Business Statistics
Test Questions
Course Introduction
Business Statistics is a foundational course that introduces students to statistical concepts and techniques essential for analyzing and interpreting data in a business context. The course covers topics such as data collection methods, descriptive statistics, probability distributions, sampling techniques, hypothesis testing, regression analysis, and forecasting. Emphasis is placed on using statistical tools to make informed business decisions, solve real-world business problems, and effectively communicate findings. Throughout the course, students gain hands-on experience with statistical software and learn to critically assess data-driven business scenarios.
Recommended Textbook
Statistical Techniques in Business and Economics 16th Edition by Douglas Lind
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Page 2
Chapter 1: What Is Statistics
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Sample Questions
Q1) The number of children in a family is a discrete variable.
A)True
B)False
Answer: True
Q2) If we test a small number of light bulbs from a large group, the small group is called a ____________.
Answer: sample
Q3) The length of a bridge, measured in meters, is an example of:
A) Categorical data
B) Either categorical or quantitative data
C) Measurement data
D) Quantitative data
Answer: D
Q4) Categorizing students as freshmen, sophomores, juniors, and seniors is an example of the ______________ level of measurement.
Answer: ordinal
Q5) The order that runners finish in a race would be an example of continuous data. A)True
B)False
Answer: False
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Chapter 2: Describing Data: Frequency Tables, Frequency
Distributions, and Graphic Presentation
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Sample Questions
Q1) 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
Q2) A ______ chart is useful for displaying a relative frequency distribution.
Answer: pie
Q3) The first three class marks for a frequency distribution of "weights of college men" recorded to the nearest pound are 105, 115, and 125. What is the lower limit for the third class?
Answer: 120
Explanation: The class interval is 10. The class marks are the same as the class midpoints. Therefore, the upper and lower limits for a class are the class mark plus or minus half of the class interval. For the third class, the lower limit is 125 - ½(10) = 120.
Q4) A frequency distribution for nominal data requires that the categories be ___________________ and _____________________.
Answer: exhaustive ; mutually exclusive
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Chapter 3: Describing Data: Numerical Measures
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Sample Questions
Q1) For a data set with an odd number of observations that have been sorted from smallest to largest values, where is the median located?
A) n
B) n/2
C) (n + 1)/2
D) n + ½
Answer: C
Q2) For a set of data arranged or sorted in numerical order, the value of the observation in the center is called the weighted mean.
A)True
B)False
Answer: False
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) When computing a weighed mean, the denominator is always __________.
Answer: the sum of the weights
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Chapter 4: Describing Data: Displaying and Exploring Data
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Sample Questions
Q1) The coefficient of skewness is the standard deviation divided by the mean.
A)True
B)False
Q2) The following stem-and-leaf display reports the number of boats shipped per week by Ottertail Boats, Inc.
11| 1 5 9
How many weeks were included in the study?
Q3) If the mean of a distribution is smaller than the median and mode, the sign of Pearson's coefficient of skewness is ______________.
Q4) The types of variables called _______________ are summarized in a contingency table.
Q5) A dot plot shows the symmetry of a distribution.
A)True
B)False
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Chapter 5: A Survey of Probability Concepts
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Sample Questions
Q1) Using the terminology of Bayes' theorem, a posterior probability can also be defined as:
A) a conditional probability
B) a joint probability
C) 1
D) 0
Q2) When the special rule of addition is used, the events must be _______________.
Q3) The probability of rolling a 3 or 2 on a single die is an example of conditional probability.
A)True
B)False
Q4) In a management trainee program, 80% of the trainees are female, while 20% are male. Ninety percent of the females attended college; 78% of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who did NOT attend college?
A) 0.20
B) 0.08
C) 0.25
D) 0.80
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Chapter 6: Discrete Probability Distributions
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Sample Questions
Q1) In the _______________________ distribution, the probability of a success is not the same on each trail.
Q2) Chances are 50-50 that a newborn baby will be a girl. For families with five children, what is the probability that all the children are girls?
A) 0.900
B) 0.031
C) 0.001
D) 0.250
Q3) A company is studying the number of daily debit card purchases. There were 20 purchases and the probability of a debit card purchase is 0.5. What is the standard deviation of the number of debit card purchases?
Q4) Which of the following is a requirement for use of the hypergeometric distribution?
A) Only two possible outcomes
B) Trials are independent
C) Probability of a success is greater than 1.0
D) Sampling with replacement
Q5) For the hypergeometric distribution there are ________________ possible outcomes.
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Chapter 7: Continuous Probability Distributions
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Sample Questions
Q1) A normally distributed random variable has _________.
A) Any value between - and + .
B) Discrete values.
C) Any value between specified minimum and maximum values.
D) Only two values, success and failure.
Q2) After arriving at the university student medical clinic, the waiting times to receive service after checking-in follow an exponential distribution with a mean of 10 minutes. How many students are served per hour?
Q3) A major credit card company has determined that customers charge between $100 and $1,100 per month. If the average monthly amount charged is uniformly distributed, the percent of monthly changes between $311 and $889 is _______.
Q4) 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% 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
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Chapter 8: Sampling Methods and the Central Limit
Theorem
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Sample Questions
Q1) For a distribution of sample means constructed by sampling 5 items from a population of 15, ___________.
A) the sample size is 15
B) there will be 3,003 possible sample means
C) the mean of the sample means will be 3
D) the standard error will be 1
Q2) The tread life of tires mounted on light-duty trucks follows the normal probability distribution with a mean of 60,000 miles and a standard deviation of 4,000 miles. Suppose you bought a set of four tires, what is the likelihood the mean tire life of these four tires is between 57,000 and 63,000 miles?
A) 0.4332
B) 0.8664
C) 1.00
D) Very likely
Q3) In stratified random sampling, a population is divided into strata using naturally occurring geographic or other boundaries. Then, strata are randomly selected and a random sample is collected from each strata.
A)True
B)False
Page 10
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Chapter 9: Estimation and Confidence Intervals
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Sample Questions
Q1) A university wants to determine the proportion of students who use a cash card to pay at the university food service. Out of 100 students surveyed, 65 students use a cash card. What is the 95% confidence interval for the population proportion?
Q2) A research firm needs to estimate within 3% the proportion of junior executives leaving large manufacturing companies within three years. A 0.95 degree of confidence is to be used. Several years ago, a study revealed that 21% of junior executives left their company within three years. To update this study, how many junior executives should be surveyed?
A) 594
B) 612
C) 709
D) 897
Q3) When the population standard deviation is known, a __________ statistic is used to compute a confidence interval.
Q4) A finite population correction factor is used to adjust the _________________.
Q5) A 95% confidence interval implies that about 95 out of 100 similarly constructed intervals will include the _____________ being estimated.
Q6) Explain the concept of a confidence interval when estimating a population mean.
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Chapter 10: One-Sample Tests of Hypothesis
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Sample Questions
Q1) The mean length of a candy bar is 43 millimeters. There is concern that the settings of the machine cutting the bars have changed. Test the claim at the 0.02 level that there has been no change in the mean length. The alternate hypothesis is that there has been a change. Twelve bars (n = 12) were selected at random and their lengths recorded. The lengths are (in millimeters) 42, 39, 42, 45, 43, 40, 39, 41, 40, 42, 43, and 42. The mean of the sample is 41.5 and the standard deviation is 1.784. Computed t = -2.913. Has there been a statistically significant change in the mean length of the bars?
A) Yes, because the computed t lies in the rejection region.
B) No, because the information given is not complete.
C) No, because the computed t lies in the area to the right of -2.718.
D) Yes, because 43 is greater than 41.5.
Q2) For a one-tailed hypothesis test, the computed test statistic is z = -2.10. What is the p-value?
Q3) A ____________ hypothesis test is indicated if the alternate hypothesis does not specify a direction.
Q4) A(n) ____________ hypothesis test is indicated if the alternate hypothesis states a direction.
Q5) The p-value is determined by the value of a ______________________.
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Chapter 11: Two-Sample Tests of Hypothesis
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Sample Questions
Q1) When is it appropriate to use the paired difference t-test?
A) When four samples are compared at once
B) When any two samples are compared
C) When two independent samples are compared
D) When two dependent samples are compared
Q2) For hypotheses that compare two population means, when is a pooled variance used?
Q3) When testing the difference between two population means, the sample variances are pooled to estimate the population variance when ________________.
A) The population variances are known and equal
B) The population means are known
C) The population variances are assumed unequal and unknown
D) The population variances are assumed equal but unknown
Q4) When the population standard deviations are equal but unknown, a test for the differences between two populations assumes that the populations are _____________ distributed.
Q5) If the null hypothesis states that there is no difference between the two population means, then the test is ______________.
Q6) The paired difference test has ___________ degrees of freedom.
Page 13
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Chapter 12: Analysis of Variance
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Sample Questions
Q1) The test statistic used to compare two variances is the ___________ statistic.
Q2) 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>)
Q3) If the computed value of F is 0.99 and the F critical value is 3.89, we would not reject the null hypothesis.
A)True
B)False
Q4) Which statement is correct about the F distribution?
A) Cannot be negative
B) Cannot be positive
C) Is the same as the t distribution
D) Is the same as the z distribution
Q5) One characteristic of the F distribution is that the computed F can only range between -1 and +1.
A)True
B)False
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Chapter 13: Correlation and Linear Regression
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Sample Questions
Q1) The coefficient of correlation and the slope of the regression line always have their __________ in common.
Q2) If the slope of a regression line is zero, the orientation of the regression line is _________, which indicates a lack of a relationship.
Q3) If there is absolutely no relationship between two variables, Pearson's r will equal
Q4) In the regression equation, what does the letter "b" represent?
A) The Y-intercept
B) The slope of the line
C) Any value of the independent variable that is selected
D) The value of Y when X = 0
Q5) The minimum and maximum values of the coefficient of determination are
Q6) What is the variable used to predict another variable called?
A) Independent variable
B) Dependent variable
C) Important variable
D) Causal variable
Q7) If the sample correlation coefficient, r, is -0.96, the dependent variable ________ as the independent variable increases.
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Chapter 14: Multiple Regression Analysis
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Sample Questions
Q1) How are scatter diagrams used to evaluate the assumptions of linear multiple regression?
Q2) If the null hypothesis, H<sub>0</sub>: <sub>1</sub> = 0, is rejected, the independent variable, X<sub>1</sub>, it has a ______ effect on the dependent variable.
Q3) The best example of a null hypothesis for a global test of a multiple regression model is _________.
A) H<sub>0</sub>: <sub>1</sub> = <sub>2</sub> = <sub>3</sub> = <sub>4</sub> = 0
B) H<sub>0</sub>: µ<sub>1</sub> = µ<sub>2</sub> = µ<sub>3</sub> = µ<sub>4</sub> = 0
C) H<sub>0</sub>: <sub>1</sub> = 0
D) If F is greater than 20.00, then reject
Q4) Stepwise regression analysis is also called a "backward elimination" method. A)True B)False
Q5) In an ANOVA for a multiple regression analysis, the three sources of variation are __________________.
Q6) In multiple regression, the form of the global hypothesis test is ____________.
Q7) What are the five assumptions of linear multiple regression?
Page 16
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Chapter 15: Nonparametric Methods: Nominal Level
Hypothesis Tests
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Sample Questions
Q1) 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. If the computed z-statistic is -1.960 and the level of significance is 0.01, your decision would be _______________.
Q2) A frequency distribution has a mean of 100 and a standard deviation of 20. The class limits for one class are 50 up to 60. What are the standard normal z-statistics for the class limits?
A) -20 and 20
B) -2.5 and -2.0
C) 2.0 and 2.5
D) -50 and -40
Q3) The chi-square test statistic used in a goodness-of-fit test has k - 1 degrees of freedom.
A)True
B)False
Q4) If we are testing for the difference between two population proportions, it is assumed that the two samples are large enough that the binomial distribution can be approximated by ______.
Q5) 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) The Kruskal-Wallis test is the nonparametric analogy to a one-way ________.
Q2) This nonparametric test requires at least ordinal level data. t is used if the assumptions required for the paired t test cannot be met. Which test is it?
A) Wilcoxon signed-rank test
B) ANOVA
C) Rank correlation
D) Kruskal-Wallis
Q3) What is a requirement that must be met before the Kruskal-Wallis one-way analysis of variance by ranks test can be applied?
A) Populations must be normal or near normal.
B) Populations must be independent.
C) Population standard deviations must be equal.
D) Data must be at least interval level.
Q4) What is a null hypothesis for a one-tailed sign test?
A) H<sub>0</sub>: = 0
B) H<sub>0</sub>: 1.00
C) H<sub>0</sub>: = 0.50
D) H<sub>0</sub>: 0.50
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Q5) In a sign test, the test statistic is based on the _______________ distribution.
Chapter 17: Index Numbers
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Sample Questions
Q1) In the numerator of a value index, the price and quantity are both from the current period.
A)True
B)False
Q2) A weighted price index that uses current-period quantities as weights is known as
A) Fisher's ideal index
B) Laspeyres index
C) Paasche's index
D) the value index
Q3) The index for a single commodity is called the __________.
Q4) If the base value is 100 and the current period value is 250, what is the index for the current period?
Q5) In 2000, an executive earned $100,000. In 2009, the executive earned $125,000. The CPI in 2000 was 172.2, and the CPI in 2009 was 214.537. Using the CPI base, 1982-1984 = 100, what was the real income in 2009?
Q6) The 2001 CPI was 171.1 (1982-84 = 100). What is the purchasing power of the dollar relative to the base?
Q7) When the CPI determines real income it is called the ___________.
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Chapter 18: Time Series and Forecasting
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Sample Questions
Q1) If the past data approximates a straight line, the equation used is = a + bt, where a is the Y-intercept and b is the slope of the line.
A)True
B)False
Q2) A logarithmic trend equation should be used when the time series trend is __________________.
A) changing in equal amounts
B) increasing by equal percentages
C) increasing in equal amounts
D) increasing or decreasing by equal percentages
Q3) Data that increases by equal percentages over a period of time appears as a ____________ on an arithmetic scaled graph.
Q4) For the third quarter, the sales are 1,500 units; the seasonal index for the quarter is 1.15. What are the deseasonalized sales for the quarter?
A) 115%
B) 15%
C) 1,304
D) 1,500
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Chapter 19: Statistical Process Control and Quality Management
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Sample Questions
Q1) Random samples of four items are selected from a manufacturing process at regular intervals and a certain quality characteristic is measured. After 25 samples, X = 15,350 and R = 411.4. To construct a range chart, what is the upper control limit (UCL) for the range?
A) 37.553
B) 411.4
C) 0.00
D) 102.85
Q2) Random samples of four items are selected from a manufacturing process at regular intervals and a certain quality characteristic is measured. After 25 samples, X = 15,350 and 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) Control charts can be developed for both variables and attributes.
A)True
B)False
Q4) A Pareto chart is typically skewed to the ________________.
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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 six and nine of them. What is the opportunity loss for purchasing six watermelons when the demand is for eight watermelons?
A) 0
B) 3
C) 4
D) 6
Q2) The maximin strategy is a __________ strategy for decision making.
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 six and nine of them. What is the opportunity loss for purchasing eight watermelons when the demand is for nine watermelons?
A) 0
B) 3
C) 4
D) 6
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