Statistics for Business and Economics
Question Bank
Course Introduction
Statistics for Business and Economics introduces students to fundamental statistical concepts and methods relevant to analyzing and interpreting data in business and economic contexts. The course covers topics such as descriptive statistics, probability distributions, sampling techniques, hypothesis testing, regression analysis, and forecasting. Emphasis is placed on real-world applications, enabling students to make informed business decisions using data-driven approaches. By the end of the course, students will develop the skills necessary to collect, analyze, and draw meaningful conclusions from quantitative information, supporting effective problem solving and strategic planning in professional environments.
Recommended Textbook
Business Statistics in Practice 3rd Canadian Edition by Bruce L. Bowerman
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Chapter 1: An Introduction to Business Statistics
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Sample Questions
Q1) Degree program entrance exam scores,such as MCAT scores,are an example of a(n)________________ variable.
A)ordinal
B)ratio
C)nominative
D)interval
E)undefined
Answer: D
Q2) A list of all of the units in a population is called a _____.
A)census
B)frame
C)random sample
D)variable
E)systematic sample
Answer: B
Q3) If we sample without replacement,we do not place the unit chosen on a particular selection back into the population.
A)True
B)False
Answer: True
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Chapter 2: Descriptive Statistics
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Sample Questions
Q1) What is the mean?
A)375
B)368
C)389.9
D)200
E)346.6
Answer: E
Q2) What is the variance?
A)0.026
B)0.052
C)0.580
D)0.1613
E)0.0007
Answer: A
Q3) Compute the population variance of the data: 16,18,23,21,17,16,24,23,9,17,11,16,22,10,15,14.
Answer: 20.5 \[\sigma
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Chapter 3: Probability
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Sample Questions
Q1) If you roll a pair of fair dice,what is the probability that the number of dots on the two dice will sum to seven?
A)1/16
B)1/8
C)1/6
D)1/4
E)1/2
Answer: C
Q2) Past company records demonstrate that 85% of new hires successfully complete their probation period.Suppose 3 newly hired individuals are randomly selected.If new hires successfully complete their probation period independently of each other,what is the probability that all will complete the probation period?
A)487
B)553
C)614
D)732
E)850
Answer: C
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Chapter 4: Discrete Random Variables
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Sample Questions
Q1) Exactly three of the individuals has type A blood?
Q2) The requirement that the probability of success remains constant from trial to trial is a property of the _______________ distribution.
Q3) Two characteristics/assumptions of the Poisson distribution include:
A)Probability of success remains constant from trial to trial and the random variable of interest is continuous.
B)The event occurring in one interval is independent of the event occurring in any other non-overlapping interval,and the random variable of interest is continuous.
C)The event occurring in one interval is independent of the event occurring in any other non-overlapping interval,and the random variable of interest is discrete.
D)The event occurring in one interval is dependent of the event occurring in any other non-overlapping interval,and the random variable of interest is continuous.
E)Probability of success remains changes from trial to trial and the random variable of interest is continuous.
Q4) Find the probability that x (number of jobs finished on time)is within one standard deviation of the mean.
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Chapter 5: Continuous Random Variables
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Sample Questions
Q1) Less than 33.2?
A)0.4332
B)0.0668
C)0.9332
D)0.8664
E)0.1336
Q2) The actual weight of hamburger patties can be modeled using a continuous probability distribution is an example of a continuous random variable.
A)True
B)False
Q3) What is the probability that a randomly selected depth is within 1 standard deviation of the mean?
Q4) For a continuous distribution,P(X 100)= P(X < 100).
A)True
B)False
Q5) The thickness of randomly selected metal piece is a ___________ random variable.
Q6) The weight of a product is normally distributed with a standard deviation of .5 grams.What should the average weight be if the production manager wants no more than 10% of the products to weigh more than 4.8 grams?
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Chapter 6: Sampling Distributions
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Sample Questions
Q1) The standard deviation of all possible sample proportions increases as the sample size increases.
A)True
B)False
Q2) The sample mean is an unbiased,_______-variance point estimate of the population mean.
Q3) Calculate the mean of the sampling distribution of the sample mean.
Q4) The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 cm and a standard deviation of 0.3 cm.What is the probability that average length of a steel sheet from a sample of 9 units is more than 29.95 cm long?
Q5) If the sampled population distribution is skewed,then in most cases the sampling distribution of the sample mean \(\bar { x }\) can be approximated by the normal distribution if the sample size n is at least 30.
A)True
B)False
Q6) The _________ theorem allows us to approximate the sampling distribution of a sample mean with a normal probability distribution whenever the sample size is sufficiently large.
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Chapter 7: Confidence Intervals
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Sample Questions
Q1) What is the value of the calculated test statistic?
A)z = 6.416
B)z = 3.208
C)z = -3.208
D)z = -6.416
E)z = 1.833
Q2) A researcher wishes to test \[H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = 0\] versus \(H _ { a } : \mu _ { 1 } - \mu _ { 2 } \neq 0\)
.A sample of 50 observations from each population yields \(\bar { x } _ { 1 }\) = 60 and \(\bar { x } _ { 2 }\) = 52.If \(\sigma _ { 1 }\) = 10 and \(\sigma _ { 2 }\) = 8,compute Cohen's d.
Q3) A __________ occurs when we do not reject H<sub>0</sub> when H<sub>0</sub> is false.
Q4) Test H<sub>0</sub>: p<sub>1</sub> - p<sub>2</sub> .01 versus H<sub>a</sub>: p<sub>1</sub> - p<sub>2</sub> > .01 at
Q5) Write the alternative hypothesis.
Q6) What is the decision at \(\alpha\) = 0.10?
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Chapter 8: Hypothesis Testing
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Sample Questions
Q1) Suppose that a realtor is interested in comparing the price of a starter homes in two small cities.The realtor conducts a survey in the two cities looking at the price of starter homes.The information collected is provided below. \[\begin{array} { l r r }
& \text { City A } & \text { City B } \\
\text { Sample Mean } & 86,900 & 84,000 \\
\text { Sample Std Dev } & 2300 & 1750 \\
\text { Sample Size } & 9 & 7
\end{array}\]
Assuming equal population variances,what is the pooled estimate of ?<sup>2</sup>?
A)4335357.143
B)1733341.178
C)5229887.366
D)4223658.224
E)4987552.168
Q2) Two parameters of the F distribution are:
Q3) In testing the equality of population variance,what two assumptions are required?
Q4) What is the p-value for this test?
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Chapter 9: Statistical Inferences Based on Two Samples
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Sample Questions
Q1) Independent random samples of are taken from each of two normally distributed populations.The relevant sample statistics are n<sub>1</sub> = 10,n<sub>2</sub> = 8, \(\bar { x } _ { 1 }\) = 50, \(\bar { x } _ { 2 }\) = 42,s<sub>1</sub>= 5,and s<sub>2</sub> = 7.If we assume the population variances are equal,give a 95% confidence for \(\mu _ { 1 } - \mu _ { 2 }\) )
A)[2.01,13.99]
B)[1.08,14.91]
C)[3.51,12.49]
D)[2.56,13.44]
E)[4.62,11.38]
Q2) What sample size is needed to estimate with 95 percent confidence the mean intake of calcium within 20 units of the true mean if the intake is normal with a variance of 1900 units?
Q3) As the stated confidence level decreases,the width of the confidence interval
Q4) As the significance level,? increases,the width of a confidence interval ________.
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Chapter 10: Experimental Design and Analysis of Variance
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Sample Questions
Q1) Test H<sub>0</sub>: there is no difference between group means at \(\alpha\) = .05.
Q2) Complete the analysis of variance table and test to determine whether the means for factor A differ at a = .10.Interpret the results.
Q3) Given the partial ANOVA table above,the calculated value of the F statistic for Factor A is ____.
A)6.333
B)2.0
C)5.0
D)3.0
E)2.5
Q4) Compute an individual 95% confidence interval for the second group mean.
Q5) What is the calculated F statistic for groups (treatment)?
Q6) Determine degrees of freedom treatment,degrees of freedom error and degrees of freedom total and state the critical value of the F statistic at a = .05.
Q7) The F-test for testing the difference between group means is equal to the _____________ mean squares divided by the ___________ mean square.
Q8) What is the degrees of freedom for treatments (groups)?
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Chapter 11: Correlation Coefficient and Simple Linear
Regression Analysis
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Sample Questions
Q1) Calculate the standard error.
Q2) Determine the normal score for the third residual in the ordered array.
Q3) What is the correlation coefficient?
A)986
B)972
C)995
D)931
E)948
Q4) In a simple linear regression model,the y-intercept term is the mean value of y when x equals _____.
Q5) The following results were obtained as a part of simple linear regression analysis: R<sup>2</sup>= 0.9162 F test statistic = 81.87 At \(\alpha\) = 0)05,the null hypothesis of no linear relationship between the dependent variable and the independent variable _____. A)is rejected.
B)cannot be tested with the given information. C)is not rejected.
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Chapter 12: Multiple Regression and Model Building
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Sample Questions
Q1) Given the regression model y = <sub>0</sub>+ <sub>1</sub>X<sub>1</sub>+ <sub>2</sub>X<sub>1</sub><sup>2</sup>+ ,if we wish to test the significance of X<sub>1</sub><sup>2</sup>,the appropriate null hypothesis is:
A)H<sub>0</sub>: X<sub>1</sub><sup>2</sup>= 0
B)H<sub>0</sub>: <sub>2</sub> 0
C)H<sub>0</sub>: <sub>2</sub> X<sub>1</sub><sup>2</sup>
D)H<sub>0</sub>: <sub>2</sub>= 0
E)H<sub>0</sub>: <sub>2</sub>- X<sub>1</sub><sup>2</sup>= 0
Q2) What is the value of R<sup>2</sup>?
A).697
B).105
C).035
D).242
E).347
Q3) Assume that the overall model is useful in predicting the game attendance and the team statistician wants to know if the mean attendance is higher on the weekends as compared to the weekdays.At alpha = .05,test to determine if the attendance is higher on weekend home games.
Q4) What is the number of observations in the sample?
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Chapter 13: Nonparametric Methods
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Sample Questions
Q1) At the \(\alpha\) = .01 level of significance,test the claim that the four newspapers have the identical distributions of readability level.
Q2) What is the appropriate null and alternative hypotheses for the claim that they distribute the same amount of coffee?
Q3) Which one of the following nonparametric methods requires that we carry out a paired difference experiment?
A)Wilcoxon signed rank test
B)Sign test
C)Kruskall-Wallis test
D)Wilcoxon rank sum test
E)Spearman's rank order correlation
Q4) What is the rejection point T<sub>0</sub> for \(\alpha\) = .05?
Q5) At \(\alpha\) = .05,can it be concluded that the oral exam scores are higher than the written exam scores?
Q6) State the null and alternative hypotheses to test the claim.Assume that the population of all battery lives is not normally distributed.
Q7) Calculate the value of T<sub>i</sub> (rank sum)for each of the three samples.
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Chapter 14: Chi-Square Tests
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Sample Questions
Q1) At a significance level of 0.05,determine the appropriate degrees of freedom and the rejection point condition for the test.
Q2) Consider the 3 × 2 contingency table below.What is the expected value for A<sub>1</sub>B<sub>2</sub>? \[\begin{array} { c c c } & { \text { Factor B } } \\ \text { Factor A } & \mathrm { B } _ { 1 } & \mathrm {~B} _ { 2 } \\
\mathrm {~A} _ { 1 } & 16 & 14 \\ \mathrm {~A} _ { 2 } & 15 & 25 \\ \mathrm {~A} _ { 3 } & 9 & 21
\end{array}\]
A)12
B)14
C)16
D)18
E)20
Q3) A chi-square test of independence is performed and the null hypothesis is rejected.Provide a one-sentence interpretation of the outcome of the test.
Q4) Calculate the expected values for all categories.
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Chapter 15: Decision Theory
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Sample Questions
Q1) The investor is considering two potential investments with the following potential returns and the probability of these returns. \(\begin{array}{|l|l|r|l|}
\hline \text { Investment } 1&&\text { Investment } 2\\
\hline \text { Profit } & \text { Probability } &{\text { Profit }} & \text { Probability } \\
\hline \$ 75,000 & 0.1 & \$ 100,000 & 0.2 \\
\hline \$ 40,000 & 0.4 & \$ 75,000 & 0.3 \\
\hline \$ \quad 0 & 0.5 & -\$ \quad 5000 & 0.5 \\ \hline \end{array}\)
Which investment should the investor choose and why?
A)Investment 2 because it has the highest expected monetary value of $40,000.
B)Investment 1 because it has the lowest expected monetary value of $23,500.
C)Investment 2 because it has the highest expected utility of 0.52.
D)Investment 1 because it has the lowest expected utility of 0.455.
E)Cannot be determined without more information.
Q2) What is the maximum amount that the quality control manager would be willing to pay for perfect information?
Q3) Which investment would the investor select if the maximin criterion is used?
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Chapter 16: Time Series Forecasting
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Sample Questions
Q1) Calculate the mean squared deviation (MSD)for Model 1.
Q2) Listed below is the price of a pair of men's boots over a 50 year time period. \[\begin{array} { | l | l | }
\hline \text { Year } & \text { Price } \\
\hline 1950 & \$ 22.45 \\
\hline 1960 & \$ 32.33 \\
\hline 1970 & \$ 44.90 \\
\hline 1980 & \$ 69.75 \\
\hline 1990 & \$ 80.05 \\
\hline 2000 & \$ 87.28 \\ \hline \end{array}\]
Find the simple index numbers for the data with 1950 as the base year.
Q3) The ________ index is a weighted aggregate price index that uses the base period quantities as weights in all succeeding time periods.
Q4) Compute the predicted value for sales for period 6 and 7.
Q5) Calculate the average seasonal factor for each quarter
Q6) Compute the predicted value of sales for period 7 and 8.
Q7) Compute the total forecast error (sum of the forecast error terms).
Q8) Calculate the year 2000 simple price index for each grain separately.
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