Download QMB 3200 Final Exam UCF QUESTIONS AND CORRECT ANSWERS (VERIFIED ANSWERS) PLUS RATIONALES and more Exams Statistics in PDF only on Docsity!
QMB 3200 Final Exam UCF QUESTIONS
AND CORRECT ANSWERS (VERIFIED
ANSWERS) PLUS RATIONALES 2025
- 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. B) 2. C) 2. D) 1. Answer: B) 2. The z-statistic is calculated as (X̄ - μ) / (σ/√n). So, (105 - 100) / (10/5) = 5 / 2 = 2.5.
- The p-value for a two-tailed test with z = 2.5 is closest to:
A) 0.
B) 0.
C) 0.
D) 0.
Answer: A) 0. For z = 2.5, the area in one tail is about 0.0062. For a two-tailed test, double that: 0.0124.
- 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.
- 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
Answer: B) Additive model An additive model assumes the time series = trend + seasonal + random components.
- 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.
- 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.
- Which of the following statements is true about the F-distribution? A) It is symmetric B) It can take negative values C) It is always right-skewed D) It is used only in regression Answer: C) It is always right-skewed The F-distribution is non-negative and right-skewed, especially with small degrees of freedom.
- If the Durbin-Watson statistic in regression is close to 0, what does it indicate? A) No autocorrelation B) Positive autocorrelation C) Negative autocorrelation D) Multicollinearity Answer: B) Positive autocorrelation A Durbin-Watson statistic near 0 indicates strong positive autocorrelation.
- In time series forecasting, what is the main drawback of the naive method?
C) F-test D) Chi-square test Answer: C) F-test The F-test determines if at least one independent variable significantly predicts the dependent variable.
- A Type II error occurs when you: A) Reject H₀ when it is true B) Fail to reject H₀ when it is false C) Reject H₁ when it is false D) Accept H₁ when it is false Answer: B) Fail to reject H₀ when it is false A Type II error means you did not detect a real effect.
- Which method is best for forecasting when you have both trend and seasonality? A) Naive B) Exponential smoothing with trend and seasonality C) Simple average D) Linear trend only
Answer: B) Exponential smoothing with trend and seasonality This method adjusts for both trend and seasonal effects.
- A Type I error occurs when you: A) Reject H₀ when it is true B) Reject H₀ when it is false C) Fail to reject H₀ when it is false D) Fail to reject H₀ when it is true Answer: A) Reject H₀ when it is true A Type I error means you incorrectly reject a true null hypothesis.
- In multiple regression, what does a significant t-test for a coefficient mean? A) The independent variable is unrelated to the dependent variable. B) The independent variable significantly contributes to predicting the dependent variable. C) The model is insignificant. D) The model is overfitted. Answer: B) The independent variable significantly contributes to predicting the dependent variable. A significant t-test shows the variable has a non-zero effect.
C) SST (Total Sum of Squares) D) None of the above Answer: D) None of the above Sums of squares measure squared distances, so they cannot be negative.
- What does multicollinearity affect most in a regression model? A) Predictive power B) Standard errors of coefficients C) R-squared value D) The dependent variable Answer: B) Standard errors of coefficients Multicollinearity inflates standard errors, making individual t-tests unreliable.
- If the Durbin-Watson statistic is close to 4, this indicates: A) Positive autocorrelation B) No autocorrelation C) Negative autocorrelation D) Multicollinearity Answer: C) Negative autocorrelation A DW near 4 implies strong negative autocorrelation in residuals.
- Which of the following is not an assumption of ANOVA? A) Normality B) Homogeneity of variances C) Independence of observations D) Equal means across groups Answer: D) Equal means across groups Equal means is the null hypothesis, not an assumption.
- Which time series component represents long-term upward or downward movement? A) Seasonal B) Cyclical C) Trend D) Irregular Answer: C) Trend Trend shows long-term progression in the data.
- What is the purpose of residual analysis in regression? A) To check if coefficients are biased B) To check model assumptions
- If α = 0.10, what is the confidence level? A) 90% B) 10% C) 95% D) 85% Answer: A) 90% Confidence level = 1 – α.
- A perfect positive correlation is: A) 1 B) 0 C) – 1 D) Infinity Answer: A) 1 Correlation values range from – 1 to +1.
- Which of these describes multicollinearity? A) High correlation among independent variables B) High correlation between Y and X
C) High residuals D) High autocorrelation Answer: A) High correlation among independent variables Multicollinearity means predictors are strongly correlated.
- Which is true about the adjusted R-squared? A) It always increases when variables are added. B) It always equals R-squared. C) It adjusts for the number of predictors. D) It measures multicollinearity. Answer: C) It adjusts for the number of predictors. Adjusted R² penalizes for adding non-significant variables.
- Which distribution is used for a small sample t-test? A) Normal B) t-distribution C) F-distribution D) Chi-square Answer: B) t-distribution The t-distribution is used when population variance is unknown and n is small.
C) Minimax regret D) EMV Answer: D) EMV Expected Monetary Value (EMV) is used under risk, not pure uncertainty.
- Which statement is true about time series data? A) Observations are independent. B) Observations are ordered in time. C) Time is not a factor. D) Random sampling is required. Answer: B) Observations are ordered in time. Time series observations are dependent and sequential.
- In multiple regression, adding an irrelevant variable will: A) Increase adjusted R² B) Decrease adjusted R² C) Always increase R² D) Both B and C Answer: D) Both B and C R² can’t decrease, but adjusted R² may decrease.
- The standard error of the estimate measures: A) The slope B) Variation of residuals C) Multicollinearity D) The correlation Answer: B) Variation of residuals It shows how much data points deviate from the regression line.
- Which is an advantage of exponential smoothing over moving averages? A) It gives equal weights to all data. B) It needs more historical data. C) It is less sensitive to recent changes. D) It gives more weight to recent data. Answer: D) It gives more weight to recent data. Exponential smoothing reacts faster to recent changes.
- The degrees of freedom for an F-test in regression are: A) (k, n–k–1) B) (n, k)
- The main advantage of multiple regression is: A) It tests only one variable B) It ignores multicollinearity C) It includes multiple predictors D) It increases standard error Answer: C) It includes multiple predictors Multiple regression models relationships with more than one independent variable.
- If two variables are perfectly correlated, then: A) The correlation is zero. B) The regression slope is zero. C) R² = 1 D) The SSE is large. Answer: C) R² = 1 Perfect correlation means all variation is explained.
- Which error term assumption is violated if residuals fan out? A) Independence B) Normality
C) Homoscedasticity D) Linearity Answer: C) Homoscedasticity Fan-shaped residuals indicate unequal variance.
- A large F-statistic in ANOVA means: A) Variances are equal B) Means are equal C) Variances are unequal D) At least one mean differs Answer: D) At least one mean differs A large F indicates significant differences among group means.
- The standard error of the mean decreases when: A) The population variance increases B) The sample size increases C) The mean increases D) The z-score increases Answer: B) The sample size increases Larger samples give smaller standard errors.
