OPRE 6301 Test 2 Questions and Answers 2026|2027
(Quantitative Introduction to Business Decision Making)
Question 1
A company wants to estimate the average time employees spend on training. They randomly
select 40 employees and find a mean of 12 hours with a standard deviation of 3 hours. Construct
a 95% confidence interval for the population mean.
• Answer: ( CI = 12 \pm (1.96 \cdot \frac{3}{\sqrt{40}}) )
• ( CI = 12 \pm 0.93 ) → (11.07, 12.93)
• Rationale: Confidence intervals use ( \bar{x} \pm z \cdot \frac{s}{\sqrt{n}} ).
Question 2
Which sampling method ensures every individual has an equal chance of being selected?
• Answer: Simple Random Sampling
• Rationale: Unlike stratified or cluster sampling, simple random sampling gives equal
probability to all members.
Question 3
In hypothesis testing, if the p-value is 0.03 and the significance level is 0.05, what decision
should be made?
• Answer: Reject the null hypothesis
• Rationale: Since ( p < \alpha ), evidence supports rejecting ( H_0 ).
Question 4
A regression analysis yields ( R^2 = 0.82 ). What does this indicate?
• Answer: 82% of the variation in the dependent variable is explained by the
independent variable(s).
• Rationale: ( R^2 ) measures explanatory power of the regression model.
Question 5
Which of the following is a Type I error?
, A. Rejecting a true null hypothesis
B. Failing to reject a false null hypothesis
C. Rejecting a false null hypothesis
D. Accepting a true null hypothesis
• Answer: A) Rejecting a true null hypothesis
• Rationale: Type I error = false positive.
Question 6
A population is normally distributed with mean 50 and standard deviation 10. What proportion
of values lie between 40 and 60?
• Answer: 68%
• Rationale: By the empirical rule, ±1 standard deviation from the mean covers 68%.
Question 7
Which test is appropriate for comparing means of two independent groups?
• Answer: Independent samples t-test
• Rationale: Used when comparing two unrelated groups (e.g., male vs. female scores).
Question 8
If a sample size increases, what happens to the width of the confidence interval?
• Answer: It decreases
• Rationale: Larger ( n ) reduces standard error, tightening the interval.
Question 9
In ANOVA, the F-statistic compares:
A. Between-group variance to within-group variance
B. Sample mean to population mean
C. Standard deviation to variance
D. Regression slope to intercept
• Answer: A) Between-group variance to within-group variance
• Rationale: ANOVA tests whether group means differ significantly.
, Question 10
Which probability distribution is used for modeling the number of events in a fixed interval of
time or space?
• Answer: Poisson distribution
• Rationale: Poisson is ideal for rare events occurring independently over time/space.
Question 11
The mean monthly sales is $20,000 with a standard deviation of $5,000. What is the z-score for a
store with $27,000 in sales?
• Answer: ( z = \frac{27,000 - 20,000}{5,000} = 1.4 )
• Rationale: Z-score measures deviation from mean in standard units.
Question 12
Which distribution is appropriate for modeling the probability of success/failure in a fixed
number of trials?
• Answer: Binomial distribution
• Rationale: Binomial handles discrete outcomes across repeated trials.
Question 13
If the null hypothesis states that the population mean is 50, and the sample mean is 54 with p-
value = 0.07 at α = 0.05, what is the decision?
• Answer: Fail to reject ( H_0 )
• Rationale: Since ( p > \alpha ), evidence is insufficient to reject.
Question 14
Which measure is most affected by extreme values?
• Answer: Mean
• Rationale: Outliers distort the mean more than median or mode.
(Quantitative Introduction to Business Decision Making)
Question 1
A company wants to estimate the average time employees spend on training. They randomly
select 40 employees and find a mean of 12 hours with a standard deviation of 3 hours. Construct
a 95% confidence interval for the population mean.
• Answer: ( CI = 12 \pm (1.96 \cdot \frac{3}{\sqrt{40}}) )
• ( CI = 12 \pm 0.93 ) → (11.07, 12.93)
• Rationale: Confidence intervals use ( \bar{x} \pm z \cdot \frac{s}{\sqrt{n}} ).
Question 2
Which sampling method ensures every individual has an equal chance of being selected?
• Answer: Simple Random Sampling
• Rationale: Unlike stratified or cluster sampling, simple random sampling gives equal
probability to all members.
Question 3
In hypothesis testing, if the p-value is 0.03 and the significance level is 0.05, what decision
should be made?
• Answer: Reject the null hypothesis
• Rationale: Since ( p < \alpha ), evidence supports rejecting ( H_0 ).
Question 4
A regression analysis yields ( R^2 = 0.82 ). What does this indicate?
• Answer: 82% of the variation in the dependent variable is explained by the
independent variable(s).
• Rationale: ( R^2 ) measures explanatory power of the regression model.
Question 5
Which of the following is a Type I error?
, A. Rejecting a true null hypothesis
B. Failing to reject a false null hypothesis
C. Rejecting a false null hypothesis
D. Accepting a true null hypothesis
• Answer: A) Rejecting a true null hypothesis
• Rationale: Type I error = false positive.
Question 6
A population is normally distributed with mean 50 and standard deviation 10. What proportion
of values lie between 40 and 60?
• Answer: 68%
• Rationale: By the empirical rule, ±1 standard deviation from the mean covers 68%.
Question 7
Which test is appropriate for comparing means of two independent groups?
• Answer: Independent samples t-test
• Rationale: Used when comparing two unrelated groups (e.g., male vs. female scores).
Question 8
If a sample size increases, what happens to the width of the confidence interval?
• Answer: It decreases
• Rationale: Larger ( n ) reduces standard error, tightening the interval.
Question 9
In ANOVA, the F-statistic compares:
A. Between-group variance to within-group variance
B. Sample mean to population mean
C. Standard deviation to variance
D. Regression slope to intercept
• Answer: A) Between-group variance to within-group variance
• Rationale: ANOVA tests whether group means differ significantly.
, Question 10
Which probability distribution is used for modeling the number of events in a fixed interval of
time or space?
• Answer: Poisson distribution
• Rationale: Poisson is ideal for rare events occurring independently over time/space.
Question 11
The mean monthly sales is $20,000 with a standard deviation of $5,000. What is the z-score for a
store with $27,000 in sales?
• Answer: ( z = \frac{27,000 - 20,000}{5,000} = 1.4 )
• Rationale: Z-score measures deviation from mean in standard units.
Question 12
Which distribution is appropriate for modeling the probability of success/failure in a fixed
number of trials?
• Answer: Binomial distribution
• Rationale: Binomial handles discrete outcomes across repeated trials.
Question 13
If the null hypothesis states that the population mean is 50, and the sample mean is 54 with p-
value = 0.07 at α = 0.05, what is the decision?
• Answer: Fail to reject ( H_0 )
• Rationale: Since ( p > \alpha ), evidence is insufficient to reject.
Question 14
Which measure is most affected by extreme values?
• Answer: Mean
• Rationale: Outliers distort the mean more than median or mode.
