OPRE 6301 Test 4 Statistics and Data Analysis Questions
and Answers Graded A+
Question 1
A company wants to test whether the average time to complete a customer order is less than 15
minutes. A sample of 40 orders yields a mean of 14.2 minutes with a standard deviation of 2.5
minutes. At the 5% significance level, what is the correct conclusion?
•
A. Fail to reject (H_0); insufficient evidence
•
B. Reject (H_0); average time < 15 minutes
•
C. Fail to reject (H_0); average time ≥ 15 minutes
•
D. Reject (H_0); average time > 15 minutes
Answer: B
Rationale: (t = \frac{14.2-15}{2.5/\sqrt{40}} = -2.02). Critical (t_{0.05,39} \approx -1.685).
Since (-2.02 < -1.685), reject (H_0). Evidence supports mean < 15 minutes.
Question 2
Which of the following is not an assumption of simple linear regression?
•
A. Linearity between predictors and response
•
B. Independence of errors
•
C. Normality of predictors
•
D. Constant variance of errors
Answer: C
Rationale: Regression assumes normality of residuals, not predictors. Predictors can be non-
normal.
,Question 3
A 95% confidence interval for the mean monthly sales is (120, 140). Which statement is correct?
•
A. There is a 95% chance the true mean lies between 120 and 140.
•
B. 95% of all monthly sales fall between 120 and 140.
•
C. If repeated samples are taken, 95% of intervals will contain the true mean.
•
D. The probability the mean is exactly 130 is 95%.
Answer: C
Rationale: Confidence intervals are about the procedure, not the probability of a fixed
parameter.
Question 4
In hypothesis testing, increasing the sample size while keeping the same population variance
will:
•
A. Increase the p-value
•
B. Decrease the test statistic
•
C. Increase the power of the test
•
D. Increase the probability of Type II error
Answer: C
Rationale: Larger samples reduce standard error, making it easier to detect true effects → higher
power.
Question 5
A chi-square test of independence yields (\chi^2 = 18.3) with df = 8. At (\alpha = 0.05), what is
the conclusion?
•
A. Fail to reject independence
•
, B. Reject independence; variables are related
•
C. Fail to reject independence; variables are unrelated
•
D. Reject independence; variables are unrelated
Answer: B
Rationale: Critical (\chi^2_{0.05,8} \approx 15.51). Since 18.3 > 15.51, reject independence →
variables are related.
Question 6
Which measure is most appropriate for detecting multicollinearity in regression?
•
A. Durbin-Watson statistic
•
B. Variance Inflation Factor (VIF)
•
C. Adjusted R²
•
D. Standard error of regression
Answer: B
Rationale: VIF quantifies how much variance is inflated due to correlation among predictors.
Question 7
If the correlation coefficient (r = -0.85), what percentage of variation in Y is explained by X?
•
A. 72%
•
B. 85%
•
C. 100%
•
, D. 0%
Answer: A
Rationale: (r^2 = (-0.85)^2 = 0.7225 \approx 72%).
Question 8
The probability that a randomly selected student passes both Statistics and Accounting is 0.25.
The probability of passing Statistics is 0.5, and passing Accounting is 0.4. Are the events
independent?
•
A. Yes, because 0.25 = 0.5 × 0.4
•
B. No, because 0.25 ≠ 0.5 × 0.4
•
C. Yes, because probabilities are equal
•
D. Cannot be determined
Answer: A
Rationale: Independence holds if (P(A \cap B) = P(A) \cdot P(B)). Here, 0.25 = 0.20, so actually
No. Correction: Answer is B.
Question 9
Which distribution is appropriate for modeling the number of customer arrivals per hour?
•
A. Normal
•
B. Poisson
•
C. Uniform
•
D. Exponential
and Answers Graded A+
Question 1
A company wants to test whether the average time to complete a customer order is less than 15
minutes. A sample of 40 orders yields a mean of 14.2 minutes with a standard deviation of 2.5
minutes. At the 5% significance level, what is the correct conclusion?
•
A. Fail to reject (H_0); insufficient evidence
•
B. Reject (H_0); average time < 15 minutes
•
C. Fail to reject (H_0); average time ≥ 15 minutes
•
D. Reject (H_0); average time > 15 minutes
Answer: B
Rationale: (t = \frac{14.2-15}{2.5/\sqrt{40}} = -2.02). Critical (t_{0.05,39} \approx -1.685).
Since (-2.02 < -1.685), reject (H_0). Evidence supports mean < 15 minutes.
Question 2
Which of the following is not an assumption of simple linear regression?
•
A. Linearity between predictors and response
•
B. Independence of errors
•
C. Normality of predictors
•
D. Constant variance of errors
Answer: C
Rationale: Regression assumes normality of residuals, not predictors. Predictors can be non-
normal.
,Question 3
A 95% confidence interval for the mean monthly sales is (120, 140). Which statement is correct?
•
A. There is a 95% chance the true mean lies between 120 and 140.
•
B. 95% of all monthly sales fall between 120 and 140.
•
C. If repeated samples are taken, 95% of intervals will contain the true mean.
•
D. The probability the mean is exactly 130 is 95%.
Answer: C
Rationale: Confidence intervals are about the procedure, not the probability of a fixed
parameter.
Question 4
In hypothesis testing, increasing the sample size while keeping the same population variance
will:
•
A. Increase the p-value
•
B. Decrease the test statistic
•
C. Increase the power of the test
•
D. Increase the probability of Type II error
Answer: C
Rationale: Larger samples reduce standard error, making it easier to detect true effects → higher
power.
Question 5
A chi-square test of independence yields (\chi^2 = 18.3) with df = 8. At (\alpha = 0.05), what is
the conclusion?
•
A. Fail to reject independence
•
, B. Reject independence; variables are related
•
C. Fail to reject independence; variables are unrelated
•
D. Reject independence; variables are unrelated
Answer: B
Rationale: Critical (\chi^2_{0.05,8} \approx 15.51). Since 18.3 > 15.51, reject independence →
variables are related.
Question 6
Which measure is most appropriate for detecting multicollinearity in regression?
•
A. Durbin-Watson statistic
•
B. Variance Inflation Factor (VIF)
•
C. Adjusted R²
•
D. Standard error of regression
Answer: B
Rationale: VIF quantifies how much variance is inflated due to correlation among predictors.
Question 7
If the correlation coefficient (r = -0.85), what percentage of variation in Y is explained by X?
•
A. 72%
•
B. 85%
•
C. 100%
•
, D. 0%
Answer: A
Rationale: (r^2 = (-0.85)^2 = 0.7225 \approx 72%).
Question 8
The probability that a randomly selected student passes both Statistics and Accounting is 0.25.
The probability of passing Statistics is 0.5, and passing Accounting is 0.4. Are the events
independent?
•
A. Yes, because 0.25 = 0.5 × 0.4
•
B. No, because 0.25 ≠ 0.5 × 0.4
•
C. Yes, because probabilities are equal
•
D. Cannot be determined
Answer: A
Rationale: Independence holds if (P(A \cap B) = P(A) \cdot P(B)). Here, 0.25 = 0.20, so actually
No. Correction: Answer is B.
Question 9
Which distribution is appropriate for modeling the number of customer arrivals per hour?
•
A. Normal
•
B. Poisson
•
C. Uniform
•
D. Exponential
