closest p-value from the table.

50)

51) For a two-tail paired t test, if the sample size is 12 and the value of the test statistic is 1.92, the p-value is between 5% and 10%.

51)

52) In conducting the sign test, if the sample size is at least 20, we calculate the p-value using the Z distribution.

52)

53) The sample standard deviation for 13 differences is 4.62. The half-width of the 95% confidence interval is 9.7921.

53)

54) In constructing a 95% confidence interval for a paired t test, if the test statistic falls outside the interval, we reject the null hypothesis at a 5% level of significance.

54)

55) In calculating the Z score for the Wilcoxon signed rank sum test for a one-tail test, the choice of W+ or W- depends on the alternative hypothesis.

55)

56) In conducting the Wilcoxon signed rank sum test, if the number of non-zero differences is 40, the value of the mean used to compute the Z score is 410.

56)

57) In conducting the sign test, we include differences that are neither positive nor negative.

57)

58) If the difference of the paired observations are not normally distributed, you use the paired t test.

58)

59) In conducting a paired t test, if there are 8 non-zero differences and 3 differences of zero, the degrees of freedom are 7.

59)

60) In computing the mean of the Z score for the Wilcoxon signed rank sum test, you find it to be 689.

The number of non-zero differences is 52.

60)

61) In conducting the Wilcoxon signed rank sum test, if the number of non-zero differences is 48, the value of the standard deviation used to compute the Z score is 97.4987.

61)

62) In conducting the Wilcoxon signed rank sum test, if the number of non-zero differences is 8, the sum of W+ and W- should be 36.

62)

63) In conducting a two-tail paired t test at a 5% level of significance, if the hypothesized difference of zero falls outside the corresponding 95% confidence interval, we fail to reject the null hypothesis.

63)

7

64) In conducting the Wilcoxon signed rank sum test, if the number of non-zero differences is 12 and W+ = 17.5, then W- = 60.5.

64)

65) In conducting a sign test, if the sample proportion is 130/250, the standard deviation of the sampling proportion is 0.0428.

65)

66) You are conducting a right-tail sign test. The sample proportion is 405/750. The value of the Z score is 2.1979.

66)

8

Answer Key Testname: CHAPTER 9 1) B 2) C 3) B 4) D 5) D 6) C 7) D 8) C 9) B 10) C 11) B 12) D 13) B 14) A 15) D 16) D 17) C 18) C 19) D 20) A 21) D 22) C 23) C 24) B 25) A 26) A 27) A 28) D 29) D 30) 0.0177 31) 1.07 32) 0.2153 33) 42 34) 84.5 35) Since the p value is less than Alpha=.025, reject H o 36) 0.616 37) 125.862 38) 26.48 39) 8.5 40) -1.383 41) 1.8974 42) 1.9881 43) 0.0154 44) 2.878 45) TRUE 46) FALSE 47) TRUE 48) FALSE 49) FALSE 50) FALSE

9

Answer Key Testname: CHAPTER 9 51) TRUE 52) TRUE 53) FALSE 54) FALSE 55) TRUE 56) TRUE 57) FALSE 58) FALSE 59) FALSE 60) TRUE 61) TRUE 62) TRUE 63) FALSE 64) TRUE 65) FALSE 66) FALSE

10

Chapter 10 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1) A hotel chain compared the number of visits over a 5-year period of those belonging to its membership program to those who do not, hypothesizing that members would stay more often.

These were the results based on random samples of both groups: Members 1 2 2 3 3 3 4 5 Non-members 1 1 1 1 1 2 2 3 If W1 is the rank sum of the members, what is its value?

A) 89 B) 83 C) 92 D) 79

1)

2) A 95% confidence interval for the difference of 2 means ranges from -1.7092 to 36.1092. If the standard error is 8.2, what are the degrees of freedom?

A) 9 B) 8 C) 11 D) 10

2)

3) A store with 2 locations sampled 6 sales from each location on a particular day. These were the results: Store A 23.95 20.53 25.85 29.47 29.19 31.07 Store B 16.57 15.25 22.77 19.54 17.06 17.07 Analysis of the data indicates both locations are normally distributed. It is assumed the locations have equal variances. If the goal is to determine if the average sale at Store A is significantly higher than that at Store B, what is the value of the t score?

A) 4.3944 B) 4.3939 C) 4.3940 D) 4.3946

3)

4) A focus group of 5 men and 5 women were asked to rate a commercial on a scale from 1 to 10 where 1 = poor and 10 = excellent: Men 7 6 2 8 8 Women 3 8 9 8 5 If W1 is the rank sum of the women, what is its value?

A) 31 B) 28 C) 33 D) 30

4)

5) Two focus groups, one of ordinary workers, the other of management, were asked to rate a new software program on a scale from 1 to 7, 1 = poor, 7 = excellent. These were the results: Workers 3 4 5 4 2 4 Management 4 6 4 3 3 7 If W1 is the rank sum of management, what is its value?

A) 35 B) 43 C) 21 D) 27

5)

6) A researcher wanted to see if one teaching method (method B) was superior to another in helping students get higher marks. Samples of students were randomly selected from both methods: A 78 65 73 76 89 82 100 86 96 99 81 66 B 55 72 73 64 46 74 50 58 79 76 70 74 Analysis of the data indicates that neither group is normally distributed. What is the value of the Z score?

A) 3.00 B) 2.87 C) 2.94 D) 3.11

6)

1

7) Two hundred people in each of two cities were asked to rate how well the federal government is doing on a scale from 1 to 5, 1 = poor, 5 = excellent. The following table shows the distribution of the responses: 1 2 3 4 5 City A 12 26 79 58 25 City B 15 31 84 48 22 If City A is used for W1, what is the value of W1?

A) 27 B) 28 C) 16 D) 25

7)

8) Suppose you are conducting a right-tail Wilcoxon rank sum test. Given W1 = 1161.5, n1 = 30 and n2 = 20, what is the z-value?

A) 0.56 B) 4.25 C) 5.45 D) 7.85

8)

9) You are given the following information:

9)

standard n mean deviation Group 1 12 16.9 2.75 Group 2 16 13.3 1.44 Analysis of the data indicates both groups are normally distributed. If you were building a 95% confidence interval by hand, what would be the half-width of the interval?

A) 1.5655 B) 1.8994 C) 1.9185 D) 1.5533

10) A researcher wanted to determine if the tuition per course at small private colleges would be significantly greater than those of large public colleges. Random samples of each had the following results: Private 820 910 855 872 750 1020 Public 650 785 690 825 700 730 Analysis of the data indicates both groups are normally distributed. It was assumed the standard deviation of the private college would be larger than that of the public colleges. What is the value of the t score?

A) 3.0528 B) 3.1001 C) 2.9979 D) 3.1270

10)

11) A theatre company conducted a survey asking people how often they attended live events using a scale from 1 to 10, 1 = never, 10 = all the time. They segregated people by income. For two of the income groups, these were a sample of the results: Under $25K 4 9 4 3 7 5 2 4 2 6 4 $75K plus 7 8 5 7 9 7 8 6 8 5 9 If the objective is to determine if those with higher income are significantly more likely to attend live events, what is the p-value of the test?

A) 100% B) 0.26% C) 99.74% D) 1%

11)

2

12) A researcher wanted to determine if people could read more pages per hour when fully awake than when sleepy. For samples of 8 people in the alert group and 6 in the other, these were the statistics: Alert Sleepy mean 20.4 17.6 standard deviation 1.2 4.5 n 8 6 Analysis of the data indicates both groups are normally distributed. It is assumed the variances are not equal. If this analysis were done on a computer, what would be the degrees of freedom? Round to the nearest whole number.

A) 6 B) 14 C) 12 D) 5

12)

13) An analyst wanted to compare weekly wages from small independent auto repair shops to those of large nationally-owned auto repair shops. Samples were taken from each type: Small 310 304 376 382 344 382 Large 378 374 371 371 346 381 373 356 Analysis of the data indicates both types of shops are normally distributed. It is assumed the variances are unequal. If we construct a 95% confidence interval of the average difference in weekly wages between large and small shops by hand, what is the lower limit of the interval?

A) -16.13 B) -20.18 C) -18.28 D) -17.03

13)

14) A researcher hypothesized the travel time to work would be significantly less in a small city than in a large city. Random samples of travel times for 12 people from each type were taken: Small 10 12 15 12 10 5 10 15 25 22 10 10 Large 20 25 30 30 40 35 32 40 45 35 30 25 Analysis of the small city data indicates it is skewed right. What is the value of the Z score?

A) -3.9837 B) -3.5248 C) -3.7028 D) -3.1754

14)

15) A non-profit organization sampled 8 donations from each of 2 different regions. These were the results (in dollars): A 5 10 20 22 25 25 35 40 B 7 12 15 15 18 20 25 30 Analysis of the data indicates both regions are normally distributed. What is the value of the t score?

A) 1.0278 B) 1.0128 C) 1.0298 D) 1.0318

15)

16) In a survey, people classified themselves as either liberal or conservative. The were asked to state on a scale from 1 to 5, 1 = strongly disagree, 5 = strongly agree, the degree to which they agreed with a statement. This is a random sample of the results: Liberal 5 2 3 4 3 5 4 5 4 4 Conservative 3 4 3 3 3 5 1 2 2 2 If liberals are more likely to agree with the statement, what is the value of the Z score?

A) 1.952 B) 1.903 C) 2.041 D) 2.172

16)

3

17) A researcher wanted to compare monthly utility bills of two cities in different provinces. These are the summary statistics: standard n mean deviation City A 40 $124.63 $10.42 City B 50 $139.07 $45.77 The researcher assumed the variances of the bills in the two cities were not equal. However, analysis of the data indicates both groups are normally distributed. Based on this, what would be the degrees of freedom to find the critical value if the analysis were done on a computer?

A) 49 B) 55 C) 88 D) 39

17)

18) If W1 = 585, n1 = 20 and n2 = 25, what is the value of the Z score?

A) 2.8552 B) 2.7903 C) 2.8604

18)

D) 2.8792

19) A researcher wanted to determine if a modified engine got better mileage than the original.

Independent trials under each engine type yielded the following results (L per 100 km): Modified 7.3 6.9 7.2 7.7 8.0 7.0 7.8 8.4 Original 8.3 9.7 7.6 8.7 9.2 7.7 7.6 8.2 Analysis of the data indicates both groups are normally distributed. What is the upper limit of the 99% confidence interval of the average difference between the original and modified engines? Hint: This is not a paired t-test.

A) 1.997 B) 1.410 C) 1.805 D) 1.420

19)

20) A survey was done of people to determine how many hours per week they spend on leisure activities on a computer. The respondents were divided into those under 18 and those 18 or older.

These are the summary statistics: standard n mean deviation Under 18 100 9.8 2.5 18 or older 120 8.6 0.6 Analysis of the data indicates both groups are normally distributed. It is assumed the variances of the 2 groups are unequal. What is the value of the t score?

A) 6.9282 B) 4.2702 C) 4.6888 D) 5.8987

20)

21) An ice cream vendor wanted to determine if average weekend daily sales were significantly higher than average weekday daily sales. Random samples had the following results: Weekend 115.84 122.74 105.85 127.79 114.33 122.84 Weekday 117.33 128.45 79.46 115.34 109.95 71.52 Analysis of the data indicates both groups are normally distributed. The vendor suspected there was a significant difference in the variances of the two groups. What is the critical value at a 5% level of significance?

A) 2.228 B) 2.447 C) 2.571 D) 1.812

21)

22) In a survey, people were asked how many times a week they exercise. The respondents were divided by age. These are the results for a handful of respondents in two of the age groups: 18-24 2 5 1 1 1 2 45-64 1 1 1 1 3 2 Both groups are skewed right. If W1 is the rank sum of the 45-64 age group, what is its value?

A) 27 B) 36 C) 9 D) 42

22)

4

23) At a bottling plant, two bottling machines filling 2 L pop bottles were compared to see if there would be any significant difference in the average amount of pop filling the bottles. Random samples from the machines had the following results: #1 1.9806 2.0472 1.9929 1.9723 2.0103 2.0467 1.9928 2.0329 #2 2.0022 2.0167 1.9238 2.0244 1.9981 1.9805 1.9973 2.0407 Analysis of the data indicates both groups are normally distributed. It is assumed the variances of the two machines would be equal. If we subtract the mean for machine #2 from that of machine #1, what is the lower limit of the 90% confidence interval of the average difference between the 2 means?

A) -0.0199 B) -0.0163 C) -0.0172 D) -0.0193

23)

24) In conducting a Wilcoxon rank sum test, the mean in the construction of the Z score is 216. If n1 = 12, what is the value of the standard deviation used to construct the Z score?

A) 28.257 B) 28.775 C) 29.403 D) 27.928

24)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

25) You have two focus groups to rate a movie on a scale from 1 to 10, 1 = poor, 10 = excellent: Group 1 7 8 8 5 9 8 Group 2 7 3 8 8 9 10 If W1 is the rank sum of group 1, what is its value?

25)

26) A researcher wanted to determine if one water filtration system (A) was more effective in removing calcium than another. In samples of water run through both system: A 2.13 1.87 2.04 1.96 1.99 2.08 B 2.06 1.98 1.97 2.12 2.04 2.02 Analysis of the data indicates both groups are normally distributed. If the mean from system A is subtracted from that of system B, what is the value of the t score? Round your answer to 3 decimals.

26)

27) You are conducting a right-tail t test assuming unequal variances. You are given the following information: standard n mean deviation Group 1 13 20.4 2.4 Group 2 15 17.6 8.9 What is the value of the t score? Round to 4 decimals.

27)

28) A realtor was comparing home prices in two cities to see if there was any significant difference in average prices. These are the statistics for a particular month: standard n mean deviation City A 17 350,246 45,207 City B 25 312,008 12,894 Analysis of the data indicates both cities' prices are normally distributed. It is assumed the variances are not equal. If the hypothesis were conducted on a computer, what would be the degrees of freedom needed to find the critical value? Round down to the next whole number.

28)

5

29) A researcher conducts a study in two different regions of Canada to determine if there is a significant difference in wait times for a particular type of surgery. These were the results (in months): standard n mean deviation Region A 62 15.4 2.3 Region B 90 18.7 4.8 Analysis of the data indicates wait times in both regions are normally distributed. It is assumed the variances are not equal. What is the value of the standard deviation used to construct the t score? Round to 4 decimals.

29)

30) Two special needs classes were taught a subject using different pedagogies. Subsequent test results had the following results: Method A 37 48 49 40 62 41 39 Method B 42 45 65 52 56 54 61 Analysis of the data indicates Method A is skewed. If W1 is from Method A, what is its value?

30)

31) A scientist measured the percentage of decay of two different isotopes of a certain chemical after a certain period of time: A 75.2 79.3 60.2 80.6 78.4 B 62.7 65.9 78.4 70.8 71.4 Analysis of isotope A indicates it is not normally distributed. If W1 is the rank sum of isotope A, what is its value?

31)

32) An entrepreneur was considering opening a coffee shop in one of two locations. A survey of how much people spend per week on coffee was conducted in the two regions. Here is a sample of the results: A 5.00 10.00 7.50 8.00 6.00 6.50 7.50 7.00 B 7.00 12.00 10.00 9.50 9.00 8.50 8.00 8.50 Analysis of the data indicates both locations are normally distributed. If the average from Region A is subtracted from that of Region B, what is the upper limit of the 95% confidence interval if the interval is build by hand? Round to the nearest cent.

32)

33) People in two different cities were surveyed to rate their satisfaction with the snow removed in their respective cities. The goal was to determine if there is any significant difference in the ratings. If W1 = 10,408, n1 = 100 and n2 = 100, what is the p-value of the test if it were done by hand? Express it as a decimal number accurate to 4 decimals.

33)

34) In conducting a Wilcoxon rank sum test, you are given W1 = 642.5, n1 = 20 and n2 = 25.

What is the value of the Z score? Round to 4 decimals.

34)

35) A researcher tested two types of automobile fuel cells to determine if Cell A lasts significantly longer. Using the same vehicle, these were the results for a sample of cells of each type (km): A 562 604 589 601 590 578 592 584 B 590 546 572 580 575 562 570 566 Analysis of the data indicates both cells are normally distributed. If a 90% confidence interval is constructed of the average difference between Cell A and Cell B, what is the lower limit of the interval if the construction is done by hand? Round to 2 decimals.

35)

6

36) You are conducting a Wilcoxon rank rum test on ranked data. You are given W1 = 1,650, n1 = 37 and n2 = 48. What is the value of the standard deviation used to compute the Z score? Round to 2 decimals.

36)

37) Two focus groups, one of women, the other of men, were asked how much they spend per month on skin care products on average: Women 25.00 10.00 50.00 40.00 35.00 30.00 30.00 Men 10.00 12.00 20.00 25.00 15.00 15.00 8.00 Analysis of the data indicates both groups are normally distributed. If you were to construct a 99% confidence interval of the average difference between women and men in monthly expenditures on skin care, what would be the half-width of the interval if the construction were done by hand? Round to the nearest dollar.

37)

38) You are constructing a 95% confidence interval for the difference of 2 means. You are given the following information: standard n mean deviation Group 1 10 150.48 10.6 Group 2 9 135.62 9.2 If you were building this confidence interval by hand, what would be the lower limit of the interval? Round to 4 decimals.

38)

39) A researcher compared junior high and senior high students on the average amount spent per week on junk food and pop. These are the results: standard n mean deviation Junior 100 7.50 1.25 Senior 100 9.40 1.30 Analysis of the data indicates both groups are normally distributed. It is assumed the variances are not equal. If the average of the junior high is subtracted from that of the senior high, what is the value of the t score? Round to 4 decimals.

39)

TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.

40) If both sample sizes are the same, the t score for the t test for 2 means will be the same regardless of whether the variances are equal or not.

40)

41) In conducting a 2-tail t test assuming equal variances, you are given the following information: standard n mean deviation Group 1 8 15.7 3.5 Group 2 10 12.8 3.8 The p-value would be greater than 10%.

41)

42) If analysis of your data indicates the populations are normally distributed and you are not dealing with ranked data, the t test is preferable to the Wilcoxon rank sum test.

42)

7

43) You are constructing a 95% confidence interval for the difference of 2 means, assuming the variances are not equal. You are given the following: standard n deviation Group 1 10 2.8 Group 2 10 6.0 If you are building the interval by hand, the t score used in the half-width is 2.262.

43)

44) Two sets of people were asked to rate a product from 1 to 5, 1 = poor, 5 = excellent. These are the results: A 1 2 2 3 3 3 4 4 B 1 1 2 2 2 3 4 5 If W1 is from Group A, its value is 73.5.

44)

45) If n1 = 5 and n2 = 6 and you can compute the rank sum for each group, the total rank sum of both groups is 66.

45)

46) In conducting a Wilcoxon rank sum test, you have W1 = 1193.5, n1 = 32 and n2 = 40. The value of the Z score is 1.84.

46)

47) You are conducting a t test assuming unequal variances on a computer. You are given the following: standard n deviation Group 1 20 5.7 Group 2 18 10.9 The degrees of freedom are 17.

47)

48) In constructing a 90% confidence interval for the difference of 2 means by hand, you are given the following information: standard n mean deviation Group 1 15 150 8.4 Group 2 15 134 5.6 The value of the half-width of the interval. is 7.76.

48)

49) In doing the Wilcoxon rank sum test, if n1 = 9 and n2 = 12, the test statistic is a Z score.

49)

50) In conducting a Wilcoxon rank sum test, you are given W1 = 830, n1 = 28 and n2 = 30. The value of the mean used in calculating the Z score is 812.

50)

51) You are conducting a 2-tail t test at a 5% level of significance to determine if there is a significant difference between the population means. You are given the following information: standard n mean deviation Group 1 15 20.2 1.25 Group 2 15 15.8 1.84 Given this information, you would reject the null hypothesis. It is assumed that the variances of the groups are equal.

51)

8

52) You are conducting a right-tail Wilcoxon rank sum test at a 5% level of significance. You are given W1 = 50, n1 = 6 and n2 = 8. Given this information, you would reject the null hypothesis.

52)

53) You are conducting a right-tail t test assuming equal variances at a 1% level of significance. You are given the following: standard n deviation Group 1 12 2.5 Group 2 15 2.52 The critical value is 2.787.

53)

54) Given this information:

54)

standard n deviation Group 1 10 5.2 Group 2 12 14.7 the standard deviation used to construct the t score in which the variances are assumed to be unequal is 4.901.

55) You are conducting a right-tail Wilcoxon rank sum test. You have W1 = 210, n1 = 13 and n2 = 17.

The p-value of the test is 0.5708.

55)

56) You are conducting a right-tail t test assuming unequal variances. You are given the following information: standard n mean deviation Group 1 12 10.6 2.3 Group 2 15 7.1 8.8 If you were conducting this test by hand, the p-value would be between 5% and 10%.

56)

57) You are conducting a 2-tail Wilcoxon rank sum test at a 5% level of significance. You have W1 = 48, n1 = 5 and n2 = 7. Given this information, you would reject the null hypothesis.

57)

58) You conducted a survey with 2 groups of people in which they stated their agreement with a statement on a scale from 1 to 5, 1 = strongly disagree, 5 = strongly agree. In order to compare the 2 groups, the appropriate test is the Wilcoxon rank sum test.

58)

59) In constructing a 95% confidence interval for the difference of 2 means by hand, you are given the following information: standard n mean deviation Group 1 20 8.7 0.75 Group 2 20 7.2 0.8 The lower limit of the interval is 1.076.

59)

9

Answer Key Testname: CHAPTER 10 1) A 2) B 3) A 4) D 5) B 6) C 7) A 8) D 9) C 10) B 11) B 12) A 13) B 14) A 15) D 16) C 17) B 18) A 19) A 20) C 21) C 22) B 23) D 24) B 25) 37 26) 0.455 27) 1.1704 28) 17 29) 0.5842 30) 38 31) 33.5 32) 3.64 33) 0.3844 34) 4.1686 35) 4.92 36) 112.82 37) 18 38) 4.3834 39) 10.5353 40) TRUE 41) TRUE 42) TRUE 43) TRUE 44) TRUE 45) TRUE 46) FALSE 47) FALSE 48) FALSE 49) FALSE 50) FALSE 10

Answer Key Testname: CHAPTER 10 51) TRUE 52) FALSE 53) FALSE 54) FALSE 55) FALSE 56) TRUE 57) TRUE 58) TRUE 59) FALSE

11

Chapter 11 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1) Traditionally, ANOVA techniques focus on: A) sample standard deviations C) sample variances

B) sample proportion distributions D) sample means distributions

1)

2) Average mail delivery time, in hours, in town is compared between the 3 courier companies with the following data: Company A Company B Company C 5 2 2 4 3 3 2 2 2 1 3 1 By using the Tukey-Kramer Confidence ANOVA output, test if there is difference between average delivery times of Company A and Company B A) We can conclude that the average of Company A and Company B differ as the confidence interval is [0.5+/- 2.87}, the interval includes a non-zero B) Interval estimation can not be used to test the average delivery times C) We can not conclude that the average of Company A and Company B delivery times differ as the confidence interval is [-1.87---2.87], the interval includes a zero D) We can conclude that the average of Company A and Company B differ as the confidence interval is [-1.87---2.87], the interval includes a zero

2)

3) Average mail delivery time, in hours, in town is compared between the 3 courier companies with the following data: Company A Company B Company C 5 2 2 4 3 3 2 2 2 1 3 1 By using the single factor ANOVA, compare the average delivery times and the Tukey-Kramer Confidence ANOVA output, compute the MSwithin number A) 1.24 B) 1.33 C) 1.44 D) 1.46

3)

4) In an ANOVA application, we need to make sure that: A) the data points are independent and randomly selected B) each of the populations have a binomial distribution C) the populations do not have the same degree of variability D) the data points are independent

4)

5) The conditions for ANOVA analysis include: A) the data point are not independent B) the data distribution is skewed C) the populations have different variances D) the data points are independent and randomly distributed

5)

1

6) The sum of squares for the between-sample variation is used to calculate: A) random variability B) mean errors C) the overall mean D) overall variability

6)

7) The overall mean is the best estimate used to estimate: A) the true means of the populations B) the true variability of the sample data C) to square the deviations D) degree of standard deviations of the samples under examination

7)

8) Average mail delivery time, in hours, in town is compared between the 3 courier companies with the following data: Company A Company B Company C 5 2 2 4 3 3 2 2 2 1 3 1 By using the ANOVA single factor model, and the Tukey-Kramer test , confirm if there is a difference between the average delivery times of Company B and Company C A) Since the interval does contain zero, we cannot conclude average delivery times of Company B and Company C differ B) Since the interval does not contain zero, we conclude average delivery times of Company B and Company C differ C) Since the MSwithin is 1.44, we conclude average delivery times of Company B and Company C do not differ D) Since the "q" value is 3.99, we conclude average delivery times of Company B and Company C differ

8)

9) n T represents the total number of observations in the data set and is used to:

9)

10) In running ANOVA applications, we assume the population variances are: A) approximately equal B) approximately represent large variances C) unequal D) approximately incorrect

10)

11) In ANOVA, we compare the between -sample and within-sample variation by first calculating: A) the sum of squares B) squared deviations C) the standard deviations D) the degree of variances

11)

12) The ANOVA technique is fairly robust and can safely be used with populations that are: A) normally distributed B) somewhat skewed C) have large variations in the data set D) somewhat positively skewed

12)

13) The goal of ANOVA is to: A) summary of statistical results B) compare the mean responses of the various treatments C) compare the distribution of the randomized blocks D) compare the standard deviation of the various treatments

13)

A) SStotal C) degree of variation

B) SSbetween D) calculate the MSwithin

2

14) In running an ANOVA application, we compare: A) the level of variation in the data set C) the mean scores

B) the residual error distribution D) the standard deviation scores

15) A cereal processing company wishes to test the number of cereal boxes filled by the 3 types filling machines used in production. The data is provided: Machine I Machine II Machine III 25.40 17.00 22.00 30.40 18.00 24.00 26.40 19.00 26.00 31.40 20.00 28.00 27.40 21.00 30.00

14)

15)

Run the Tukey-Kramer Confidence Interval and determine if the mean filling time of Machine I and II differ at the 0.05 level of significance.

A) Means can not be compared as the sample sizes are too small B) Yes, the mean filling times differ at the 0.05 level of significance.

C) No, the mean filling times do not differ at the 0.05 level of significance.

D) Means cannot be compared as the sample sizes are all the same.

16) The mean square between sample variability is called: A) MSbetween B) total random error C) SSbetween D) sum of squares

16)

17) When the population variances are assumed to be approximately equal, the ANOVA application does yield: A) a large deviation in the sum of squares B) a reasonable comparison of the mean scores C) a large set of variances in the data set D) an equality of the variances

17)

18) Average mail delivery time, in hours, in town is compared between the 3 courier companies with the following data: Company A Company B Company C 5 2 2 4 3 3 2 2 2 1 3 1 By using the ANOVA single factor model, compute MSwithin for average delivery times A) 0.69 B) 0.52 C) 4.25 D) 1.45

18)

19) MSwithin can be considered as a good measure against which we measure MSbetween. This comparison provides us with information for: A) sample variability B) the degree of spread with the sampling applications C) sampling distribution information D) within-sample variability

19)

3

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

20) We wish to compare the taste choices of the 3 brands of vitamin soft drinks sold at a super store. The taste preference is rated on a scale of [1-5] whereby 1= the best taste , 5= the worst taste. The random data set for the brands is provided below: Brand X 3 2 1 2 3 3 4 1 2

Brand Y 1 2 3 4 3 4 3 4 1

20)

Brand Z 4 5 2 1 2 2 3 3 4

Set up a completely randomized ANOVA design and compute the sum of squares between groups and within groups

21) A large super store has randomly collected data on its customers buying habits. The store considered the number of items purchased by different customer profiles. The data is shown below:

21)

Male customers Female customers Senior customers 5 11 3 3 12 5 2 8 8 4 9 4 Run randomly designed single factor ANOVA design and compute the F value and the matching p value

22) For the following ANOVA application, state the Null Hypothesis.

ANOVA Source of Variation SS df MS F Between Groups 36.96296 2 18.48148 0.780602 Within Groups 568.222 23.67593 Total

605.1852

26

4

22) P-value 0.469417

F crit 3.402826

23) For the following ANOVA application, test the Null Hypothesis at alpha level =.05 level of 23) significance. Use the p value criterion ANOVA Source of Variation SS df MS F P-value F crit Between Groups 36.96296 2 18.48148 0.780602 0.469417 3.402826 Within Groups 568.222 23.67593 Total

605.1852

2

24) A random study designed to examine the stock returns of large, small and medium size companies listed on the Toronto Stock Exchange (TSX) shows the following % returns: Small Size Medium Size Large Size 10 4 11 12 5 12 13 9 14 9 10 16 -5 11 10 14 15 9 -2 16 5 10 8 8 8 9 9

24)

Run randomly designed single factor ANOVA design and compute the missing parts of the ANOVA Table.

ANOVA Source of Variation Between Groups Within Groups

SS 36.96296 568.222

Total

605.1852

df

MS 18.48148 23.67593

2

F

P-value

F crit

26

25) A large super store has randomly collected data on its customers buying habits. The store considered the number of items purchased by different customer profiles. The data is shown below: Male customers Female customers Senior customers 5 11 3 3 12 5 2 8 8 4 9 4 Run randomly designed single factor ANOVA design and compute the variance between groups and within groups

5

25)

26) A random study designed to examine the stock returns of large, small and medium size companies listed on the Toronto Stock Exchange (TSX) shows the following % returns: Small Size Medium Size Large Size 10 4 11 12 5 12 13 9 14 9 10 16 -5 11 10 14 15 9 16 5 -2 10 8 8 8 9 9

26)

Run randomly designed single factor ANOVA design and compute the variance of the small, medium and large size company stock returns.

27) A random study designed to examine the stock returns of large, small and medium size companies listed on the Toronto Stock Exchange (TSX) shows the following % returns: Small Size Medium Size Large Size 10 4 11 12 5 12 13 9 14 9 10 16 -5 11 10 14 15 9 16 5 -2 10 8 8 8 9 9

27)

Run randomly designed single factor ANOVA design and compute the MSbetween and MSwithin.

28) A random study designed to examine the stock returns of large, small and medium size companies listed on the Toronto Stock Exchange (TSX) shows the following % returns: Small Size Medium Size Large Size 10 4 11 12 5 12 13 9 14 9 10 16 -5 11 10 14 15 9 16 5 -2 10 8 8 8 9 9 Run randomly designed single factor ANOVA design and compute the degrees of freedom (df) for within groups.

6

28)

29) We wish to compare the taste choices of the 3 brands of vitamin soft drinks sold at a super store. The taste preference is rated on a scale of [1-5] whereby 1= the best taste , 5= the worst taste. The random data set for the brands is provided below: Brand X 3 2 1 2 3 3 4 1 2

Brand Y 1 2 3 4 3 4 3 4 1

29)

Brand Z 4 5 2 1 2 2 3 3 4

Set up a completely randomized ANOVA design and compute the F critical value

30) A large super store has randomly collected data on its customers buying habits. The store considered the number of items purchased by different customer profiles. The data is shown below:

30)

Male customers Female customers Senior customers 5 11 3 3 12 5 2 8 8 4 9 4 Run randomly designed single factor ANOVA Table

31) We wish to compare the taste choices of the 3 brands of vitamin soft drinks sold at a super store. The taste preference is rated on a scale of [1-5] whereby 1= the best taste , 5= the worst taste. The random data set for the brands is provided below: Brand X 3 2 1 2 3 3 4 1 2

Brand Y 1 2 3 4 3 4 3 4 1

31)

Brand Z 4 5 2 1 2 2 3 3 4

Set up a completely randomized ANOVA design and compute the sample means

32) From the F Table, calculate critical value of F (2,27) for the 0.05 level of significance.

7

32)

33) A random study designed to examine the stock returns of large, small and medium size companies listed on the Toronto Stock Exchange (TSX) shows the following % returns: Small Size Medium Size Large Size 10 4 11 12 5 12 13 9 14 9 10 16 -5 11 10 14 15 9 16 5 -2 10 8 8 8 9 9

33)

Run randomly designed single factor ANOVA design and compute the p-value for the F test.

34) We wish to compare the taste choices of the 3 brands of vitamin soft drinks sold at a super store. The taste preference is rated on a scale of [1-5] whereby 1= the best taste , 5= the worst taste. The random data set for the brands is provided below: Brand X 10 12 13 9 -5 14 16 10 8

Brand Y 4 5 9 10 11 15 -2 8 9

34)

Brand Z 11 12 14 16 10 9 5 8 9

Set up a completely randomized ANOVA design and compute the F test and the associated p value

TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.

35) The ANOVA techniques assumes that all the populations have the same variability .

35)

36) As long as the the largest sample variance is less than 2 times as large as the smallest variance, ANOVA application will yield reasonable results.

36)

37) When interaction is present in a two-way ANOVA, we use a t-test application for determination of significance.

37)

38) A response variable is a qualitative variable that can be measured or observed.

38)

39) If the sample data does not meet the normality criterion in running the ANOVA application, there are tests known as "non-parametric" that can be used to analyze the data set.

39)

40) ANOVA application assumes that the population variances are not approximately equal.

40)

8

41) In making multiple comparisons to decide which means differ, we use [nT-k] as the appropriate

41)

42) In running the One-Way ANOVA, the first step is to calculate the sum of squares of each sample.

42)

43) The F Test will be about equal to 1 or less when the null hypothesis is true.

43)

44) The two-factor ANOVA is more concerned with the interaction effect between the two factors rather then the relationship between the factors.

44)

45) In general, the degrees of freedom is the total number of observations in the data set minus one.

45)

46) If the confidence interval does not contain zero, then we can assume that the two means compared are different.

46)

47) If the sample sizes are too small, ANOVA findings may be in jeopardy.

47)

48) The residual variation is often called an "error."

48)

49) In a One-Way ANOVA application, our focus is on measuring the degree of deviation from the mean score.

49)

50) Factor is an explanatory characteristic that is used to distinguish one group from the other.

50)

51) To get the sum of squares for between-sample variation, we weigh the squared deviation from each sample mean by the number of data points in the sample.

51)

52) The F Test does not have a range of possible values when computed.

52)

53) If we reject the null hypothesis, we have strong evidence that at least one of the population means differ.

53)

54) The Total Sum of Squares is a measure of determining variation of all the data points from the overall mean.

54)

55) If there is evidence of interaction between the two factors in a two-way ANOVA, the residual mean square is used as a standard against which the other mean squares are compared.

55)

56) The Tukey-Kramer procedure allows us to construct a 100% confidence interval so that all of the confidence intervals will contain the true difference between the means being compared.

56)

57) The sum of squares for each sample has [ni-1] degrees of freedom.

57)

58) The appropriate level of q-scores depends only on the desired level of confidence.

58)

59) in two-way ANOVA, the first hypothesis test considers the interaction between the two factors.

59)

degrees of freedom.

9

60) The ANOVA technique is greatly impacted by some degree of data skewness.

60)

61) It is not important to have a truly randomized data set in running an ANOVA application.

61)

62) The ANOVA test for comparison of population means is not impacted by the inequality of variances.

62)

63) The ANOVA application is greatly affected by inequality of variances.

63)

64) The total variation in a two-factor ANOVA is split into a sum of squares of each factor, the sum of squares of interaction and the residual sum of squares.

64)

65) The Total Sum of Squares computation is a key requirement for the hypothesis test.

65)

10

Answer Key Testname: CHAPTER 11 1) C 2) C 3) C 4) A 5) D 6) C 7) A 8) A 9) D 10) A 11) A 12) B 13) B 14) C 15) B 16) A 17) B 18) D 19) D 20) 1.56, 32.44 21) F= 14.38, p=0.0016 22) Ho: µ1=µ2=µ3

23) Since the p value = 0.46 < Alpha=.05, fail to reject the Null Hypothesis 24) ANOVA TABLE COMPLETED Source of Variation SS df MS F Between Groups 36.96296 2 18.48148 0.780602 Within Groups 568.2222 24 23.67593 Total

605.1852

26

25) 92.67, 29 26) 36.75,23.50, 10.78 27) 18.48, 23.68 28) 24 29) 3.40

11

P-value 0.469417

F crit 3.402826

Answer Key Testname: CHAPTER 11 30) Anova: Single Factor SUMMARY Groups Male Female Senior

Count 4 4 4

Sum 14 40 20

Average 3.50 10.00 5.00

ANOVA Source of Variation Between Groups Within Groups

SS 92.67 29.00

Total

121.67 11.00

31) 2.33 2.78 2.89 32) F=3.35 33) 0.78 34) .781, .469 35) TRUE 36) FALSE 37) FALSE 38) FALSE 39) TRUE 40) FALSE 41) TRUE 42) FALSE 43) TRUE 44) TRUE 45) TRUE 46) TRUE 47) TRUE 48) TRUE 49) TRUE 50) TRUE 51) TRUE 52) FALSE 53) TRUE 54) TRUE 55) TRUE 56) FALSE 57) TRUE 58) FALSE 59) TRUE 60) FALSE 61) FALSE 62) TRUE 63) FALSE

df 2.00 9.22

MS 46.33 3.22

12

Variance 1.67 3.33 4.67

F 14.38

p-value F crit 0.00158 4.26

Answer Key Testname: CHAPTER 11 64) TRUE 65) FALSE

13

Chapter 12 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1) A researcher asked men and women if they had made a major purchase (house, car, etc.) in the past 12 months to determine if there was any significant difference in the percentages of the genders.

What would be the degrees of freedom for the critical value if this were done as a chi-square test?

A) 2 B) 3 C) 4 D) 1

1)

2) A researcher suspected the percentage of people seriously injured in an accident when not wearing a seat belt was significantly more than 10% higher than the corresponding percentage of those wearing a seal belt. This table summarizes the researchers findings: seat belt no seat belt n 500 400 # injured 12 52 What is the p-value of the test?

A) Extremely close to zero B) 0.6295 C) 0.3639 D) 0.6361

2)

3) During the 2010 Winter Olympics, the TV stations monitored the type of sports watched by the audiences and reported the following percent distribution on a sample of 600 viewers: Ice hockey=31% Down hill skiing= 55% Snowboarding= 14% Determine the expected frequency of the downhill skiing viewers A) 329 B) 84 C) 330 D) 186

3)

4) A factory set up a contingency table cross-referencing 6 job categories by 3 income categories. If the goal were to determine if income depends on the job category, what would be the degrees of freedom?

A) 10 B) 9 C) 15 D) 18

4)

5) A box of coloured buttons has five colours: red, blue, brown, yellow and green. A box of these buttons had the following distribution: red blue brown yellow green 12 14 13 10 14 If there is supposed to be an equal distribution of the colours, how many brown buttons would you expect in this box?

A) 12 B) 12.6 C) 13 D) 12.4

5)

6) In a survey of 300 executives, 42% of them work through lunch at least once a week, while of 500 hourly workers, 35% of them work through lunch at least once a week. If the objective is to determine if the percentage of executives who work through lunch is significantly higher, what is the p-value of the test?

A) 0.0239 B) 0.9761 C) 0.0246 D) 0.07

6)

1

7) A clothing store wanted to see if the amount spent per year depended on the person's gender. A survey of 600 customers had the following results: < $100 $100 to $500 $500 or over Total Male 62 112 126 300 Female 65 108 127 300 What is the value of the test statistic?

A) 0.1475 B) 0.1476 C) 0.0019 D) 0.0018

7)

8) You construct a 95% confidence interval of the difference between two proportions and find -0.064 < p1 - p2 < 0.048. What is the difference of the sample proportions used in constructing the interval?

A) -0.008 B) 0.008 C) -0.032 D) 0.032

8)

9) A charitable organization divided donors by annual household income and contribution amount per year: Under $50K $50K or more Total Under $100 189 458 647 $100 or more 75 168 243 Total 264 626 890 If the percentage who give at least $100 per year were equal for both income groups, how many of those whose income is under $50,000 would you expect would donate at least $100 per year?

A) 72.08 B) 71 C) 73 D) 72

9)

10) In a furniture store, it is expected that 34.5% will spend less than $500, 42.8% will spend between $500 and $1,000, 19.8% will spend between $1,000 and $2,500 and the rest will spend over $2500.

For a sample of 2000 customers, this was the distribution: Under $500 $500 to $1,000 $1,000 to $2,500 $2,500 or more 712 842 405 41 If the goal is to determine if the actual percentages are significantly different than the expected percentages, what is the value of the test statistic?

A) 7.2498 B) 6.0274 C) 6.1177 D) 8.1613

10)

11) During the 2010 Winter Olympics, the TV stations monitored the type of sports watched by the audiences and reported the following percent distribution for a sample of 600 viewers: Ice hockey=31% Down hill skiing= 55% Snowboarding= 14% Compute the Chi-square test statistic. It was expected that there was an equal proportion of people watching each event.

A) 382.00 B) 383.24 C) 51.22 D) 152.76

11)

12) A researcher wants to see to what degree a student's grade depends on hours spent studying. The researcher summarized the results in a contingency table with 6 grade categories and 3 study categories. What is the critical value, testing at a 5% level of significance?

A) 20.483 B) 28.869 C) 37.156 D) 18.307

12)

2

13) A TV executive wants to determine if there is any significant difference in the percentage of people who watch a certain TV program between two cities. In City A, 400 people were surveyed; 62 watch the program. In City B, 500 people were surveyed; 84 watch the program. What is the value of the Z score?

A) 0.5237 B) -0.5257 C) 0.5298 D) 0.5277

13)

14) A researcher wants to investigate whether annual income depends on education levels. A survey of 500 people had the following results: some college/ less than college/ university high school high school university graduate total 16 67 54 40 177 < $25K $25K to under $50K 7 42 76 78 203 $50K or over 2 23 33 62 120 total 25 132 163 180 500 What is the value of the test statistic?

A) 43.0963 B) 42.7238 C) 44.0627 D) 47.9565

14)

15) A fast-food restaurant divided customers into 4 spending categories: under $5, $5 to under $10, $10 to under $20, $20 or more. If it wanted to determine if the actual percentage were significantly different than its expected percentages, what would be the critical value at a 10% level of significance?

A) 6.251 B) 9.348 C) 11.143 D) 7.779

15)

16) A researcher asked people if they own the latest version of a cell phone and divided them by gender: Yes No Total Male 14 236 250 Female 10 240 250 Total 24 476 500 If the researcher wants to determine if there is a significant difference in the percentage of each gender that answer yes, what would be the value of the test statistic if this were done as a chi-square test?

A) 0.7193 B) 0.7003 C) 0.8481 D) 0.8368

16)

3

17) In a study conducted by the dean of the business school for student satisfaction of the cafeteria food by the student gender, the following data was collected: Male students Female students Liked 225 55 Did not like 25 155

17)

By using the two independent proportion test, determine if there is evidence that the proportion of male students who liked the cafeteria food is different from the proportion of female student who liked the cafeteria food. Use the p value criteria and use = 0.05 level of significance

A) since the p value is < than

= 0.05, we can reject the Ho and confirm there is indeed a difference on the proportion of male and female students who like the cafeteria food B) sample size is too small to test Ho

C) since the p value is > than

= 0.05, we fail to reject the Ho and confirm there is an indeed no

difference on the proportion of male and female students who like the cafeteria food D) standard error of 0.0457 will not enable us to conduct the test of the hypothesis

18) A human resources manager wanted to determine if the ethnic backgrounds of its employees is roughly equivalent to that of the general population. The manager has 6 ethnicity categories. In conducting the test, what would be the critical value at a 5% level of significance?

A) 12.592 B) 11.070 C) 16.75 D) 18.548

18)

19) An electronics company wants to compare the percentage of people aged 18-24 who play a certain game to those aged 25-30. Of 300 people aged 18-24 who were surveyed, 18 play the game. Of 400 people aged 25-30 who were surveyed, 21 play the game. If we subtract the percentage of the 25-30 age group who play the game from that of the 18-24 age group, what is the upper limit of the 95% confidence interval?

A) 3.01% B) 4.21% C) 3.66% D) 4.18%

19)

20) A computer manufacturer uses three qualities of chips: low, medium and high. In theory, 24% of its computers should have low quality chips, 68% medium, and the rest high. In a sample of computers, this was the distribution of the chips: Low Medium High 188 540 22 If we test to determine if the actual percentage used match the theoretical percentage, what is the value of the test statistic?

A) 67.6435 B) 26.1869 C) 2.9883 D) 0.4065

20)

21) In theory, 25.2% of shoes sold should be sizes 7-8. In a certain shoe store, of 1000 pairs sold, 208 were size 7-8. If the goal is to determine if there is a significant difference between the actual and expected percentage of size 7-8 shoes sold at this store, what is the test statistic?

A) 7.6825 B) 10.0609 C) 11.7521 D) 11.4507

21)

4

22) An accounting firm segregated its CAs and CMAs by years of service to determine if there was any significant difference in the distribution of the two groups: Under 5 5 to under 10 10 or more Total CA 24 27 11 62 CMA 16 16 11 43 Total 40 46 19 105 What is the value of the test statistic?

A) 0.9933 B) 0.9803 C) 1.0124 D) 1.0089

22)

23) Of 400 households with annual income above $75,000, 209 of them had at least one member with post-secondary education. Of 250 households with annual incomes below $35,000, 118 of them had at least one member with post-secondary education. If the goal is to determine if those with higher income are more likely to have post-secondary education, what is the value of the test statistic?

A) 1.2545 B) 1.2604 C) 1.2473 D) 1.2528

23)

24) Suppose sample proportion 1 = 17/500 and sample proportion 2 = 12/400. If you were constructing a 95% confidence interval of the difference between the population proportions, what would be the half-width of the interval?

A) 0.0305 B) 0.0194 C) 0.0230 D) 0.0195

24)

25) A bookstore estimate that 10.2% of books cost less than $20, 64.3% cost between $20 and $35 and the rest at least $35. For a sample of 160 titles, this was the distribution: Under $20 $20 to $35 $35 or more 13 108 39 If the goal is to determine if there is a significant difference between the expected and actual distribution, what is the value of the test statistic?

A) 1.0096 B) 1.0803 C) 1.1737 D) 1.0269

25)

26) In a study of 800 people, 452 earn between $25,000 and $50,000 and 245 are between the ages of 45 and 65. How many people in this sample would you expect would earn between $25,000 and $50,000 and be between the ages of 45 and 65?

A) 138.425 B) 139 C) 138 D) 135.375

26)

27) In constructing a confidence interval for the difference of two proportions, sample proportion 1 = 180/200 and sample proportion 2 = 24/300. If the half-width of the interval is .0434, what is the level of confidence?

A) 99% B) 98% C) 90% D) 95%

27)

28) In a survey of 500 people, they were divided by age and whether or not they owned their own home: Under 30 30 or over Total Yes 24 200 224 No 156 120 176 Total 180 320 500 Based on a 95% confidence interval, what is the maximum difference between the two age groups in the percentage who own their own home?

A) 56.43% B) 55.21% C) 55.17% D) 56.67%

28)

5

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

29) A political candidate wanted to determine if there is any significant difference in the percentage of men and women who would vote for him. This table summarizes the results: Men Women n 200 200 # vote 78 63 What is the p-value of the test? Express it as a decimal number accurate to 4 decimals.

29)

30) A researcher wanted to determine if there was more than a 15% spread between the percentage of professionals using a particular brand of communications device and that of ordinary office workers. Of 150 polled professionals, 108 use the device. Of 500 polled office workers, 240 use the device. What is the p-value of this test? Express it as a decimal number accurate to 4 decimals.

30)

31) A researcher asked people if they had upgraded their computer in the past five years, dividing them by annual household income: Yes No $75K or more 28 16 Under $75K 84 372 If the goal is to determine if those earning $75,000 or more per year are more likely to upgrade than those earning less than $75,000 per year, what is the z-value of the test?

Express it as a decimal number accurate to 4 decimals.

31)

32) In an exercise survey, 82 of 250 people aged under 30 said they exercise at least twice a week. The corresponding percentage of those aged 30 or over was 120 out of 400. If we subtract the smaller sample proportion from the larger, what is the lower limit of the 95% confidence interval of the difference of the proportions? Express it as a decimal number accurate to 4 decimals.

32)

33) In a plot of farm land divided into five parts, the percentage of plants in each part should be the same. If the farm harvested 4,813 plants, how many would you expect to be harvested from each part?

33)

34) A theme part wanted to construct a 95% confidence interval of the difference in the percentage of people with children and without children who would be likely to visit the park in the next 12 months. Of 400 households with children, 35 would be likely. Of 250 households without children, 19 would be likely. What would be the half-width of the confidence interval? Express it as a decimal number accurate to 4 decimals.

34)

35) A researcher wanted to determine if those living in urban areas would be more likely to recycle than those living in rural areas. Of 500 surveyed in an urban area, 107 recycle. Of 200 surveyed in a rural area, 41 recycle. What is the value of the test statistic? Round to 4 decimals.

35)

6

36) The human resources department conducted a survey of all the managers for their level of educational attainment and discovered the following results: Education Level Attained High School College University Masters Higher than masters Total

% of Mgrs 5 yrs No of Mgrs ago currently 12 22 55 245 23 45 24 35

Expected No of Mgrs 43 196 82 86

4 100

14 357

10 357

36)

Compute the chi-square value and the table showing the observed and the expected values.

37) Type of Drink Coffee Tea Soft Drink Other Total

Percent Teens (past) 10 20 45 25 100

No of Teens (today) 45 77 225 112 459

37)

Expected Number of Teens 46 92 207 115 459

A soft drink company conducted a survey with teenagers to determine their drinking habits and tabulated the results shown above. Compute the chi-square value for this analysis

38) A researcher wanted to determine to what degree people agreed with a certain statement, 38) segregating by gender. These were the results: Strongly Somewhat Neither agree/ Somewhat Strongly disagree disagree disagree agree agree Male 3 52 108 68 2 Female 4 48 104 73 1 If the conditions for the appropriate test are met, what is the critical value testing at a 10% level of significance?

39) A political analyst wanted to determine if support for a bill depended on a person's political affiliation. A poll had the following results: Liberal Conservative Other Support 62 90 14 Not support 83 67 9 Based on this, how many conservatives would you expect to support the bill? Round to 4 decimals.

7

39)

40) A poll divided the respondents into six occupation categories and four income categories to determine to what degree a person's income depends on occupation. If the test is conducted at a 1% level of significance, what is the critical value if no categories need to be collapsed?

40)

41) A researcher polled 500 people to determine if the amount spend per month on clothing depended on the person's gender. These were the results: Under $50 $50 to $100 $100 or more Total Male 104 108 38 250 Female 83 62 105 250 Total 187 170 143 500 What is the value of the test statistic? Round to 3 decimals.

41)

42) In a study conducted by the dean of the business school for student satisfaction of the cafeteria food by the student gender, the following data was collected: Male students Female students Liked 225 55 Did not like 25 155

42)

By using the two independent proportion test, determine if there is evidence that the proportion of male students who liked the cafeteria food is different from the proportion of female student who liked the cafeteria food. Use = 0.05 level of significance and compute the z value

43) A store estimated the percentage of people falling into four age groups (under 25, 25-34, 35-64, 65 or over) would be 12%, 26%, 39% and 23% respectively. In a poll of 200 customers, the number in each age group were 27, 55, 70 and 48 respectively. What is the value of the test statistic? Round to 4 decimals.

43)

44) In an election, the general results for Parties A, B, C and D were 32.3%, 29.6%, 20.7% and 17.4% respectively. In a region with 54,000 voters, how many would you expect would have voted for Party C?

44)

45) Since more people now seek higher education, a researcher wondered if the percentages from 10 years ago needed to be updated: Graduate Less than High Some college/ college/ Post high school school university university graduate 2.4% 63.4% 10.3% 20.1% 3.8% For a recent poll, the number of people in the above categories were 10,302, 48, 118 and 22 respectively. What is the value of the test statistic? Round to 4 decimals.

45)

46) A researcher wanted to determine if the election results for six parties matched the poll results. However, the bottom two parties had to be combined due to a paucity of expected voters. If the researcher conducts the test at a 5% level of significance, what is the critical value?

46)

8

TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.

47) In conducting a goodness-of-fit test at a 10% level of significance, if there are five categories, but two of them must be combined, the critical value is 7.779.

47)

48) In a poll, the respondents were divided by gender and income: Under $25K $25K to $50K $50 or more Total Male 28 30 42 100 Female 24 32 44 100 Total 52 62 86 200 If we are testing to determine if income depends on gender, the value of the test statistic is 0.4187.

48)

49) In conducting a goodness-of-fit test, the theoretical distribution of three categories is 10%, 30% and 60%. The observed values are 12, 28 and 64. The value of the test statistic is 0.619.

49)

50) In testing the null hypothesis that p1 = p2, the p-value for the Z test and chi-square test would be identical.

50)

51) You have 400 observations split across 5 categories for a goodness-of-fit test: 100, 80, 64, 88, 68. If the distribution is supposed to be equal for the 5 categories, the test statistic wold be 10.84.

51)

52) In conducting a goodness-of-fit test across four categories, the theoretical distribution is 12%, 25%, 30% and 33%. The observed values are 4, 8, 10 and 8. In order to satisfy the conditions of the test, you would need to combine categories.

52)

53) In testing the null hypothesis p1 = p2 , if both sample sizes are the same, the value of the test

53)

54) In constructing a 99% confidence interval for the difference of two proportions, the first sample proportion is 18/250 and the second is 20/400. The half-width of the interval is 4.57%.

54)

55) In conducting a goodness-of-fit test across five categories, the theoretical distribution is 10%, 15%, 24%, 25% and 26%. The observed values are 89, 140, 207, 212 and 252. For the third category, the difference between the observed and expected value is 4.

55)

56) In conducting a chi-square test for independence, if the dimensions of the contingency table are 2 rows by 3 columns, the test statistic will have 6 terms.

56)

57) A survey segregated people by annual income and how much per month they spend eating out: Under $25K $25K to $50K $50 or more Total Under $50 840 480 100 1,420 $50 to $100 120 640 890 1,650 $100 or more 0 20 1,420 1,440 Total 960 1,140 2,410 4,510 The number of people earning less than $25,000 and spending between $50 and $100 per month eating out would be expected to be 352.

57)

58) In testing the null hypothesis p1 = p2 , the pooled estimate of the proportion is used in the estimate

58)

statistic will be the same regardless of whether or not you use the pooled proportion.

of the standard error.

9

59) If your alternative hypothesis isp1 = p2 > 6%, the first sample proportion is 20/100 and the second

59)

60) If a contingency table has 3 rows and 6 columns, the degrees of freedom for the critical value for the chi-square test for independence would be 18.

60)

61) In conducting a test for two proportions, if the number of successes in one sample is 12 and the number of successes in the other sample is 8, it is acceptable to use the Z test.

61)

62) In constructing a 95% confidence interval for the difference of two proportions, you have -0.0236 < p1 - p2 < 0.0404. The means the half-width of the interval is 3.2%.

62)

63) If you are testing the null hypothesis p1 = p2 and you construct a confidence interval for the

63)

64) You survey 200 people at a bookstore to determine if they bought a hardcover or paperback. You have the following results: Male Female Total Hardcover 10 30 40 Paperback 40 120 160 Total 50 150 200 If you are testing to determine if the book type purchased depends on gender, the p-value of the test would be 100%.

64)

65) In conducting a goodness-of-fit test, if the data is divided into 5 categories, the critical value at a 5% level of significance would be 9.488 if no categories need to be combined.

65)

66) In constructing a 99% confidence interval of the difference of two proportions, the first sample proportion is 17/200 and the second is 16/250. The upper limit of the interval is 8.47%.

66)

sample proportion is 12/100, the p-value is 0.3483.

difference of the two proportions, you use the pooled estimate of the proportion in computing the half-width of the interval.

10

Answer Key Testname: CHAPTER 12 1) D 2) A 3) C 4) A 5) B 6) A 7) A 8) A 9) A 10) C 11) D 12) D 13) B 14) A 15) A 16) B 17) A 18) B 19) B 20) B 21) A 22) D 23) D 24) C 25) A 26) A 27) C 28) A 29) 0.1164 30) 0.0179 31) 6.86 32) -0.0455 33) 962.6 34) 0.0430 35) 0.2634 36) Chi-square value = 70.22 observed 22 245 45 35 10 357

expected 42.840 196.350 82.110 85.680 14.280 421.260

70.22 4 2.04E-14

chi-square df p-value

O-E -20.840 48.650 -37.110 -50.680 -4.280 -64.260

(O - E)² / E 10.138 12.054 16.772 29.977 1.283 70.224

11

% of chisq 14.44 17.17 23.88 42.69 1.83 100.00

Answer Key Testname: CHAPTER 12 37) observed 45 77 225 112 459

expected 45.900 91.800 206.550 114.750 459.000

O-E -0.900 -14.800 18.450 -2.750 0.000

(O - E)² / E 0.018 2.386 1.648 0.066 4.118

4.12 chi-square 3 df .2490 p-value Chi-square= 4.12 38) 4.605 39) 80.1908 40) 30.578 41) 46.197 42) z value= 14 43) 1.4555 44) 11,178 45) 4.8019 46) 9.488 47) FALSE 48) TRUE 49) FALSE 50) TRUE 51) FALSE 52) TRUE 53) FALSE 54) FALSE 55) FALSE 56) TRUE 57) FALSE 58) TRUE 59) TRUE 60) FALSE 61) FALSE 62) TRUE 63) FALSE 64) TRUE 65) TRUE 66) FALSE

12

% of chisq 0.43 57.95 40.02 1.60 100.00

Chapter 13 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1) For a sample of 7 students, the number of hours of studying per week and the grade of a course were recorded: Hours 2 2.5 3 3.5 4 4.5 5 Grade 55 64 62 71 73 68 75 What is the regression coefficient of the variables?

A) 0.8004 B) 0.8694 C) 0.7812 D) 0.7559

1)

2) For a sample of 9 vehicles, the engine size (cc) and highway mileage (L / 100 km) were recorded: Size 1,200 1,500 1,850 2,200 2,450 2,700 3,000 3,250 3,500 Mileage 5.2 6.4 7.3 7.4 7.1 7.9 8.2 8.7 8.4 For an increase of 100 cc in engine size, how does the mileage change (L / 100 km)?

A) Deteriorate by 0.1289 B) Deteriorate by 1.2889 C) Improve by 1.2889 D) Improve by 0.1289

2)

3) For a sample of 7 people, the hours of exercise per week and weight (km) were measured: Exercise 0.25 1.5 3.0 4.25 6.0 7.5 9.75 Weight 98 95 88 83 80 76 78 For each additional hour of exercise, what is the expected change in weight?

A) Increase by 2.36 kg B) Decrease by 2.36 kg C) Increase by 0.37 kg D) Decrease by 0.37 kg

3)

4) For a sample of 7 households, annual household income (thousands) and annual amount given to charity were recorded: Income 28.9 35.7 42.6 52.9 64.3 77.0 85.4 Charity 25 40 95 152 267 350 504 What is the regression coefficient of the variables?

A) 0.9828 B) 0.9659 C) 0.9730 D) 0.9902

4)

5) Richmond City Public Library has recently increased the number of its holdings of books and magazines. In an attempt to to assess the impact of the increase, City's Planning Department ran a regression application between the number of holdings and the number of visitors ,per day, to the library with the following data: Number of Total visitors holdings per day 25000 252 25700 235 32000 260 32497 270 45600 325 What percentage of the variation with the per day number of visitors to the library is explained by the volume of the holdings in the library A) 94.09% B) 92.12% C) 97.00% D) 9.59%

5)

1

6) For a sample of 8 companies, the number of employees and gross annual sales (in thousands) were recorded: Employees 2 5 10 17 21 24 32 10 Sales 51.2 132.1 260.3 385.4 480.6 634.0 794.3 992.3 What percentage of the variation in gross annual sales is explained by the number of employees?

A) 36.83% B) 99.54% C) 99.02% D) 99.69%

6)

7) For a sample of 7 buses, the distance travelled (km) and the number of hours to travel the distance were recorded: Distance 75 182 243 315 420 560 764 Time 1.9 5.2 5.9 8.4 10.1 13.5 18.8 Based on a distance of 300 km, what is the upper limit of the 95% confidence interval of the average time to travel this distance?

A) 7.1676 B) 7.9572 C) 6.4309 D) 8.6639

7)

8) For a sample of 7 trucks, the distance travelled (km) and the number of hours to travel the distance were recorded: Distance 100 224 360 475 520 675 720 Time 2.4 5.2 7.8 8.9 10.8 12.8 15.5 If the distance is 450 km, what many hours should we expect the trip to take?

A) 9.34 B) 9.26 C) 9.31 D) 9.33

8)

9) For a sample of 8 children, their IQ and time to solve a particular puzzle (minutes) were recorded: IQ 60 69 73 78 82 86 90 95 Time 10.25 9.75 8.0 7.5 6.75 5.75 4.0 2.75 What percentage of the variation in the time to solve the puzzle is explained by IQ? A) 96.07% B) 95.12% C) 97.53% D) 97.24%

9)

10) For a sample of 9 people, the number of hours per week spent social computing and watching TV were recorded: Computer 5 8 10 12 15 17 20 22 28 TV 15 11 7 4 7 5 6 2 1 For 15 hours of social computing, what is the residual?

A) -1.4912 B) 1.4912 C) -0.4418 D) 0.4418

10)

11) For a sample of 8 companies, the annual gross income (millions) and technology expenditures (thousands) were recorded: Income 0.645 1.24 2.67 5.78 7.62 10.07 15.44 21.8 Technology 21.0 41.7 57.2 130.9 269.3 282.6 324.3 384.7 For a company with annual gross income of $7.5 million, what is the upper limit of the 95% prediction interval of its annual expenditure on technology rounding to the nearest dollar?

A) $130,774 B) $223,332 C) $315,336 D) $38,770

11)

12) For a sample of 6 companies, annual gross income (thousands) and average monthly expenditures on office supplies were recorded: Income 5.0 21.7 42.8 62.9 84.3 100.6 Office supplies 9.25 36.72 75.09 100.24 190.67 272.44 For companies with annual gross income of $52,540, what is the upper limit of the 95% confidence interval of monthly expenditures on office supplies rounded to the nearest dollar?

A) $145.99 B) $200.00 C) $26.34 D) $80.35

12)

2

13) A sample of 8 companies were taken measuring their current debt load (thousands) and annual gross profit (thousands): Debt 2 3.2 5.6 7.3 8.7 10.4 15.7 20.4 Profit 120.4 118.6 98.3 94.7 80.4 81.1 74.4 68.3 For an increase in debt load of $1,000, what is the average change in profit?

A) Decrease by $2,845 B) Increase by $1,181 C) Decrease by $1,181 D) Increase by $2,845

13)

14) For a sample of 7 shirts, the thread count and life of the shirt (years) were recorded: Count 100 150 200 250 300 350 400 Life 1.2 1.8 2.5 2.3 3.7 4.3 3.9 What percentage of the variation in a shirt's life is explained by the thread count?

A) 89.41% B) 94.55% C) 90.27% D) 96.2%

14)

15) For a group of 9 people, the distance to work (km) and the commute time (minutes) were recorded: Distance 3.2 4.8 6.4 8.4 10.7 12.8 16.5 18.6 20.5 Time 5 7 10 13 12 17 24 36 55 If the distance to work is 12 km, how long would we expect the travel time to be, rounding to the nearest minute?

A) 22 B) 18 C) 9 D) 21

15)

16) A study conducted by the human resources analyst found the following relationship between the 16) employees' annual salary and the number of casual absenteeism days, per year, as follows: No of days casual Annual salary absenteeism 22000 10 25000 9 35000 8 45000 4 56000 2 100000 1 75000 6 82000 2 95000 1 Run a trendline application between these two variable and determine if a linear trend can be established.

A) there is a negative linear relationship between these two variables, with the the best fit equation of y = -0.0001 + 10.92 B) there is a positive linear relationship between these two variables, with the the best fit equation of y = 0.0001 + 10.92 C) the data set is too small to make this determination D) these two variables are not related

3

17) For a sample of 8 regions, the average winter temperature and amount of snowfall (cm) were measured during one winter: -2.4 -7.4 -10.1 -15.2 -20.4 -28.6 Temperature 5.2 0.2 Snow 2.5 5.7 10.4 18.5 27.3 33.4 41.7 58.3 For an average winter temperature of -5.2 degrees, what is the lower limit of the 95% confidence interval of the average amount of snowfall?

A) 18.9441 B) 10.882 C) 14.6711 D) 22.7333

17)

18) For a sample of 9 homes, the size (thousands of square feet) and the selling price (thousands) were recorded: Size 1.0 1.2 1.34 1.44 1.52 1.69 1.73 1.82 2.42 Price 160.2 199.9 198.7 225.4 240.7 248.0 250.1 284.4 341.3 For a home with 1,600 square feet, what is the expected selling price?

A) $202,547 B) $204,612 C) $242,110 D) $234,009

18)

19) For a sample of 8 people, their weight (km) and heart rate at rest were measured: Weight 68.1 71.2 72.4 76.3 80.4 88.7 91.2 100.4 Heart rate 52 55 56 60 62 61 64 66 For a weight of 77 km, what would we expect the average heart rate to be?

A) 56.0 B) 60.7 C) 62.4 D) 57.9

19)

20) For a sample of 6 homes, the amount spent in the past 5 years on renovations and current home value (thousands) were recorded: Renovation 1,000 5,200 7,200 8,000 9,500 10,000 Value 240 287 275 305 412 464 If a homeowner spent $6,500 on renovations, what is the lower limit of the 95% prediction interval of the home value rounded to the nearest dollar?

A) $154,397 B) $387,981 C) $259,409 D) $492,994

20)

21) For a sample of 8 books, the number of pages and the price were recorded: Pages 256 312 378 425 479 508 560 610 Price 25.99 29.98 35.49 36.99 42.99 47.98 52.99 55.99 For books with 450 pages, based on the 95% confidence interval, what is the lower limit of the average price?

A) $37.90 B) $40.52 C) $45.78 D) $43.16

21)

22) For a sample of 9 athletes, the average amount of time per week training and the average time to run 1,500 m (minutes) were measured: Training 30 32 34 37 42 48 52 56 63 Run 4.91 4.83 4.72 4.56 4.33 4.25 4.16 4.03 3.92 For an athlete who trains 40 hours per week, what is the upper limit of the prediction interval of the time to run 1,500 metres, rounded to 2 decimals?

A) 4.33 B) 4.72 C) 4.59 D) 4.46

22)

23) For a sample of 9 regions, the average summer temperature and amount of rainfall (mm) was measured during one summer: Temperature 18 22.1 23.5 24.6 25.8 26.7 27 28.7 29.8 Rain 56.2 52.1 48.3 49.7 40.2 36.1 37.3 25.4 20.5 What percentage of the variation in rainfall is explained by average summer temperature?

A) 87.24% B) 91.23% C) 85.89% D) 92.6%

23)

4

24) For a sample of 8 companies, the number of employees and gross annual sales (in thousands) were recorded: Employees 3 7 12 18 22 29 35 42 Sales 74.3 100.2 280.7 460.7 500.4 662.8 900.4 970.6 For each additional employee, how do gross annual sales change on average?

A) Decrease by $24,499 B) Increase by $24.50 C) Decrease by $24.50 D) Increase by $24,499

24)

25) A sample of 6 customers is taken, measuring the amount of time spent in a store (minutes) and how much they spent: Time 5 10 15 20 25 30 Amount 10.25 16.24 24.62 45.62 72.39 97.34 For 15 minutes, what is the residual?

A) -10.86 B) 10.86 C) 9.84 D) -9.84

25)

26) For a sample of 6 computers, the number of transistors (millions) and the clock speed (Ghz) were recorded: Transistors 150 248 362 526 778 904 Clock Speed 3.2 3.02 2.75 2.42 2.03 1.78 For a computer with 322,640,000 transistors, what would we expect the clock speed to be?

A) 3.0127 B) 4.8612 C) 2.8546 D) 2.6214

26)

27) For a sample of 8 people, their annual household income (thousands) and average amount per month spent eating out were recorded: Income 25.2 30.7 41.3 48.7 56.9 67.0 78.9 85.2 Eating 20.12 25.18 45.62 44.08 62.80 78.40 90.15 120.47 For a decrease in annual household income by $1,500, what is the change in the average amount per month eating out?

A) Increase by $2.30 B) Decrease by 94 cents C) Increase by 94 cents D) Decrease by $2.30

27)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

28) For a sample of 7 people, their gross annual income (thousands) and annual amount invested (thousands) were measured: Income 45.2 50.7 59.2 62.3 68.8 72.0 83.8 Investment 0.6 1.2 2.8 3.5 4.8 6.9 15.9 It is suspected the last observation is an outlier. If it is removed, what is the difference in the average increase in investment for each additional $100 in income? Round to the nearest cent.

28)

29) For a sample of 8 calculators, the number of function and average selling price were recorded: Functions 25 42 87 96 102 115 147 163 Price 9.00 11.25 14.67 16.24 18.95 21.67 27.54 32.99 What percentage of the variation in the price is explained by the number of functions?

Express it as a decimal number accurate to 4 decimals.

29)

5

30) For a sample of 7 people, their weight (kg) and walking speed (km/hour) were measured: Weight 51 62 68 76 83 89 95 Speed 6.4 6.2 5.9 5.2 4.4 3.8 3.2 If a person weighs 70 kg, what would we expect their average walking speed to be? Round to 1 decimal.

30)

31) An excerpt from Excel's regression output is provided for the data set of number of visitors who came to Vancouver for the 2010 Winter Olympics and the per diem spending they had in City . Using the output, test for evidence of a positive slope between the two variables at =.05

31)

Regression output variables coefficient Intercept 737,074.1828 No. of visitors 137.9564

std. error 65.7543

32) For a sample of 8 plants of the same type, the amount of water per day they received (ml) and height after six weeks (cm) were measured: Water 10 15 20 25 30 35 40 45 Height 15.2 16.9 17.2 18.7 20.1 20.3 22.7 24.3 For a plant receiving 25 ml of water per day, what is the residual? Round to 1 decimal.

32)

33) A census conducted every five years in a country counted the number of people (millions).

These were the census results for a certain period of time: Year 1805 1810 1815 1820 1825 1830 Population 2.52 2.73 2.94 3.12 3.27 3.31 From the year 1812 to 1822, what would be the expected increase in the population? Round to the nearest hundred.

33)

34) Richmond City Public Library has recently increased the number of its holdings of books and magazines. In an attempt to to assess the impact of the increase, City's Planning Department ran a regression application between the number of holdings and the number of visitors ,per day, to the library with the following data Number of Total visitors holdings per day 25000 252 25700 235 32000 260 32497 270 45600 325

34)

Run a regression application between these two variables and determine the lower and upper limits of the confidence interval for the number of holdings.

6

35) For a sample of 7 pieces of steel, the percentage of iron and the hardness measured on a certain scale were measured: Iron 5 5.2 5.5 5.8 6.0 6.2 6.4 Hardness 58 59.2 64.8 66.1 69.9 70.4 73.0 What percentage of the variation in the hardness is explained by the percentage of steel.

Express it as decimal number accurate to 3 decimals.

35)

36) Richmond City Public Library has recently increased the number of its holdings of books and magazines. In an attempt to to assess the impact of the increase, City's Planning Department ran a regression application between the number of holdings and the number of visitors ,per day, to the library with the following data Number of Total visitors holdings per day 25000 252 25700 235 32000 260 32497 270 45600 325

36)

Run a regression application between these two variables and determine prediction equation for the expected number of visitors to the library.

37) For a group of 9 people on a diet, their average caloric intake per day and weight loss (kg) over six months were measured: Calories 950 980 1012 1020 1034 1042 1052 1066 1085 Loss 18.2 17.9 15.7 12.0 10.8 9.1 8.3 6.2 5.1 What is the correlation coefficient of caloric intake and weight loss? Express it as a decimal number accurate to 4 decimals.

37)

38) For a sample of 8 homes up for sale, the square footage (thousands) and the final selling price (thousands) were recorded: Size 1.2 1.33 1.42 1.57 1.6 1.75 1.83 2.04 Price 279.7 302.9 317.6 356.8 382.1 390.7 415.9 412.7 For each additional 100 square feet, what is the expected increase in the average selling price? Round to the nearest whole number.

38)

39) Richmond City Public Library has recently increased the number of its holdings of books and magazines. In an attempt to to assess the impact of the increase, City's Planning Department ran a regression application between the number of holdings and the number of visitors ,per day, to the library with the following data.

Number of Total visitors holdings per day 25000 252 25700 235 32000 260 32497 270 45600 325

39)

Run a regression application between these two variables and determine the t and the p values for the regression intercept.

7

40) For a certain make of car, 6 used vehicles were sampled. Their age and sale price (thousands) were recorded: Age 2 4.5 6 7.5 8 9.5 Price 25.1 18.7 15.2 12.5 10.4 8.7 For a 7-year old car of this make, what is the lower limit of the 95% prediction interval of the price? Round to the nearest hundred.

40)

41) For a sample of 8 machines, their age (years) and annual maintenance budget (thousands) were recorded: Age 2 5 7 9 13 14 17 19 Budget 0.52 1.34 1.52 1.63 1.81 1.79 1.92 2.32 For machines that are 10 years old, what is the upper limit of the 95% confidence interval of the average maintenance budget? Round to the nearest dollar.

41)

42) For a restaurant, a sample of 7 hours were randomly selected. The number of customers and the gross income rounded to the nearest dollar for each hour were recorded: Customers 25 41 57 64 68 79 87 Income 242 384 596 602 714 752 912 If the restaurant has 60 customers in an hour, what is the upper limit of the prediction interval of the gross income for that hour? Round to the nearest dollar.

42)

43) For a sample of 9 real estate agents, their number of years as an agent their annual gross income (thousands) were recorded: Years 1 2 3 4 9 10 15 18 24 Income 15.2 18.6 42.9 62.9 84.7 99.7 125.4 160.7 200.8 For each additional year as an agent, what is the expected increase in average annual gross income? Round to the nearest dollar.

43)

44) For a sample of 7 stores, their square footage (thousands) and average heating cost rounded to the nearest dollar were measured: Size 0.52 0.83 1.49 2.12 2.59 2.99 3.64 Heat 125 173 210 247 302 342 408 For a store measuring 1,600 square feet, what is the upper limit of the 95% confidence interval of the average monthly heating cost? Round to the nearest dollar.

44)

45) For a sample of 9 carpets, their weight (ounces) and duration (years) were measured: Weight 12 15 18 21 24 27 30 33 36 Duration 5 7 9 10 14 18 19 22 25 For a carpet that weighs 30 ounces, what is the residual? Round to 2 decimals.

45)

46) For a sample of 9 corporations, their gross annual income (millions) and training budget (millions) were measured: Income 2.5 7.4 12.8 18.8 26.4 30.7 45.8 60.2 75.7 Training 0.43 1.25 2.84 3.41 4.02 4.99 5.78 6.21 6.54 For an increase of $10,000 in gross annual income, what is the average increase in the training budget? Round to the nearest hundred.

46)

8

TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.

47) If you calculate all the residuals for the values of x and y used to create the least-squares line, the residuals will sum to zero.

47)

48) For a given value of x, the confidence interval for y is narrower than the prediction interval for y.

48)

49) In constructing a confidence interval for y, the t score used for the half-width of the interval has n-1 degrees of freedom.

49)

50) For a sample of 9 regions, the number of growing days was used to predict annual crop yields (thousands of kg): Days 90 95 102 127 134 139 142 158 169 Yield 25 102 185 257 346 420 502 590 650 For a growing period of 130 days, the lower limit of the 95% confidence interval of average yields is 244,710 kg.

50)

51) In constructing a model, if the correlation regression coefficient is close to zero, the model slope will also be close to zero.

51)

52) If you are working with time series data and in plotting the dates against the residuals, you find no discernable pattern, this indicates the residuals are independent over time.

52)

53) In constructing the line of best fit, it is necessary that the y values are normally distributed.

53)

54) The residual for a certain value of x is computed by subtracting the actual y value from the predicted y value.

54)

55) If you plot the x values against the residuals and there is a discernable pattern, the assumption of constant variability in residuals is satisfied.

55)

56) For a sample of 8 athletes, the average amount of sleep (hours) and reaction time (seconds) were recorded: Sleep 6.25 6.5 6.75 7 7.25 7.5 7.75 8 Reaction 0.15 0.12 0.1 0.11 0.09 0.095 0.087 0.082 If an athlete sleeps 7.5 hours, the upper limit of the 95% prediction interval of reaction time is 0.1038 seconds.

56)

57) Residuals in a regression application represent the difference between the actual y and the predicted y.

57)

58) You conduct a test at a 5% level of significance to determine if the slope is positive. The p-value is 0.238. From this, you would conclude there is a positive linear relationship between the x and y variables.

58)

59) The residuals in a regression application are important as they allow us to check whether the sample data appear to conform to the requirements of the least-squares regression application.

59)

9

60) In constructing a confidence interval for y, the interval will be narrowest at the point of the sample means.

60)

61) In constructing a confidence interval for y, it is acceptable to use a value of x outside the range of values used to construct the least-squares line.

61)

62) A line of best fit is y = 2.3 - 1.7x. The ordered pair (2, -1) was used in the construction of this model.

For this data pair, the residual is 0.1.

62)

63) In finding outliers, the standardized residuals should have a magnitude of 2 or more.

63)

64) Annual corporate income (millions) is used to predict average annual amount given to charity. The model constructed is: charity = 500.25 + 147.36(income). Based on this model, for each additional income of $100,000, the average charitable contribution increases by $14.74.

64)

65) For a sample of 7 golfers, average hours per week practising and average golf score were recorded: Practise 2 5 7.5 12 15.5 18 20.5 Score 108 102 98 92 88 85 80 Based on the constructed model, there is a strong positive linear relationship between the number of hours practising and average golf score.

65)

66) If the correlation between x and y is 0.9203, then the percentage of variation in y that is explained by the regression model is 92.03%

66)

67) Suppose annual household income (thousands) is used to predict average monthly expenditures eating out. You are given the model: eat = 25.60 + 0.02(income). If someone earns $45,000 per year, the model predicts the person spends $26.50 per month on average eating out.

67)

68) In creating the least squares line, y = bo + b1 x.

68)

10

Answer Key Testname: CHAPTER 13 1) B 2) D 3) B 4) A 5) A 6) A 7) B 8) B 9) B 10) D 11) C 12) A 13) A 14) A 15) A 16) A 17) C 18) C 19) D 20) A 21) B 22) B 23) C 24) D 25) A 26) C 27) D 28) 14.67 29) 0.9358 30) 5.4 31) Both the b0 and b1 coefficients are positive indicating a possible positive relationship between the two variables. That is, more visitors to the City, more per diem spending 32) -0.1 33) 328,600 34) 0.0022 and 0.0058 35) 0.976 36) Visitors expected = 139.68 + 0.00430 ( number of books) 37) -0.9652 38) 17,906 39) 7.3107850.005285 40) 11,300 41) 1.742 42) 699 43) 7849 44) 235 45) -0.43 46) 800 47) TRUE 48) TRUE 49) FALSE

11

Answer Key Testname: CHAPTER 13 50) FALSE 51) TRUE 52) TRUE 53) FALSE 54) FALSE 55) FALSE 56) FALSE 57) TRUE 58) FALSE 59) TRUE 60) TRUE 61) FALSE 62) TRUE 63) TRUE 64) TRUE 65) FALSE 66) FALSE 67) TRUE 68) TRUE

12

Chapter 14 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1) A multiple regression application was used to study how an individual's income (Y in dollars) is influenced by age (X1 in years), level of purchases preference for automobiles (X2 ranging from 1 =

1)

2) A multiple regression application was used to study how an individual's income (Y in dollars) is influenced by age (X1 in years), level of purchases preference for automobiles (X2 ranging from 1 =

2)

luxury car, 2 = basic commuter, 3 = medium size car ). The following is a partial result of a computer program that was used on a sample of 10 individuals. The data table is provided for this application.

Income (Y) Car Type (X1) Age (X2) 10000 3 30 20000 2 24 20100 3 24 30000 2 35 40000 2 46 40200 3 57 50000 1 57 60000 2 58 60300 1 45 70000 1 48 Compute the lower and upper confidence interval values for 95% confidence for the age (X2) variable A) lower interval value=-2271 , upper interval value=-2929 B) lower interval value= 243, upper interval value=1452 C) can not be computed, not sufficient data is provided D) lower interval value= 1452, upper interval value=243

luxury car, 2 = basic commuter, 3 = medium size car ). The following is a partial result of a computer program that was used on a sample of 10 individuals. The data table is provided for this application. Compute the coefficient of determination Income (Y) Car Type (X1) Age (X2) 10000 3 30 20000 2 24 20100 3 24 30000 2 35 40000 2 46 40200 3 57 50000 1 57 60000 2 58 60300 1 45 70000 1 48 Compute the multiple R Square value A) 0.78 B) 0.50 C) 0.82 D) 0.91

1

3) It is important that in running a t test for the significance, all of the following need to be included in the application: A) that all the explanatory variables that are significant contributors to the dependent variables should be included in the application B) that all the explanatory variables should be included in the application C) only the independents that have minimal error should be included in the application D) that all the residual error terms should be included in the application

3)

4) The coefficients in a multiple regression function are estimated by minimizing the sum of squared residuals. This application requires that a number of multiple regression models be created and tested for confirmation that: A) the predicted values be as close as possible to the observed values B) the residual errors be randomly distributed C) a combination of independent variables provide the best fit model D) regression function does provide a good fit for the independent variables chosen for the model

4)

5) The error term is assumed to be a random variable with a mean of: A) zero B) some, unpredicted random value C) -1 D) +1

5)

6) The standards deviation of error term is the same for every combination of x-values. This confirms that the different combinations of the x-values are not: A) irrelevant as the error term is changeable with each application B) are linearly connected C) related D) normally distributed as the standard deviation of the error term is the same for combination of x-values

6)

7) A multiple regression model must have at least: A) minimum of three independent variables C) one independent variable

7)

B) at least two independent variables D) no more than five independent variables

2

8) A multiple regression application was used to study how an individual's income (Y in dollars) is influenced by age (X1 in years), level of purchases preference for automobiles (X2 ranging from 1 =

8)

9) The total sum of squares (SST) is equal to: A) the sum of squares explained by the regression by the regression function (SSR) errors plus the sum of squares (SSE) B) the sum of squares explained by the regression by the regression function (SSR) errors plus the sum of squares total (SST) C) the sum of squares explained by the regression by the F test plus the sum of squares (SSE) D) the sum of squares explained by the regression residual errors plus the sum of squares (SSE)

9)

10)

10)

luxury car, 2 = basic commuter, 3 = medium size car ). The following is a partial result of a computer program that was used on a sample of 10 individuals. The data table is provided for this application.

Income (Y) Car Type (X1) Age (X2) 10000 3 30 20000 2 24 20100 3 24 30000 2 35 40000 2 46 40200 3 57 50000 1 57 60000 2 58 60300 1 45 70000 1 48 Compute the F critical value A) 1.816 B) 0.0002 C) 0.018 D) 16.89

Number of Sales Volume Sales sales agents =(Y) Expenses= X1 = X2 10 2 5 12 2 3 13 4 2 14 3 7 11 2 8 15 5 7 16 6 6 18 7 5 19 4 5 20 4 3 Find the regression equation for the above data set A) Y sales= 11.20 + 1.33 (X1 ) + (-0.31) (X2 )

B) Y sales= 11.20 - 0.31(X2 ) D) Y sales= 11.20 + 1.33 (X1 ) + (-0.31) (X2 )

C) Y sales= 11.20 + 1.33 (X1 )

3

11) A multiple regression application was used to study how an individual's income (Y in dollars) is influenced by age (X1 in years), level of purchases preference for automobiles (X2 ranging from 1 =

11)

luxury car, 2 = basic commuter, 3 = medium size car ). The following is a partial result of a computer program that was used on a sample of 10 individuals. The data table is provided for this application.

Income (Y) Car Type (X1) Age (X2) 10000 3 30 20000 2 24 20100 3 24 30000 2 35 40000 2 46 40200 3 57 50000 1 57 60000 2 58 60300 1 45 70000 1 48 Perform a t test and determine whether or not the coefficient of the variable "age" (X2 ) is significantly different from zero. Let = 0.05.

A) Since the t critical value = 3.32, and the equivalent p value=.012< significant B) Since the t critical value = 3.32, and the equivalent p value=.015< significant C) Since the t critical value = 3.32, and the equivalent p value=0.11> significant D) Since the t critical value = 3.32, and the equivalent p value=.018< significant

12) Stock Value ($)=Y 15 17 22 21 34 35 37 43 44 54

Earnings per share ($)=X1 2 1 1.50 4 2.25 0.75 0.80 0.95 1.25 1.45

= 0.05, the coefficient is = 0.05, the coefficient is = 0.05, the coefficient is = 0.05, the coefficient is

12)

Dividend payout ratio (%)=X2 35 33 21 24 27 28 29 22 33 31

Compute the t statistic and the p value for the earnings per share (X1) variable.

A) t statistic= 4.71, p value=0.30 B) t statistic= 0.142, p value=0.30 C) t statistic= 1.65, p value=0.30 D) t statistic= -1.12, p value=0.30

4

13) A multiple regression application was used to study how an individual's income (Y in dollars) is influenced by age (X1 in years), level of purchases preference for automobiles (X2 ranging from 1 =

13)

luxury car, 2 = basic commuter, 3 = medium size car ). The following is a partial result of a computer program that was used on a sample of 10 individuals. The data table is provided for this application. Find the multiple regression prediction equation for this data set Income (Y) Car Type (X1) Age (X2) 10000 3 30 20000 2 24 20100 3 24 30000 2 35 40000 2 46 40200 3 57 50000 1 57 60000 2 58 60300 1 45 70000 1 48

A) Y predicted= 29763. 81 + 12823.3(X1 ) + 847.70 (X2 ) B) Y predicted= 16386 +12823.3 (X1 ) + 847.70 (X2 )

C) Y predicted= 29763. 81 + (-12823.3) (X1 ) + 847.70 (X2 ) D) Y predicted= 29763. 81 + (-12823.3) (X1 ) + 847.70 (X2 ) 14) Stock Value ($)=Y 15 17 22 21 34 35 37 43 44 54

Earnings per share ($)=X1 2 1 1.50 4 2.25 0.75 0.80 0.95 1.25 1.45

14)

Dividend payout ratio (%)=X2 35 33 21 24 27 28 29 22 33 31

For a multiple regression, compute the adjusted R Square value.

A) R Square adjusted value=-0.088 B) R Square adjusted value=13.56 C) R Square adjusted value=0.154 D) R Square adjusted value=0.391

5

15) A study conducted by the Central Mortgage and Housing Corporation on the recent sales dollar volume of average single family homes in Vancouver yielded the following results: Average home price (in Home size dollars)= Y (square Number of Number of dependent footage)= X1 bedrooms= X2 bathrooms= X3 554000 1250 3 3 560000 1280 3 3 625000 1350 4 4 726000 1450 4 4 785000 1500 5 3 675000 1800 5 4 556000 1100 3 2 450000 1050 2 2 560000 1125 2 2 680000 1455 4 3 Run a multiple regression application and determine which of the response variables are the most significant ones explaining the average home price. Use the Adjusted R Square value criteria A) home size , number of bathrooms and the number of bedrooms with the Adjusted R Square value=0.88 B) home size and the number of bedrooms with the Adjusted R Square value=0.78 C) home size and the number of bedrooms with the Adjusted R Square value=0.75 D) home size and the number of bedrooms with the Adjusted R Square value=0.72

15)

16) A regression analysis has 10 independent variables and 150 observations. The degrees of freedom for the error of the sum of squares is: A) 150 degrees of freedom B) 149 degrees of freedom C) 140 degrees of freedom D) 139 degrees of freedom

16)

17) A study conducted by the Central Mortgage and Housing Corporation on the recent sales dollar volume of average single family homes in Vancouver yielded the following results: Average home price (in Home size Number of dollars) = Y (square Number of bathrooms = dependent footage) = X1 bedrooms = X2 X3 554000 1250 3 3 560000 1280 3 3 625000 1350 4 4 726000 1450 4 4 785000 1500 5 3 675000 1800 5 4 556000 1100 3 2 450000 1050 2 2 560000 1125 2 2 680000 1455 4 3 Run a multiple regression application and the F test model fit criteria to determine if the regression model is significant.

A) Is significant at the 0.05 level B) Is significant at the 0.02 level C) Is significant at the 0.01 level D) Is not statistically significant

17)

6

18) In a multiple regression application SSR = 2,000 and SSE = 500 The F statistic for this function is: A) F test needs degrees of [ n - k (k + 1) ] to compute the critical value B) not sufficient information is provided: C) F test is not relevant for this application D) t test is more relevant in this case

18)

19) The equation relating the predicted value of the dependent variable to the value of the independent is called: A) simple linear multiple regression B) multiple linear application C) multiple regression D) multiple linear applications

19)

20)

20)

Stock Value ($)=Y 15 17 22 21 34 35 37 43 44 54

Earnings per share ($)=X1 2 1 1.50 4 2.25 0.75 0.80 0.95 1.25 1.45

Dividend payout ratio (%)=X2 35 33 21 24 27 28 29 22 33 31

For the above data set, run a multiple regression application and find the regression equation for the stock value (Y).

A) Y stock value = 49.33 + 5.30 (X1) + 0.31(X2) B) Y stock value = -49.33 + (-5.30) (X1) + (-0.31) (X2) C) Y stock value = 50.33 + 5.30 (X1) + (-0.31) (X2) D) Y stock value = 49.33 + (-5.30) (X1) + (-0.31) (X2)

21) In assessing the level of significance of a multiple regression function, we conduct a hypothesis by testing: A) how much variation coefficient terms is explained by the regression relationship B) how much variation in the residual error distribution is explained by the regression relationship C) how much variation in the x-variables is explained by the regression relationship D) how much variation in the y-variable is explained by the regression relationship

21)

22) If the hypothesis test of the overall regression model indicates a significant relationship between the response variable and at least one of the explanatory variables, the next step is: A) to figure out which of the explanatory variables is significant in increasing the overall model F value B) to figure out which of the explanatory variables has a large p value for level of significance C) to figure out which of the explanatory variables is insignificant D) to figure out which of the explanatory variables is significant

22)

7

23) In a multiple regression analysis involving 20 independent variables and 1000 observations, SST = 900 and SSE = 150. The adjusted coefficient of determination is: A) 0.17 B) 0.83 C) 0.50 D) 0.75

23)

24) The following linear application represents: y = 0 + 0 X1 + 2 X2 + + p Xp + A) predicted linear multiple regression B) multiple regression function C) predicted multiple regression function D) a linear, multiple relationship

24)

25)

25)

Dividend Stock Value Earnings per payout ratio ($)=Y share ($)=X1 (%)=X2 15 2 35 17 1 33 22 1.50 21 21 4 24 34 2.25 27 35 0.75 28 37 0.80 29 43 0.95 22 44 1.25 33 54 1.45 31 Test the level of significance of of the dividend payout ratio coefficient (X2) variable at 0.05 level of significance.

A) since the p value=0.143 > 0.05 level of significance, we fail to reject Ho

B) since the p value=0.30 > 0.05 level of significance, we fail to reject Ho

C) since the p value=0.76 < 0.05 level of significance, we reject Ho

D) since the p value=0.76 > 0.05 level of significance, we fail to reject Ho 26)

Standard Number of deviation of investments 91 day T Bill bond yields made into returns (%)= Y (%)=X1 T-Bills (#)=X2 1.35 5 10000 1.66 6 12500 2.00 7 13000 1.88 5.5 14500 1.89 4 11250 1.44 3.5 22000 1.45 4.5 24000 1.67 2 21000 1.89 1.25 15600 2.11 2.45 21800 Run a multiple regression application and compute the Adjusted R Square value.

A) adjusted R Square value= -0.23 B) adjusted R Square value= 0.29 C) adjusted R Square value= 0.579 D) adjusted R Square value= 0.209

27) The adjusted R Square value will generally be smaller then the unadjusted Square value because: A) SST is divided by n - 1 B) SSE is too small C) n - (k + 1) adjustment D) SSE is too large 8

26)

27)

28)

Dividend Stock Value Earnings per payout ratio ($)=Y share ($)=X1 (%)=X2 15 2 35 17 1 33 22 1.50 21 21 4 24 34 2.25 27 35 0.75 28 37 0.80 29 43 0.95 22 44 1.25 33 54 1.45 31 For this data set, a multiple regression application is run and the following output is provided:

Intercept Earnings per share ($)=X1 Dividend payout ratio (%)=X2

Coefficients 49.32987383

Standard Error 29.87064998

-5.29942662

4.716415045

-0.306617964

0.95656041

ANOVA df SS Regression 2 233.7487692 Residual 7 1287.851231 Test to see if the Y dependent variable is significantly related to the independent variables. Use 0.05 level of significance.

A) since the p value =0.76 > 0.05, there is a significant relationship B) since the p value =0.56 > 0.05, there is no significant relationship C) since the p value =0.14 > 0.05, there is no significant relationship D) since the p value =0.76 > 0.05, there is no significant relationship

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28)

29) ANOVA

29)

df SS MS F Significance F Regression 2 67.33267773 33.66633887 0.028646696 Residual 7 38.2673222 Total 9 105.6 The partial ANOVA table is provided for a multiple regression application. Fill the missing parts of the table A) ANOVA df SS MS F Significance F Regression 2 67.33267773 33.66633887 6.158371114 0.028646696 Residual 7 38.26732227 5.466760324 Total 9 105.6

B) ANOVA Regression Residual Total

df 2 7 9

SS 67.33267773 38.26732227 107.6

MS 43.66633887 9.466760324

F 9.158371114

Significance F 0.028646696

df 2 8 10

SS 67.33267773 38.26732227 110.6

MS 33.66633887 5.466760324

F 6.158371114

Significance F 0.028646696

df 2 7 9

SS 77.33267773 38.26732227 105.6

MS 33.66633887 6.466760324

F 6.158371114

Significance F 0.028646696

C) ANOVA Regression Residual Total

D) ANOVA Regression Residual Total

30) The owner of a stationary store is interested in determining whether the average purchase amount of laptop computers differs by age. She has collected a random sample of customers in three age categories: Under 30, 30-50, over 50. Given the following sample data collected, does it appear that there is a relationship between customer age and the value of the laptop computer purchases Laptop 1=under 30, Purchase 0=Not under 1=30-50, 0=Not Amount 30 30-50 500 1 0 450 1 0 650 1 0 452 0 1 350 0 1 450 0 1 567 0 1 650 0 1 600 0 1 Determine the degrees of freedom (df) for Within Group variation A) 7 B) 6 C) 2 D) 26 10

30)

31) The owner of a stationary store is interested in determining whether the average purchase amount of laptop computers differs by age. She has collected a random sample of customers in three age categories: Under 30, 30-50, over 50. Given the following sample data collected, does it appear that there is a relationship between customer age and the value of the laptop computer purchases Laptop Purchase 1 = under 30, 1 = 30-50, Amount 0 = Not under 30 0 = Not 30-50 500 1 0 450 1 0 650 1 0 452 0 1 350 0 1 450 0 1 567 0 1 650 0 1 600 0 1 Compute the SSR value for Between Groups variation A) 953.3889 B) 1697795 C) 86123 D) 68510

31)

32) The t statistic for test of significance of the explanatory variables is computed with: A) [n-(k+2) ] degrees of freedom B) [n-(k+1) ] degrees of freedom C) [n-(k-1) ]degrees of freedom D) [n+(k+1) ]degrees of freedom

32)

33) It is important to use the following test to determine for the significance level of each independent variable: A) t-test B) Z value test C) p value test D) F test

33)

34) The owner of a stationary store is interested in determining whether the average purchase amount of laptop computers differs by age. She has collected a random sample of customers in three age categories: Under 30, 30-50, over 50. Given the following sample data collected, does it appear that there is a relationship between customer age and the value of the laptop computer purchases Laptop Purchase 1 = under 30, 1 = 30-50, Amount 0 = Not under 30 0 = Not 30-50 500 1 0 450 1 0 650 1 0 452 0 1 350 0 1 450 0 1 567 0 1 650 0 1 600 0 1 Compute the F test for this application and the matching p value A) F value=519, p value < 0.00 B) F value=3588, p value> 0.00 C) F=.078361, p value > .90 D) F=225, p value> 0.00

34)

35) In a multiple regression application, SST = 600 and SSE = 25. The coefficient of determination is: A) 0.02 B) 0.98 C) 0.96 D) 0.04

35)

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36) We have to refer to the sampling distribution of the F statistics to: A) decide whether any specific F statistic is unusual enough for us to reject the alternate hypothesis B) decide whether any specific F statistic is unusual enough for us to reject the alternate hypothesis C) decide whether any specific F statistic is unusual enough for us to reject the null hypothesis D) decide whether any specific p value is unusual enough for us to reject the null hypothesis

36)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

37) This Section Intentionally Left Blank

37)

TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.

38) Adjusted R Square will normally be greater than the R Square, coefficient of determination, value.

38)

39) When the p value is very small, it is easier to reject the null hypothesis.

39)

40) One method of indicating the best possible regression model is to create regressions for all possible combinations of the explanatory variables being examined.

40)

41) F test should be conducted for the individual coefficients if the t -test shows degree of importance.

41)

42) Adding more explanatory variables to the regression model will never reduce the R Square value.

42)

43) The standard deviation of the error term is the same for every combination of x-values.

43)

44) The a linear regression model does not show a good fit with the data set, we have no further analytic options available to analyze the data.

44)

45) In a regression application, the variability of the error term shows constant variability.

45)

46) SST = SSR - SSE.

46)

47) The analysis of of the residuals is required to check whether the sample data appear to conform to the requirements of the least-squares regression model.

47)

48) The adjusted R Square value provides a measure of the strength of the relationship between explanatory and the response variable.

48)

49) The coefficients of b0 and b1 are computed by minimizing the sum of squared residuals.

49)

50) A histogram is created to determine the normality of the residual error terms.

50)

51) Small p values are likely more strongly related to the response variable.

51)

52) Outliers in the distribution of the outliers provides an opportunity to determine if there are any coding errors in the regression application.

52)

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53) The number of explanatory variables does not give some indication of the data requirements of the model.

53)

54) It is legitimate to make predictions from the regression model for values of the explanatory variables that are outside the range of the values in the data set on which the regression model is based.

54)

55) The standard error in a regression model provides some indication how wide the interval and confidence interval should be.

55)

56) The normal distributions of actual y values around a predicted y values from the regression relationship will not have the same variability for every specific combinations of x values.

56)

57) The additional plots of the residual error term can indicate if the explanatory variables might have a problem.

57)

58) An influential observation of the residuals may have an extreme effect on the regression model.

58)

59) In a regression model, the coefficients should represent a reasonable cause and effect relationship between all the explanatory variables.

59)

60) Outliers and influencial observations with the residual terms in a regression function need to be examined in order to determine if there are any coding errors in the data set.

60)

61) The test of the coefficient of explanatory variables is conducted by use of a t-test.

61)

62) The regression model does not have to be a stable model as small changes in the explanatory variables may impact the beta coefficients.

62)

63) A histogram of the residuals is created to check for normality.

63)

64) A regression prediction interval predicts a particular value of y for a set of specific values of the x-variables.

64)

65) Adding an explanatory variable increases the degrees of freedom for the t score.

65)

66) The coefficients in a regression function are estimated by maximizing the sum of squared residuals.

66)

67) Constructing confidence intervals in a multiple regression model is only possible by use of matrix algebra.

67)

68) The p -values of the individual coefficients do provide some indication of how important each explanatory variable is.

68)

69) A plot of the residuals against the predicted values from the model can provide an indication of whether the variability of the error term is continuous.

69)

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70) A model with less variability in the error terms will produce narrower and possibly more useful prediction interval.

70)

71) SSR can be computed as: SSR= SST + SSE.

71)

72) Construction of a prediction interval in a multiple regression application does not require designation of a confidence level.

72)

73) The total sum of squares (SST) is equal to the sum of squares explained by the regression function.

73)

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Answer Key Testname: CHAPTER 14 1) B 2) D 3) B 4) A 5) A 6) C 7) B 8) D 9) A 10) D 11) A 12) D 13) A 14) A 15) D 16) D 17) A 18) B 19) C 20) D 21) D 22) D 23) B 24) C 25) D 26) A 27) C 28) B 29) A 30) A 31) A 32) B 33) A 34) C 35) C 36) C 37) 38) FALSE 39) TRUE 40) TRUE 41) FALSE 42) TRUE 43) TRUE 44) FALSE 45) TRUE 46) FALSE 47) TRUE 48) TRUE 49) TRUE 50) TRUE 15

Answer Key Testname: CHAPTER 14 51) TRUE 52) TRUE 53) FALSE 54) FALSE 55) TRUE 56) FALSE 57) TRUE 58) TRUE 59) FALSE 60) TRUE 61) TRUE 62) FALSE 63) TRUE 64) TRUE 65) FALSE 66) FALSE 67) TRUE 68) TRUE 69) FALSE 70) TRUE 71) FALSE 72) FALSE 73) TRUE

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