QMB 3200 Final Exam UCF QUESTIONS
AND CORRECT ANSWERS (VERIFIED
ANSWERS) PLUS RATIONALES 2025
1. A hypothesis test is conducted with a null hypothesis H₀: μ = 100 and
an alternative hypothesis H₁: μ ≠ 100. The sample mean is 105, the
population standard deviation is 10, and n = 25. What is the z-statistic?
A) 1.5
B) 2.5
C) 2.0
D) 1.0
Answer: B) 2.5
The z-statistic is calculated as (X̄ - μ) / (σ/√n). So, (105 - 100) / (10/5) =
= 2.5.
2. The p-value for a two-tailed test with z = 2.5 is closest to:
,A) 0.0124
B) 0.0062
C) 0.0250
D) 0.0500
Answer: A) 0.0124
For z = 2.5, the area in one tail is about 0.0062. For a two-tailed test,
double that: 0.0124.
3. If the level of significance is α = 0.05 and the p-value is 0.0124, you
should:
A) Fail to reject H₀
B) Reject H₀
C) Accept H₀
D) Increase α
Answer: B) Reject H₀
Because the p-value (0.0124) is less than α (0.05), we reject the null
hypothesis.
4. In simple linear regression, what does the coefficient of determination
(R²) represent?
A) The slope of the regression line
B) The proportion of variation explained by the model
,C) The standard error of estimate
D) The y-intercept
Answer: B) The proportion of variation explained by the model
R² indicates how much of the variability in the dependent variable is
explained by the independent variable.
5. Which of the following is true about multicollinearity in multiple
regression?
A) It causes biased coefficient estimates.
B) It violates the assumption of linearity.
C) It causes standard errors to increase.
D) It is required for regression.
Answer: C) It causes standard errors to increase.
Multicollinearity does not bias coefficients but inflates standard errors,
making t-tests less reliable.
6. For a time series with trend and seasonal components, which model
would be appropriate?
A) Moving average
B) Additive model
C) Naive model
D) Control chart
, Answer: B) Additive model
An additive model assumes the time series = trend + seasonal + random
components.
7. Which is NOT an assumption for the error term in multiple regression?
A) Errors have constant variance
B) Errors are normally distributed
C) Errors are correlated
D) Errors have mean zero
Answer: C) Errors are correlated
The errors should NOT be correlated; this violates the independence
assumption.
8. In hypothesis testing for ANOVA, what is the null hypothesis?
A) All means are equal
B) All means are different
C) Variances are equal
D) The grand mean is zero
Answer: A) All means are equal
ANOVA tests whether there is evidence that at least one group mean is
different.
AND CORRECT ANSWERS (VERIFIED
ANSWERS) PLUS RATIONALES 2025
1. A hypothesis test is conducted with a null hypothesis H₀: μ = 100 and
an alternative hypothesis H₁: μ ≠ 100. The sample mean is 105, the
population standard deviation is 10, and n = 25. What is the z-statistic?
A) 1.5
B) 2.5
C) 2.0
D) 1.0
Answer: B) 2.5
The z-statistic is calculated as (X̄ - μ) / (σ/√n). So, (105 - 100) / (10/5) =
= 2.5.
2. The p-value for a two-tailed test with z = 2.5 is closest to:
,A) 0.0124
B) 0.0062
C) 0.0250
D) 0.0500
Answer: A) 0.0124
For z = 2.5, the area in one tail is about 0.0062. For a two-tailed test,
double that: 0.0124.
3. If the level of significance is α = 0.05 and the p-value is 0.0124, you
should:
A) Fail to reject H₀
B) Reject H₀
C) Accept H₀
D) Increase α
Answer: B) Reject H₀
Because the p-value (0.0124) is less than α (0.05), we reject the null
hypothesis.
4. In simple linear regression, what does the coefficient of determination
(R²) represent?
A) The slope of the regression line
B) The proportion of variation explained by the model
,C) The standard error of estimate
D) The y-intercept
Answer: B) The proportion of variation explained by the model
R² indicates how much of the variability in the dependent variable is
explained by the independent variable.
5. Which of the following is true about multicollinearity in multiple
regression?
A) It causes biased coefficient estimates.
B) It violates the assumption of linearity.
C) It causes standard errors to increase.
D) It is required for regression.
Answer: C) It causes standard errors to increase.
Multicollinearity does not bias coefficients but inflates standard errors,
making t-tests less reliable.
6. For a time series with trend and seasonal components, which model
would be appropriate?
A) Moving average
B) Additive model
C) Naive model
D) Control chart
, Answer: B) Additive model
An additive model assumes the time series = trend + seasonal + random
components.
7. Which is NOT an assumption for the error term in multiple regression?
A) Errors have constant variance
B) Errors are normally distributed
C) Errors are correlated
D) Errors have mean zero
Answer: C) Errors are correlated
The errors should NOT be correlated; this violates the independence
assumption.
8. In hypothesis testing for ANOVA, what is the null hypothesis?
A) All means are equal
B) All means are different
C) Variances are equal
D) The grand mean is zero
Answer: A) All means are equal
ANOVA tests whether there is evidence that at least one group mean is
different.
