Statistical Analysis for Business Decisions
Review Questions
Course Introduction
Statistical Analysis for Business Decisions introduces students to the fundamental concepts and methods of statistics that are crucial for effective decision-making in the business environment. The course covers descriptive statistics, probability distributions, sampling methods, hypothesis testing, regression analysis, and data interpretation, all within the context of real-world business problems. Emphasizing both conceptual understanding and practical application, students will learn to analyze data, draw informed conclusions, and support strategic business decisions using statistical tools and software. This course equips students with the analytical skills needed to interpret business data, minimize risk, and drive organizational success.
Recommended Textbook
Statistical Techniques in Business and Economics 16th Edition by Douglas Lind
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Chapter 1: What Is Statistics
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Q1) A company was studying the demographics of their customers. As part of the study, they collected the following variables: gender, marital status, credit rating (low, medium, high), annual income, and age. Label each variable as qualitative or quantitative, discrete or continuous, and nominal, ordinal, interval, or ratio. Answer: Gender: qualitative, discrete, nominal; Marital status: qualitative, discrete, nominal; Credit rating: qualitative, discrete, ordinal; Annual income: quantitative, continuous, ratio; Age: quantitative, continuous, ratio.
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 "highest" level of measurement is ______________. Answer: ratio
Q4) A variable such as eye color is also referred to as a(n) _____________ variable. Answer: qualitative
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Chapter 2: Describing Data: Frequency Tables, Frequency
Distributions, and Graphic Presentation
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Q1) Ages (rounded to the nearest whole year) of employees at a large company were grouped into a distribution with the following class limits:
20 up to 30
30 up to 40
40 up to 50
50 up to 60
60 up to 70
What is the midpoint for the class 40 up to 50?
Answer: 45
Explanation: The class interval is 10, so the midpoint for any class would be half of the class interval added to a class lower limit (in this case, 40 + 5 = 45), or subtracted from a class upper limit (50 - 5 = 45).
Q2) In a relative frequency distribution, the sum of the relative class frequencies is _____________________.
Answer: 100
Q3) A ______ chart is useful for displaying a relative frequency distribution. Answer: pie
Q4) To construct a bar chart, the class frequencies are plotted on the _________. Answer: Y or vertical axis
Page 4
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Chapter 3: Describing Data: Numerical Measures
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Sample Questions
Q1) When computing a weighed mean, the denominator is always __________.
Answer: the sum of the weights
Q2) Sometimes, a data set has two values that have the highest and equal frequencies. In this case, the distribution of the data can best be described as __________.
A) Symmetric
B) Bimodal (having two modes)
C) Positively skewed
D) Negatively skewed
Answer: B
Q3) According to Chebyshev's theorem, 75% of the observations lie within plus and minus 2.00 average mean deviations.
A)True
B)False
Answer: False
Q4) The only time the variance equals the standard deviation is when
Answer: both equal 1
Q5) The difference between the maximum and minimum values in a set of data is called the _______.
Answer: range
5
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Chapter 4: Describing Data: Displaying and Exploring Data
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Sample Questions
Q1) A sample of the homes currently offered for sale revealed that the mean asking price is $75,900, the median is $70,100, and the modal price is $67,200. The standard deviation of the distribution is $5,900. What is Pearson's coefficient of skewness in this sample?
Q2) What does the interquartile range describe?
A) The range of the lower 50% of the observations
B) The range of the middle 50% of the observations
C) The range of the upper 50% of the observations
D) The ranges of the lower 25% and the upper 25% of the observations
Q3) A box plot shows ___________.
A) The mean and variance
B) The relative symmetry of a distribution for a set of data
C) The 10<sup>th</sup> and 90<sup>th</sup> percentiles of a distribution
D) The deciles of a distribution
Q4) Quartiles divide a frequency distribution into _______ equal parts.
Q5) The range of the coefficient of skewness is ____________.
A) Values greater than or equal to zero or always positive
B) Values less than or equal to zero or always negative
C) Both positive and negative values
D) Values between -1 and +1
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Chapter 5: A Survey of Probability Concepts
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Q1) The ABCD football association is considering a Super Ten Football Conference. The top 10 football teams in the country, based on past records, would be members of the Super Ten Conference. Each team would play every other team in the conference during the season and the team winning the most games would be declared the national champion. How many games would the conference commissioner have to schedule each year? (Remember, Oklahoma versus Michigan is the same as Michigan versus Oklahoma.)
A) 45
B) 50
C) 125
D) 14
Q2) The probability of rolling a 3 or 2 on a single die is an example of mutually exclusive events.
A)True
B)False
Q3) If a set of outcomes is collectively exhaustive and mutually exclusive, the sum of the probabilities equals __________.
Q4) The _________ approach to probability is based on a person's belief, opinion, or judgment.
Q5) A measured or observed activity is called a(n) ___________.
Page 7
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Chapter 6: Discrete Probability Distributions
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Sample Questions
Q1) If = 1/5 and n = 100, the standard deviation of this binomial distribution is _____.
Q2) The Poisson distribution or, the law of improbable events, is _______________ skewed.
Q3) When observing a checkout line at a food store, the average number of people served is 15 per hour. Using the Poisson distribution, what is the standard deviation of the number of people served in an hour?
Q4) An insurance agent has appointments with four prospective clients tomorrow. From past experience the agent knows that the probability of making a sale on any appointment is 1 out of 5. Using the rules of probability, what is the likelihood that the agent will sell a policy to 3 of the 4 prospective clients?
A) 0.250
B) 0.500
C) 0.410
D) 0.026
Q5) There are eight flights from Minneapolis to St. Cloud each day. The probability that any one flight is late is 0.10. Using the binomial probability formula, what is the probability that 1 or more are late?
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Chapter 7: Continuous Probability Distributions
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Q1) A study conducted by a local tennis center revealed that 25 percent of its new members have novice level tennis skills. A membership drive in a metropolitan area resulted in 500 new members. It has been suggested that the normal approximation to the binomial be used to calculate various probabilities. In this problem, can the normal approximation to the binomial be applied? Explain.
Q2) A group of normal distributions can have equal arithmetic means but different standard deviations.
A)True
B)False
Q3) If an average of 12 customers is served per hour, what is the probability that the next customer will arrive in 3 minutes or less?
A) 0.55
B) 0.30
C) 0.45
D) 0.39
Q4) In a uniform distribution, with a minimum, a, and maximum, b, the probability that the random variable, x, is between a and (b - a)/2 is ___________.
Q5) To apply the normal approximation to a binomial distribution, what must be true?
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Chapter 8: Sampling Methods and the Central Limit
Theorem
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Sample Questions
Q1) A marketing firm is studying consumer preferences for winter fashions in four different months. From a population of women 18 to 21 years of age, a random sample of 100 women was selected in January. Another random sample of 100 women was selected in March. Another random sample of 100 women was selected in June. Another random sample of 100 women was selected in September. What is the number of samples?
A) 4
B) 100
C) 400
D) 1
Q2) A university has 1,000 computers available for students to use. Each computer has a 250-gigabyte hard drive. The university wants to estimate the space occupied on the hard drives. A random sample of 100 computers showed a mean of 115 gigabytes used with a standard deviation of 20 gigabytes. What is the probability that a sample mean is greater than 120 gigabytes?
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
Page 10
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Chapter 9: Estimation and Confidence Intervals
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Q1) A group of statistics students decided to conduct a survey at their university to estimate the average (mean) amount of time students spent studying per week. They sampled 554 students and found a mean of 22.3 hours per week. Assuming a population standard deviation of six hours, what is the 95% level of confidence?
A) [21.80, 22.80]
B) [16.3, 28.3]
C) [21.64, 22.96]
D) [20.22, 22.0]
Q2) In relative terms, a _______ standard deviation leads to a narrower confidence interval.
Q3) One factor in determining the size of a sample is the degree of confidence selected. This is usually 0.95 or 0.99, but it may be any degree of confidence you specify.
A)True
B)False
Q4) Making generalized statements about a population based on sample information is called _________________.
Q5) The interval within which a population parameter is expected to lie is called a __________.
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Chapter 10: One-Sample Tests of Hypothesis
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Q1) In hypothesis testing, what is the level of significance?
A) The risk of rejecting the null hypothesis when it is true.
B) A value symbolized by the Greek letter .
C) A value between 0 and 1.
D) It is selected before a decision rule can be formulateD.
E) All apply.
Q2) A test statistic is a value computed from sample information that is used to test the null hypothesis.
A)True
B)False
Q3) One of the major U.S. tire makers wishes to review its warranty for their rainmaker tire.
The warranty is for 40,000 miles. The distribution of tire wear is normally distributed with a population standard deviation of 15,000 miles. The tire company believes that the tire actually lasts more than 40,000 miles. A sample of 49 tires revealed that the mean number of miles is 45,000 miles. If we test the hypothesis with a 0.05 significance level, what is the probability of a Type II error if the actual tire mileage is 42,000 miles?
Q4) How is a significance level determined and how is it related to Type I error?
Q5) 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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Q1) If we are testing for the difference between two population means and assume that the two populations have equal but unknown standard deviations, the variances are pooled to compute the best estimated variance.
A)True
B)False
Q2) When dependent samples are used to test for differences in the means, we pool the sample variances.
A)True
B)False
Q3) A statistics professor wants to compare grades in two different classes of the same course. This is an example of _________ populations.
Q4) If we are testing for the difference between two population means and assume that the two populations have equal and unknown standard deviations, the standard deviations are ______ to compute a point estimate of the population variance.
Q5) When the population standard deviations are unknown, the purpose of pooling the sample variances when testing the difference between two populations is to
Q6) The paired difference test has ___________ degrees of freedom.
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Chapter 12: Analysis of Variance
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Q1) For an ANOVA test, rejecting the null hypothesis does not identify which treatment means differ significantly.
A)True
B)False
Q2) What distribution does the F distribution approach as the sample size increases?
A) Binomial
B) Normal
C) Poisson
D) Exponential
Q3) What is the purpose of using a blocking variable in a two-way ANOVA?
Q4) Below is the information for a completely randomized experimental design involving four treatments, where 12 observations were recorded for each treatment for a total of 48 observations. SST = 210 (Sum of Squares Between Groups)
SS Total = 840 (Sum of Squares Total)
The computed value of F, or the test statistic, is ______.
A) 0.25
B) 12.0
C) 4.88
D) 8.0
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Chapter 13: Correlation and Linear Regression
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Q1) The hypothesis to test the slope of a regression equation is H<sub>0</sub>: = 0.
A)True
B)False
Q2) The coefficient of correlation and the slope of the regression line always have their __________ in common.
Q3) The relationship between interest rates as a percent (X) and housing starts (Y) is given by the linear equation = 4094 - 269X. What will be the number of housing starts if the interest rate is 8.25%?
Q4) The relationship between interest rates as a percent (X) and housing starts (Y) is given by the linear equation = 4094 - 269X. At what interest rate will there be no permits for housing starts?
Q5) A random sample of 15 recent home sales was selected to test the hypothesis that the area of a home, in square feet, and the selling price are positively correlated. The rejection region will fall in the ________ tail of a t distribution.
Q6) The _______________ principle is applied when calculating the regression coefficients.
Q7) What are the inputs and the output of linear regression?
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Chapter 14: Multiple Regression Analysis
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Q1) Stepwise regression analysis is also called a "backward elimination" method.
A)True
B)False
Q2) In multiple regression, the form of the global hypothesis test is ____________.
Q3) A researcher is studying the relationship between 10 different variables and a critical measure of business performance. What method can be used to select the best set of variables to predict performance?
A) Stepwise regression
B) ANOVA
C) Simple linear regression
D) Residual analysis
Q4) When does multicollinearity occur in a multiple regression analysis?
A) When the dependent variables are highly correlated
B) When the regression coefficients are correlated
C) When the independent variables are highly correlated
D) When the independent variables have no correlation
Q5) In a multiple regression analysis, the statistic used to evaluate the presence of correlated independent variables is __________________.
Q6) The stepwise regression procedure is also called ________.
Page 16
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Chapter 15: Nonparametric Methods: Nominal Level
Hypothesis Tests
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Q1) The claim that "40% of those persons who retired from an industrial job before the age of 60 would return to work if a suitable job was available" is to be investigated at the 0.02 significance level. If 74 out of the 200 workers sampled said they would return to work, what is our decision?
A) Do not reject the null hypothesis because -0.879 lies in the region between +2.326 and -2.326.
B) Do not reject the null hypothesis because -0.879 lies in the region between +2.576 and -2.576.
C) Reject the null hypothesis because 37% is less than 40%.
D) Do not reject the null hypothesis because 37% lies in the area between 0% and 40%.
Q2) 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?
Q3) A manufacturer claims that less than 1% of all its products do not meet the minimum government standards. A survey of 500 products revealed that 10 did not meet the standard. Thus, if = .01, the critical value is ____________.
Q4) The null hypothesis in the goodness-of-fit test is __________.
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Chapter 16: Nonparametric Methods: Analysis of Ordinal
Data
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Q1) A nonparametric test:
A) assumes that the populations are normally distributed. B) assumes that the populations have equal standard deviations. C) makes no assumptions about the population distributions. D) assumes that the populations follow a standard normal distribution.
Q2) A nonparametric test cannot be applied when the data are: A) nominal.
B) ordinal. C) interval. D) ratio.
Q3) The test statistic for the null hypothesis that the correlation among the ranks is equal to zero is a chi-square statistic. A)True B)False
Q4) In a sign test, the test statistic is based on the _______________ distribution.
Q5) The _____________ of the differences between "before and after" measurements is evaluated in a Wilcoxon signed-rank test.
Q7) The Kruskal-Wallis test is the nonparametric analogy to a one-way ________. Page 18
Q6) The Wilcoxon rank-sum compares two populations based on the sum of the ________.
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Chapter 17: Index Numbers
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Q1) All indexes have the same base, namely 1982-84, written 1982-84 = 100.
A)True
B)False
Q2) Another term for real income is _______________.
Q3) Cost-of-living adjustments are based on the _______________________.
Q4) List some example items that are included in the CPI that represent a typical "market basket" of goods.
Q5) In a weighted index, the __________ variable is usually the weight.
Q6) A company has data on annual revenue for ten years beginning in 1995. The company wants to compute an index using the revenues from 1995, 1996, and 1997 as the base. If the revenues for the three years were (in $millions) $1.5, $1.3, and $2.0, what is the base value?
Q7) A major disadvantage of the unweighted price index is that
Q8) An example of a weighted index is P = p<sub>t</sub>/p<sub>0</sub>.
A)True
B)False
Q10) What is the purpose of an index? Page 20
Q9) The __________ method for computing a weighted price index uses base year weights.
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Chapter 18: Time Series and Forecasting
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Q1) To calculate monthly typical seasonal indexes, after computing the ratio-to-moving averages, the averages must be:
A) divided by 12.
B) multiplied by 12.
C) summed and divided by 12.
D) centereD.
Q2) In a time series, economic periods of prosperity followed by recession are described as a(n) ___________.
A) secular trend
B) seasonal variation
C) cyclical variation
D) erratic variation
Q3) The _____________ method is useful in smoothing out a time series.
Q4) If the exports (in $millions) for the period 2006 through 2010 were $878, $892, $864, $870, and $912, respectively, what are these values called?
A) Moving average
B) Linear trend equation
C) Logarithmic trend equation
D) Time series data
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Chapter 19: Statistical Process Control and Quality Management
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Q1) Mean charts are designed to determine whether a process is in or out of control based on sample means.
A)True
B)False
Q2) Which probability distribution is used to develop a percent defective chart?
A) Normal distribution
B) Chi-square distribution
C) Poisson distribution
D) Binomial distribution
Q3) A Pareto chart is useful because it is based on the theory that 80% of the observations are accounted for by 20% of the ________.
Q4) Control charts are used to determine if a process is:
A) in or out of control.
B) measurable.
C) fixable.
D) testable.
Q5) A fishbone diagram is used to determine if a process is out of control.
A)True
B)False
Q6) Explain the risks of acceptance sampling. Page 23
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Chapter 20: An Introduction to Decision Theory
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Q1) The expected value under conditions of uncertainty subtracted from the expected value under conditions of certainty will result in:
A) the value of perfect information.
B) an expected opportunity loss.
C) an expected monetary value.
D) an expected decision strategy.
Q2) What is the practical value of knowing the value of perfect information?
Q3) A maximin strategy will always choose the act or alternative that:
A) maximizes the expected monetary value.
B) minimizes the maximum regret or opportunity loss.
C) maximizes the potential payoff regardless of the state of nature.
D) guarantees a payoff for any state of nature.
Q4) In a payoff table, another name for alternatives is _______.
Q5) A decision maker selects a course of action called an ________________.
Q6) The average return for a particular act or decision alternative is called the _____________________.
Q7) __________________ examines the effect that changes in the probabilities for states of nature have on selecting an alternative or act.
Q8) A ________ decision-making strategy maximizes the maximum gain.
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