, BUSI 230 — WEEK 8 EXAM PRACTICE
Introduction to Probability and Statistics | Liberty University
100-Question Original Practice Examination | 2026/2027 Edition
1. A prediction model has four residuals: -2, 3, -1, and 0. What is their sum of squared errors?
A) 36.
B) 14.
C) 6.
D) 0.
Correct Answer: B) 14.
Rationale: Square each residual and add: (-2)² + 3² + (-1)² + 0² = 4 + 9 + 1 + 0 = 14. Squared errors avoid sign cancellation
and penalize larger deviations.
2. Which design calls for a paired-samples t-test?
A) Comparing three unrelated branches simultaneously.
B) Comparing two independent defect proportions.
C) Comparing employee performance before and after the same training program.
D) Comparing independent teams from two companies.
Correct Answer: C) Comparing employee performance before and after the same training program.
Rationale: Paired observations arise when the same person or matched unit contributes both measurements. The test
evaluates within-pair differences, removing some individual variability. Independent groups do not satisfy the pairing structure.
3. Which test is most appropriate for a mean with unknown population standard deviation and a
smallapproximately normal sample?
A) A two-proportion z-test.
B) A Pearson correlation test.
C) A chi-square goodness-of-fit test.
D) A one-sample t-test.
Correct Answer: D) A one-sample t-test.
Rationale: The one-sample t procedure accounts for estimation of the population standard deviation from the sample.
Approximate normality matters for very small samples. Other procedures target categorical frequencies, proportions, or
association.
4. A significant chi-square independence test establishes which result?
A) One variable causes the other.
B) There is evidence of association between the categorical variables.
C) All category probabilities are equal.
BUSI 230 | Week 8 Practice Examination | 2026/2027 1
, D) The association is necessarily strong.
Correct Answer: B) There is evidence of association between the categorical variables.
Rationale: Rejecting independence supports an association, not causality or a specified strength. Effect measures such as
Cramér’s V and the study design are needed for fuller interpretation.
5. A sample proportion is 0.16 and the hypothesized proportion is 0.10 with null standard error 0.03.
Whatis the z statistic?
A) 5.33.
B) 2.00.
C) 0.06.
D) 0.20.
Correct Answer: B) 2.00.
Rationale: The standardized difference is (0.16 - 0.10)/0.03 = 0.06/0.03 = 2. This calculation assumes the one-sample
proportion z-test conditions are adequate.
6. An observed response is 21 and the regression prediction is 17. What is the residual?
A) 4.
B) -4.
C) 38.
D) 0.81.
Correct Answer: A) 4.
Rationale: Residual equals observed response minus predicted response: 21 - 17 = +4. The model underpredicted this
observation by four response units. Residuals help diagnose model fit.
7. A business claims its defect rate is at most 4%. For a test seeking evidence that the rate is
higher,which alternative is appropriate?
A) The sample defect proportion is 0.04.
B) The population defect proportion is greater than 0.04.
C) The population proportion equals 0.04.
D) The population defect proportion is less than 0.04.
Correct Answer: B) The population defect proportion is greater than 0.04.
Rationale: An increase in the defect rate is the outcome the analyst seeks to establish, so the alternative is right-tailed. The
null retains the benchmark and its equality boundary. The sample proportion is a statistic, not the hypothesized population
parameter.
8. Which outcome is a categorical variable appropriate for frequency analysis?
A) Preferred payment method.
B) Monthly spending in dollars.
C) Time spent shopping in minutes.
BUSI 230 | Week 8 Practice Examination | 2026/2027 2
Introduction to Probability and Statistics | Liberty University
100-Question Original Practice Examination | 2026/2027 Edition
1. A prediction model has four residuals: -2, 3, -1, and 0. What is their sum of squared errors?
A) 36.
B) 14.
C) 6.
D) 0.
Correct Answer: B) 14.
Rationale: Square each residual and add: (-2)² + 3² + (-1)² + 0² = 4 + 9 + 1 + 0 = 14. Squared errors avoid sign cancellation
and penalize larger deviations.
2. Which design calls for a paired-samples t-test?
A) Comparing three unrelated branches simultaneously.
B) Comparing two independent defect proportions.
C) Comparing employee performance before and after the same training program.
D) Comparing independent teams from two companies.
Correct Answer: C) Comparing employee performance before and after the same training program.
Rationale: Paired observations arise when the same person or matched unit contributes both measurements. The test
evaluates within-pair differences, removing some individual variability. Independent groups do not satisfy the pairing structure.
3. Which test is most appropriate for a mean with unknown population standard deviation and a
smallapproximately normal sample?
A) A two-proportion z-test.
B) A Pearson correlation test.
C) A chi-square goodness-of-fit test.
D) A one-sample t-test.
Correct Answer: D) A one-sample t-test.
Rationale: The one-sample t procedure accounts for estimation of the population standard deviation from the sample.
Approximate normality matters for very small samples. Other procedures target categorical frequencies, proportions, or
association.
4. A significant chi-square independence test establishes which result?
A) One variable causes the other.
B) There is evidence of association between the categorical variables.
C) All category probabilities are equal.
BUSI 230 | Week 8 Practice Examination | 2026/2027 1
, D) The association is necessarily strong.
Correct Answer: B) There is evidence of association between the categorical variables.
Rationale: Rejecting independence supports an association, not causality or a specified strength. Effect measures such as
Cramér’s V and the study design are needed for fuller interpretation.
5. A sample proportion is 0.16 and the hypothesized proportion is 0.10 with null standard error 0.03.
Whatis the z statistic?
A) 5.33.
B) 2.00.
C) 0.06.
D) 0.20.
Correct Answer: B) 2.00.
Rationale: The standardized difference is (0.16 - 0.10)/0.03 = 0.06/0.03 = 2. This calculation assumes the one-sample
proportion z-test conditions are adequate.
6. An observed response is 21 and the regression prediction is 17. What is the residual?
A) 4.
B) -4.
C) 38.
D) 0.81.
Correct Answer: A) 4.
Rationale: Residual equals observed response minus predicted response: 21 - 17 = +4. The model underpredicted this
observation by four response units. Residuals help diagnose model fit.
7. A business claims its defect rate is at most 4%. For a test seeking evidence that the rate is
higher,which alternative is appropriate?
A) The sample defect proportion is 0.04.
B) The population defect proportion is greater than 0.04.
C) The population proportion equals 0.04.
D) The population defect proportion is less than 0.04.
Correct Answer: B) The population defect proportion is greater than 0.04.
Rationale: An increase in the defect rate is the outcome the analyst seeks to establish, so the alternative is right-tailed. The
null retains the benchmark and its equality boundary. The sample proportion is a statistic, not the hypothesized population
parameter.
8. Which outcome is a categorical variable appropriate for frequency analysis?
A) Preferred payment method.
B) Monthly spending in dollars.
C) Time spent shopping in minutes.
BUSI 230 | Week 8 Practice Examination | 2026/2027 2
