Statistical Methods for Business
Final Test Solutions
Course Introduction
Statistical Methods for Business introduces students to the fundamental concepts and techniques of statistics as applied to business decision-making. The course covers descriptive statistics, probability distributions, hypothesis testing, confidence intervals, correlation and regression analysis, and analysis of variance. Emphasis is placed on interpreting data, drawing valid conclusions, and utilizing statistical software for real-world business applications. By the end of the course, students will be equipped to analyze business problems quantitatively, make informed decisions, and communicate statistical findings effectively.
Recommended Textbook
Statistical Techniques in Business and Economics 15th Edition by Douglas A. Lind
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Page 2
Chapter 1: What Is Statistics
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Sample Questions
Q1) A variable that can have any value within a specific range is called _______________.
Answer: continuous
Q2) Statistics is defined as a body of techniques used to facilitate the collection, organization, presentation, analysis and interpretation of information for the purpose of making better decisions.
A)True
B)False
Answer: True
Q3) The science of collecting, organizing, presenting, analyzing, and interpreting of data is called __________________.
Answer: statistics
Q4) The ordinal level of measurement is considered the "lowest" level of measurement. A)True
B)False
Answer: False
Q5) The lowest level of measurement that has some sort of ranking is __________. Answer: ordinal
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Chapter 2: Describing Data: Frequency Tables, Frequency
Distributions, and Graphic Presentation
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Sample Questions
Q1) A cumulative frequency distribution is used when we want to determine how many observations lie above or below certain values.
A)True
B)False
Answer: True
Q2) A small sample of computer operators shows monthly incomes of $1,950, $1,775, $2,060, $1,840, $1,795, $1,890, $1,925 and $1,810. What are these ungrouped numbers called?
A) Histogram
B) Class limits
C) Class frequencies
D) Raw data
Answer: D
Q3) To convert a frequency distribution to a relative frequency distribution, divide each class frequency by the sum of the class frequencies.
A)True
B)False
Answer: True
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Chapter 3: Describing Data: Numerical Measures
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Sample Questions
Q1) The lengths of time (in minutes) several underwriters took to review applications for similar insurance coverage are: 50, 230, 52 and 57. What is the median length of time required to review an application?
A) 54.5
B) 141.0
C) 97.25
D) 109.0
Answer: A
Q2) Ten experts rated a newly developed chocolate chip cookie on a scale of 1 to 50. Their ratings were: 34, 35, 41, 28, 26, 29, 32, 36, 38 and 40. What is the mean deviation?
A) 8.00
B) 4.12
C) 12.67
D) 0.75
Answer: B
Q3) What is the difference between the largest and the smallest values in a set of data?
Answer: Range
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5
Chapter 4: Describing Data: Displaying and Exploring Data
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Sample Questions
Q1) A dot plot is best applied for a data set with
A) 1,000 observations.
B) 50 observations.
C) More than one variable.
D) A one mode.
Q2) What is the difference between a scatter diagram and a contingency table?
Q3) A dot plot is best applied when
A) The mean, median and mode are equal.
B) The general shape of a distribution is symmetric.
C) The relationship between two variables is summarized.
D) A single variable is summarized.
Q4) What is the common purpose of a scatter diagram and a contingency table?
Q5) A dot plot shows the
A) The general shape of a distribution.
B) The mean, median, and mode.
C) The relationship between two variables.
D) The interquartile range.
Q6) The Pearson's coefficient of skewness (Sk) measures the amount of skewness and may range from -3.0 to +3.0. It is computed by subtracting the median from the mean, multiplying the result by 3 and dividing by _______________.
Page 6
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Chapter 5: A Survey of Probability Concepts
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Sample Questions
Q1) To summarize the frequencies of two nominal or ordinal variables and compute conditional probabilities, what table can be used? _______________
Q2) When are two outcomes independent? Explain in terms of the rules of probability. A. In other words, the probability of A is unaffected by B.
Q3) A tire manufacturer advertises, "the median life of our new all-season radial tire is 50,000 miles. An immediate adjustment will be made on any tire that does not last 50,000 miles." You purchased four of these tires. What is the probability that all four tires will wear out before traveling 50,000 miles?
A) 1/10 or 0.10
B) ¼ or 0.25
C) 1/64 or 0.0156
D) 1/16 or 0.0625
Q4) When the special rule of addition is used, the events must be _______________.
Q5) Draw a Venn diagram showing the probability for two mutually exclusive events and a Venn diagram showing the probability for two events that are not mutually exclusive. Explain the difference in the two diagrams.
Q6) What is the difference between a permutation and a combination?
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Chapter 6: Discrete Probability Distributions
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Sample Questions
Q1) In a binomial, hypergeometric, and Poisson distribution, the random variable is
Q2) The variance shows the skewness of a probability distribution.
A)True
B)False
Q3) Elly's hot dog emporium is famous for its chilidogs. Elly's latest sales indicate that 30% of the customers order their chilidogs with hot peppers. Suppose 18 customers are selected at random. What is the probability that between two and six people inclusive want hot peppers? ________
Q4) When observing a check-out line at a food store, the average number of people served is 30 per hour. Using the Poisson distribution, what is the probability that 20 people check out in any given hour?
Q5) The mean of a probability distribution is called its expected value.
A)True
B)False
Q6) For any probability distribution, the standard deviation is the ______________.
Q7) If n = 900 and \(\pi\) = ?, what is the variance of this binomial distribution?
Q8) In a binomial experiment, the probability of a _________ remains constant.
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Chapter 7: Continuous Probability Distributions
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Sample Questions
Q1) The mean amount spent by a family of four on food per month is $500 with a standard deviation of $75. Assuming that the food costs are normally distributed, what is the probability that a family spends less than $410 per month?
A) 0.2158
B) 0.8750
C) 0.0362
D) 0.1151
Q2) The standardized z value measures distance between an outcome, X, and the mean by the number of _____________________.
Q3) From past history, the scores on a statistics test are normally distributed with a mean score of 70 and a standard deviation of 5. To earn a "C" on the test, a student must be in the top 25% of the class. What should a student score to receive a "C"? _______
Q4) What is the formula to convert any normal distribution to the standard normal distribution? _______________________
Q5) For the exponential distribution, the mean and standard deviation are equal. A)True B)False
Q6) The exponential distribution can be used to predict ________.
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Chapter 8: Sampling Methods and the Central Limit
Theorem
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Sample Questions
Q1) When dividing a population into subgroups so that a random sample from each subgroup can be collected, what type of sampling is used?
A) Simple random sampling
B) Systematic sampling
C) Stratified random sampling
D) Cluster sampling
Q2) The American Auto Association reports the mean price per gallon of regular gasoline is $3.10 with a population standard deviation of $0.20. Assume a random sample of 16 gasoline stations is selected and their mean cost for regular gasoline is computed. What is the probability that the sample mean is between $2.98 and $3.12?
Q3) If 40 samples of size 21 were selected from a population of 22,493, we would expect the mean of the sample means and the population mean to be close but not exactly equal.
A)True
B)False
Q4) The difference between the population mean and a sample mean is called
Q5) A population consists of 12 values. How many samples of size six are possible?
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Q6) A population consists of ten values. How many samples of size six are possible?
Chapter 9: Estimation and Confidence Intervals
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Sample Questions
Q1) Explain the concept of a confidence interval when estimating a population mean.
Q2) To compute a confidence interval, a __________ is used when the population standard deviation is unknown.
Q3) Which of the following is NOT necessary to determine how large a sample to select from a population?
A) Level of confidence in estimating the population parameter
B) Size of the population
C) Maximum allowable error in estimating the population parameter
D) Estimate of the population variation
Q4) A sample mean is the best point estimate of
A) the population standard deviation
B) the population median
C) the population mean
D) the sample standard deviation
Q5) What type of estimate states the range within which a population parameter probably lies? _____________
Q6) A finite population correction factor is used to adjust the _________________.
Q7) The finite population correction factor is used to adjust the z-statistic.
A)True
B)False
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Chapter 10: One-Sample Tests of Hypothesis
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Sample Questions
Q1) It is claimed that in a bushel of peaches, less than ten percent are defective. A sample of 400 peaches is examined and 50 are found to be defective. What is the critical value for \(\alpha\) = 0.025?
A) 1.96
B)\(\pm\) 1.65
C) -1.96
D) -1.65
Q2) What is the critical value of t for the alternative hypothesis µ < 12, a level of significance of 0.005 and a sample size of 20? _______
Q3) A manufacturer wants to increase the shelf life of a line of cake mixes. Past records indicate that the average shelf life of the mix is 216 days. After a revised mix has been developed, a sample of nine boxes of cake mix had a mean of 217.222 and a standard deviation of 1.2019. At the 0.025 significance level, decide if the sample data support the claim that shelf life has increased. State your decision in terms of the null hypothesis.
Q4) How is a significance level determined and how is it related to Type I error?
Q5) How is the significance level related to a p-value when the null hypothesis is rejected?
Q6) When planning an experiment, how is a significance level related to sample size?
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Chapter 11: Two-Sample Tests of Hypothesis
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Sample Questions
Q1) When the population standard deviations are unknown, what is the purpose of pooling the sample variances when testing the difference between two population means? ___________
Q2) If the decision is to reject the null hypothesis of no difference between two population proportions at the 5% level of significance, what are the alternative hypothesis and rejection region?
A) H<sub>0</sub>: \(\pi\)<sub>1</sub> \(\neq\) \(\pi\)<sub>2</sub>; z > 1.65 and z < -1.65
B) H<sub>0</sub>: \(\pi\)<sub>1</sub> \(\neq\)\(\pi\)<sub>2</sub>; z > 1.96 and z < -1.96
C) H<sub>0</sub>: \(\pi\)<sub>1</sub> > \(\pi\)<sub>2</sub>; z < - 1.65
D) H<sub>0</sub>: \(\pi\)<sub>1</sub> > \(\pi\)<sub>2</sub>; z < -1.96F
Q3) If we are testing for the difference between two population proportions, it is assumed that the two populations follow the ________________ distribution.
Q4) When testing for a difference between the means of two dependent samples the sample test statistic is a _____________.
Q5) If a hypothesis states that one population mean is greater than another population mean, then the test is _______________.
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Chapter 12: Analysis of Variance
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Sample Questions
Q1) When a blocking effect is included in an ANOVA, the analysis is more likely to detect differences in the treatment means.
A)True
B)False
Q2) If an ANOVA test is conducted and the null hypothesis is rejected, what does this indicate?
A) Too many degrees of freedom
B) No difference between the population means
C) A difference between at least one pair of population means
D) All population means are different
Q3) In a two-way ANOVA table with interaction, what are the error degrees of freedom?
Q4) ANOVA requires that the populations should be ______, ______, and _____.
Q5) In a two-way ANOVA, the sources of variation are
A) Total variation and error variation.
B) Total variation, treatment variation, and error variation.
C) Total variation, treatment variation, blocking variation and error variation.
D) Treatment variation and blocking variation.
Q6) What test statistic is used to compare two variances? ________________
Q7) What is the purpose of using a blocking variable in a two-way ANOVA?
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Chapter 13: Correlation and Linear Regression
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Sample Questions
Q1) Which value of r indicates a stronger correlation than 0.40?
A) -0.30
B) -0.50
C) +0.38
D) 0
Q2) One assumption underlying linear regression is that the Y values are statistically dependent. This means that in selecting a sample, the Y values chosen, for a particular X value, depend on the Y values for any other X value.
A)True
B)False
Q3) Perfect correlation means that the scatter diagram will appear as a _____________________.
Q4) What principle minimizes the sum of the squares of the vertical deviations about the line? _______________
Q5) In the equation = a + bX, what is ?
A) Slope of the line
B) Y intercept
C) Predicted value of Y, given a specific X value
D) Value of Y when X = 0
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Chapter 14: Multiple Regression Analysis
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Sample Questions
Q1) Stepwise regression analysis is also called a "backward elimination" method.
A)True
B)False
Q2) If there are four independent variables in a multiple regression equation, there are also four
A) Y-intercepts.
B) regression coefficients.
C) dependent variables.
D) constant terms.
Q3) In multiple regression analysis, when the independent variables are highly correlated, this situation is called ___________________.
A) Autocorrelation
B) Multicollinearity
C) Homoscedasticity
D) Curvilinearity
Q4) In multiple regression, what statistic accounts for the variance of additional independent variables? _____________
Q5) In a multiple regression analysis, how many sources of variation are listed? Name the sources of variation. _____________
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Chapter 15: Index Numbers
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Sample Questions
Q1) The Paasche method uses the amounts consumed in the base period, q<sub>0</sub>, as weights to determine a price index.
A)True B)False
Q2) Sean McCarthy earns $20,000 a year; John Nowak, $35,000. What is John's income as an index using Sean's income as the base?
A) 175.0
B) 75.0
C) 100.0
D) 57.1
Q3) Suppose your annual 2001 salary was $40,000 and your 2006 salary was $52,000. Assume the annual CPI rose from 177.1 to 202.9 during this period of time. In which year was your "real" income larger? ________
Q4) If the Laspeyres' index is 135.41 and the Paasche index is 145.34, what is the Fisher's Ideal Index?
Q5) What is the purpose of an index?
Q6) If the base value is 100 and the current period value is 250, what is the index for the current period?
Page 17
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Chapter 16: Time Series and Forecasting
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Sample Questions
Q1) To calculate quarterly typical seasonal indexes, how many periods are included in the ratio-to-moving-average method?
A) Two
B) Four
C) Six
D) Twelve
Q2) The forecast for the third quarter is 3,000 units; the seasonal index for the quarter is 0.75. What are the seasonally adjusted sales for the quarter?
A) 3,000
B) 3,079
C) 2,250
D) 1,015
Q3) Episodic and residual variations can be projected into the future.
A)True
B)False
Q4) If we eliminate trend, cyclical and irregular variation from a monthly sales series, what time series component remains? _________________________
Q5) In the linear trend equation, what variable represents the Y-intercept? ______
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Chapter 17: Nonparametric Methods: Goodness-Of-Fit
Tests
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Sample Questions
Q1) For any chi-square goodness-of-fit problem, the number of degrees of freedom is found by
A) n - k - 1.
B) k - 1.
C) n + 1.
D) n + k.
Q2) To determine if a set of ungrouped, raw data is normally distributed, we can use
A) Graphical methods.
B) A chi-square test.
C) ANOVA.
D) Regression.
Q3) If we wanted to see if tossing a die (a cube with the sides numbered one through six) had an equal chance of showing each side or number, what statistical test should be applied?
Q4) For a chi-square test involving a contingency table, suppose the null hypothesis is rejected. We conclude that the two variables are
A) linear.
B) curvilinear.
C) not related.
D) related.
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Chapter 18: Nonparametric Methods: Analysis of Ranked
Data
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Sample Questions
Q1) What is a null hypothesis for a one-tail sign test?
A) H<sub>0</sub>: \(\pi\) = 0
B) H<sub>0</sub>: \(\pi\) \(\le\)1.00
C) H<sub>0</sub>: \(\pi\) = 0.50
D) H<sub>0</sub>:\(\pi\) \(\le\) 0.50
Q2) One difference between the Kruskal-Wallis method and one-way ANOVA is that the Kruskal-Wallace tests do not require the population ___________ to be the same.
Q3) In a Kruskal-Wallis test, the null hypothesis states equality among five different populations. The sample size for each population exceeds five. What is the critical value for the test using a 0.05 significance level?
A) 1.960
B) 5.05
C) 9.488
D) 2.776
Q4) In a sign test, the test statistic is based on the _______________ distribution.
Q5) When are nonparametric methods best applied?
Q6) The Spearman coefficient of rank correlation method ____________ the observations in each sample.
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Q7) The Kruskal-Wallis Test is the nonparametric analogy to a one-way ________.
Chapter 19: Statistical Process Control and Quality Management
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Sample Questions
Q1) The following are examples of attributes: the width of a cracked weld, the length of time that a relay works; the amount of water in a radiator, the diameter of a tire.
A)True
B)False
Q2) Random samples of 4 items are selected from a manufacturing process at regular intervals and a certain quality characteristic is measured. After 25 samples, \(\Sigma\)X = 15,350 and \(\Sigma\) R = 411.4
To construct a mean chart, what is the value for R bar used to compute the limits?
A) 411.4
B) 614
C) 16.46
D) 102.88
Q3) What type of variation can be reduced, or even eliminated and is usually nonrandom in nature?
A) Chance
B) External
C) Assignable
D) Co-variation
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Chapter 20: An Introduction to Decision Theory
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Sample Questions
Q1) Maximizers advocate a maximin strategy.
A)True
B)False
Q2) The manager of Paul's fruit and vegetable store is considering the purchase of a new seedless watermelon from a wholesale distributor. Since this seedless watermelon costs $4, will sell for $7, and is highly perishable, he only expects to sell between 6 and 9 of them. What is the opportunity loss for purchasing 8 watermelons when the demand is for 9 watermelons?
A) 0
B) 3
C) 4
D) 6
Q3) __________________ examines the effect that changes in the probabilities for states of nature have on selecting an alternative or act.
Q4) What is the difference between the expected monetary value under conditions of certainty and the expected monetary value under uncertainty called? ___________
Q5) To compute an expected monetary value, it requires that ______________ are estimated for each state of nature.
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