Business Statistics
Study Guide Questions
Course Introduction
Business Statistics introduces students to the fundamental concepts and techniques of statistical analysis as they apply to business decision-making. The course covers data collection methods, descriptive statistics, probability distributions, sampling, hypothesis testing, regression analysis, and the interpretation of statistical results. Emphasizing real-world business scenarios, students will learn how to analyze and interpret quantitative data to make informed decisions, assess risk, and solve complex business problems efficiently. Hands-on use of statistical software and case studies further develop the practical skills needed for data-driven decision-making in various business contexts.
Recommended Textbook
Statistical Techniques in Business and Economics 15th Edition by Douglas A. Lind
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Chapter 1: What Is Statistics
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Sample Questions
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) The "highest" level of measurement is ______________. Answer: ratio
Q3) A group of women tried five brands of finger nail polish and ranked them according to preference. What level of measurement is this?
A) Nominal
B) Ordinal
C) Interval
D) Ratio
Answer: B
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Chapter 2: Describing Data: Frequency Tables, Frequency
Distributions, and Graphic Presentation
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Sample Questions
Q1) Refer to the following class marks or midpoints for a frequency distribution of "weights of college men" recorded to the nearest pound: The first three class marks are 105, 115, and 125. What is the class interval? _____
Answer: 10
Q2) When data is collected using a qualitative, nominal variable, what is true about a frequency distribution that summarizes the data?
A) Upper and lower class limits must be calculated.
B) A pie chart can be used to summarize the data.
C) Number of classes is equal to the number of variable's values plus 2.
D) The "5 to the k rule" can be applied.
Answer: B
Q3) In a deck of cards, a class of all cards that are hearts and a class of all cards that are kings are NOT ______________.
Answer: mutually exclusive
Q4) For a frequency distribution of qualitative data, if the observations can be assigned to only one class, the classes are ___________________________.
Answer: mutually exclusive
Page 4
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Chapter 3: Describing Data: Numerical Measures
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Sample Questions
Q1) The mean monthly income of a group of college students is $500; the standard deviation is $20. According to Chebyshev's theorem, at least what percent of the incomes will lie between $400 and $600? _______________________
Answer: 75%
Q2) A statistic computed by summing all of the values of a distribution and dividing by the number of values is called ____________.
Answer: arithmetic mean
Q3) What is the difference between the largest and the smallest values in a set of data?
Answer: Range
Q4) 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
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5
Chapter 4: Describing Data: Displaying and Exploring Data
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Sample Questions
Q1) In a negatively skewed distribution, the coefficient of skewness is
Q2) What unit of measurement is used to express the coefficient of skewness?
Q3) Outliers are clearly presented in a
A) Dot plot.
B) Stem-and-leaf display.
C) Box plot.
D) Contingency table.
Q4) A scatter diagram of sales versus production may be constructed by plotting the minimum, first quartile, median, third quartile, and the maximum values of each variable.
A)True
B)False
Q5) A dot plot shows the relative symmetry of a distribution.
A)True
B)False
Q6) Draw a negatively or positively skewed distribution and show the relative locations of the mean, median, and mode.
Q7) Percentiles divide a frequency distribution into _________ equal parts.
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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) If there are five vacant parking places and five automobiles arrive at the same time, in how many different ways they can park? _____
Q3) Six basic colors are used in decorating a new condominium. They are applied to a unit in groups of four colors. One unit might have gold as the principal color, blue as a complementary color, red as the accent color and touches of white. Another unit might have blue as the principal color, white as the complimentary color, gold as the accent color and touches of red. If repetitions are permitted, how many different units can be decorated?
A) 7,825
B) 25
C) 125
D) 1,296
Q4) The joint probability of two events, A and B, that are not independent is computed as: P(A and B) = P(A) P(B|A).
A)True
B)False
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Chapter 6: Discrete Probability Distributions
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Sample Questions
Q1) The random variable for a Poisson probability distribution can assume an infinite number of values.
A)True
B)False
Q2) A probability distribution shows the outcomes of an experiment and the ___________________ of each one occurring.
Q3) What is unique to the Poisson distribution?
Q4) Explain the difference between the application of the binomial and the hypergeometric probability distributions.
Q5) Which is true for a binomial distribution?
A) There are three or more possible outcomes.
B) Probability of success remains the same from trial to trial.
C) Value of p is equal to 1.50.
D) It approximates the Poisson distribution.
Q6) As a general rule of thumb, if the items selected for a sample are not replaced and the sample size is less than 5 percent of the population, the binomial distribution can be used to approximate the hypergeometric distribution.
A)True
B)False
Page 8
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Chapter 7: Continuous Probability Distributions
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Sample Questions
Q1) In a uniform distribution, with a minimum, a, and maximum, b, the probability that the random variable, x, is between a and b is ___________.
Q2) The distribution of the annual incomes of a group of middle management employees approximated a normal distribution with a mean of $37,200 and a standard deviation of $800. About 68 percent of the incomes lie between what two incomes?
A) $30,000 and $40,000
B) $36,400 and $38,000
C) $34,800 and $39,600
D) $35,600 and $38,800
Q3) The employees of Cartwright Manufacturing are awarded efficiency ratings. The distribution of the ratings approximates a normal distribution. The mean is 400, the standard deviation 50. What is the area under the normal curve between 400 and 482?
A) 0.5000
B) 0.4495
C) 0.3413
D) 0.4750
Q4) What proportion of the area under a normal curve is to the left of z = 1.40?
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Page 9
Chapter 8: Sampling Methods and the Central Limit
Theorem
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Sample Questions
Q1) Which sampling method would you use if every k-th item in the population sequence is selected? ______________________
Q2) A population consists of the following five values: 3, 8, 11, 13, and 16. From this population, there are 10 different samples of size 3. The means of the 10 samples of size 3 are: 7.33, 8, 9, 9, 10, 10.67, 10.67, 11.67, 12.33, 13.33. Compute the mean of the distribution of the sample means and the population mean. What is true about the two values?
Q3) The Central Limit Theorem states that if the sample size, n, is sufficiently large, the sampling distribution of the means will be approximately normal, even when the population is skewed or uniform.
A)True
B)False
Q4) Based on the central limit theorem, sampling error will decrease as sample size increases.
A)True
B)False
Q5) If the size of a sample equals the size of the population, the sample error is ________.
Page 10
Q6) A population consists of 12 values. How many samples of size six are possible?
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Chapter 9: Estimation and Confidence Intervals
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Sample Questions
Q1) A research firm conducted a survey to determine the mean amount people spend at a popular coffee shop during a week. They found the amounts spent per week followed a normal distribution with a population standard deviation of $4. A sample of 49 customers revealed that the mean is $25. What is the 95 percent confidence interval estimate of µ?
Q2) What kind of distribution is the t distribution?
A) Continuous
B) Discrete
C) Subjective
D) z distribution
Q3) A population is estimated to have a standard deviation of 25. We want to estimate the population mean within 2, with a 95 percent level of confidence. How large a sample is required?
Q4) Thirty-six items are randomly selected from a population of 150 items. The sample mean is 25 and the sample standard deviation 3. What is the finite population correction factor?
Q5) What does the t distribution approach as the sample size increases?
Q6) A confidence interval is narrower when the sample size __________________.
Q7) A sample mean is a _______________ of the population mean.
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Chapter 10: One-Sample Tests of Hypothesis
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Sample Questions
Q1) A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What is the alternate hypothesis?
A) µ = 6.6
B) µ \(\neq\) 6.6
C) µ \(\ge\) 6.6
D) µ > 7.6
Q2) 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, what is the critical value?
Q3) The researcher must decide on the level of significance before formulating a decision rule and collecting sample data.
A)True
B)False
Q4) How is the significance level related to a p-value when the null hypothesis is rejected?
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Chapter 11: Two-Sample Tests of Hypothesis
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Sample Questions
Q1) Which condition must be met to conduct a test for the difference in two sample means using a z-statistic?
A) Data must be at least of nominal scale
B) Populations must be normal
C) Standard deviations of the two populations must be known
D) Samples are dependent
Q2) If samples taken from two populations that are dependent, then a test of ______ differences is applied.
Q3) When independent samples, with unknown, unequal standard deviations, are used to test for differences in the means, we pool the sample variances.
A)True
B)False
Q4) For hypotheses that compare two population means, what test statistic is used when the population standard deviations are known?
Q5) When testing for a difference between the means of two dependent samples n<sub>1</sub> and n<sub>2</sub> are _______________.
Q6) The paired difference test has ___________ degrees of freedom.
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Chapter 12: Analysis of Variance
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Sample Questions
Q1) When testing for differences between treatment means, the degrees of freedom for the t statistic are:
A) k
B) (n - 1)
C) (n - k)
D) (1/n<sub>1</sub> + 1/n<sub>2</sub>)
Q2) What is the shape of the F distribution? ______________________
Q3) In a two-way ANOVA, a blocking variable is used to
A) increase the error sum of squares.
B) decrease the error sum of squares.
C) increase the treatment sum of squares.
D) decrease the treatment sum of squares.
Q4) If we want to determine which treatment means differ, we compute a confidence interval for the difference between each pair of means.
A)True
B)False
Q5) How many mean square errors are summarized in a two-way ANOVA table?
Q6) When a second source of variance is included in the ANOVA analysis without interaction, that source is called a _________________.
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Chapter 13: Correlation and Linear Regression
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Sample Questions
Q1) If the coefficient of correlation is -0.81, what is the coefficient of determination?
Q2) If the value of r is -0.96, what does this indicate about the dependent variable as the independent variable increases? ___________
Q3) The Pearson product-moment correlation coefficient, r, requires that variables are measured with:
A) An interval or ratio scale.
B) An ordinal or ratio scale.
C) A nominal or ordinal scale.
D) A nominal or ratio scale.
Q4) In the regression equation, what does the letter "X" represent?
A) Y intercept
B) Slope of the line
C) The independent variable
D) The dependent variable
Q5) If the coefficient of determination is 0.81, what is the coefficient of correlation?
Q6) Perfect correlation means that the scatter diagram will appear as a
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Chapter 14: Multiple Regression Analysis
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Sample Questions
Q1) For a global test of a multiple regression equation, the F-statistic is based on the regression and residual degrees of freedom.
A)True
B)False
Q2) In an ANOVA table for a multiple regression analysis, total variation is separated into
A) treatment and error variation
B) regression and residual variation
C) treatment and block variation
D) block and error variation
Q3) In multiple regression analysis, what scale is used to measure a dummy variable?
Q4) What test statistic is used to test the significance of (X<sub>1</sub>)(X<sub>2</sub>) in a multiple regression model?
Q5) The variance inflation factor is used to select or remove independent variables to reduce the effects of multicollinearity in a multiple regression equation.
A)True
B)False
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Chapter 15: Index Numbers
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Sample Questions
Q1) What do we call a percent that measures the change in price, quantity, value or some other item of interest from one time period to another?
Q2) 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. What was your real income in 2006? _______
Q3) 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 based. If the revenues for the three years were (in $millions): $1.5, $1.3, and $2.0, what is the base value?
Q4) 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? ________
Q5) In 2000, an executive earned $100,000. In 2010, the executive earned $125,000. The CPI in 2000 was 172.2; the CPI in 2009 was 214.537. Using the CPI base, 1982-1984 = 100, what was the real income in 2009?
Q6) A value index method computes a simple aggregate index. A)True B)False
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Chapter 16: Time Series and Forecasting
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Sample Questions
Q1) Which one of the following is not a component of a time series?
A) Secular trend
B) Moving average
C) Seasonal variation
D) Irregular variation
Q2) A linear trend equation is used to represent time series values when the data are changing by equal?
A) Percents
B) Proportions
C) Amounts
D) Both "A" and "B" are correct
Q3) What is the general equation for the logarithmic trend equation to forecast ?
A) log a + log b (t)
B) log a t log b (t)
C) a t b(t)
D) ab(t)
Q4) Define autocorrelation.
Q5) A graph of a deseasonalized time series does NOT show ________.
Q6) A useful method for smoothing a time series to examine trend is called a ______.
Q7) For the trend equation, log = log (a) + log (b t), the time series is _____.
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Chapter 17: Nonparametric Methods: Goodness-Of-Fit
Tests
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Sample Questions
Q1) The Anderson-Darling tests a null hypothesis that the sample data are _____________ distributed.
Q2) If the computed value of a chi-square statistic is greater than the critical value, what is the decision regarding the null hypothesis? _________
Q3) A scatter plot is a useful graphical method to determine if a set of sample data is from a normal population.
A)True
B)False
Q4) What is our decision for a goodness-of-fit test with a computed value of chi-square of 1.273 and a critical value of 13.388?
A) Do not reject the null hypothesis
B) Reject the null hypothesis
C) Unable to reject or not reject the null hypothesis based on data
D) Should take a larger sample
Q5) For hypothesis tests using a chi-square statistic, the rejection region is in the _____________ tail of the chi-square distribution.
Q6) In a contingency table, the decision to reject the null hypothesis is based on a __________ test statistic.
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Chapter 18: Nonparametric Methods: Analysis of Ranked
Data
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Sample Questions
Q1) To apply the Kruskal-Wallis test, the samples selected from the populations must be dependent.
A)True
B)False
Q2) What is the test statistic for Spearman's rank correlation?
A) t
B) z
C) F
D) Chi-square
Q3) What is the value of the Spearman rank-order correlation coefficient that indicates no association between the two variables? _____
Q4) Which of the following values of Spearman's (rho) indicates the strongest relationship between two variables?
A) -0.91
B) -0.05
C) +0.64
D) +0.89
Q5) A nonparametric test is also called a __________ test.
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Q6) The Wilcoxon Rank-Sum compares two populations based on the sum of the
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Chapter 19: Statistical Process Control and Quality Management
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Sample Questions
Q1) Equipment failure would be an example of ____________ variation.
A) chance
B) external
C) assignable
D) standard variation
Q2) 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
Q3) 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
Q4) In acceptance sampling, there is one unique operating characteristic curve for a specified sampling plan.
A)True
B)False
Page 22
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Chapter 20: An Introduction to Decision Theory
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Q1) 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 7 watermelons when the demand is for 6 watermelons?
A) 0
B) 3
C) 4
D) 6
Q2) In decision theory, a payoff is expressed as a profit or a ______.
Q3) 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 payoff value for the purchase of 9 watermelons when the demand is for 7 watermelons?
A) 6
B) 13
C) 20
D) 27
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