Spring A 2026 MATH.40.HSF2 Statistics: Week 14: Final Exam Preparation

Week 14: Final Exam Preparation

Instructions

Submit your Microsoft Word file in the submission folder in Week 14. You may also submit your Excel file.
Use the exact format provided.
No late submissions or extensions will be accepted.
You may consult materials, but you may not consult any other person.
Projects will not be returned.
This project is worth 20% of your final grade.

Name:

THE SCENARIO

You are the Director of Admissions for a large business school. Students seeking admission must take the GMAT (Graduate Management Admission Test). You want to gather inferential statistics about students’ GPAs. You also wish to determine whether a student’s GMAT score is useful for predicting GPA at graduation.

THE DATA

The GMAT scores and GPAs at graduation of 20 randomly selected students are provided in the file GMAT Data.xlsx.

X-variable: GMAT score
Y-variable: GPA

INSTRUCTIONS FOR ANALYSIS

Answer all questions below.
Perform all calculations using Excel or PHStat.
Attach output where required.
If calculating manually, show formulas and all steps.
Unsupported answers will receive zero credit.
Round all calculations to at least four decimal places.

QUESTIONS

1. Descriptive Statistics [4 POINTS]

Find the mean and standard deviation of the sample GPA.

Paste Excel descriptive statistics output.
State the sample mean.
State the sample standard deviation.

2. Confidence Interval for Mean (Unknown σ) [6 POINTS]

Assume the population is normally distributed and the population standard deviation is unknown.

Construct a 95% confidence interval for the true mean GPA.
Paste PHStat output.
State the margin of error.

3. Sample Size Determination (Known σ) [4 POINTS]

Assume:

Population standard deviation = 0.30
Confidence level = 95%
Margin of error ≤ 0.10
Determine the required sample size.
Paste PHStat output.

4. Hypothesis Test for Regression Slope [14 POINTS]

Test whether GMAT score is a significant predictor of GPA.

State null and alternative hypotheses.
State significance level.
Report test statistic and p-value.
State decision rule.
State decision.
Provide conclusion.

5. Hypothesis Test for Mean GPA [6 POINTS]

Test whether the mean GPA is greater than 3.2.

Paste PHStat output.
State conclusion.

6. Repeat Hypothesis Test (New Alpha) [4 POINTS]

Repeat Question 5 with α = 0.05.

Paste PHStat output.
Describe what changed.

7. True/False Statements [6 POINTS]

Mark each statement as TRUE (T) or FALSE (F):

The p-value is the probability that the null hypothesis will be rejected.
The second test has a smaller reject region than the first.
The test statistic measures the distance between the mean being tested and the sample mean.
The null hypothesis will be rejected provided alpha exceeds the p-value.
The critical value is the boundary between the reject and do-not-reject regions.
The p-value is the probability of obtaining a test statistic equal to or more extreme than the sample result if the null hypothesis is true.

8. Confidence Interval for Proportion [8 POINTS]

Given: 8 out of 20 students are women

Construct a 95% confidence interval for the population proportion.
Paste PHStat output.
Interpret the interval.

9. Precision of Interval [2 POINTS]

Comment on the precision of the confidence interval.
Provide a reason.

10. Sample Size for Proportion [4 POINTS]

Assume:

Population proportion = 0.45
Margin of error ≤ 0.05
Confidence level = 95%
Determine required sample size.
Paste PHStat output.

LINEAR REGRESSION SECTION

11. Scatter Plot [4 POINTS]

Create and paste a scatter plot of GMAT vs GPA.

12. Regression Output [4 POINTS]

Perform regression using PHStat.
Paste full regression output.

13. Regression Equation & Metrics [10 POINTS]

From the regression output:

Write the regression equation.
Identify the slope.
Identify the y-intercept.
State the standard error of estimate.
State the coefficient of determination (R²).

14. Hypothesis Test for Linear Relationship [8 POINTS]

Test at α = 0.05:

State null and alternative hypotheses.
Report p-value.
State decision.
State conclusion.

15. Interpretation [6 POINTS]

Interpret the y-intercept.
Interpret the slope.
Predict GPA for GMAT = 600.

16. Residual Analysis [12 POINTS]

Paste residual plot.
Comment on:
- Linearity assumption
- Equal variance assumption

17. Normality of Residuals [8 POINTS]

Paste normal probability plot.
State whether normality assumption is satisfied.
Provide justification.

18. Confidence & Prediction Intervals [4 POINTS]

For X = 600:

Construct 95% confidence interval for mean response.
Construct 95% prediction interval.
Paste PHStat output.

19. Model Evaluation [4 POINTS]

Discuss how good the regression model is.
Provide supporting reasons.

20. Additional Predictors [4 POINTS]

Suggest at least two other independent variables that could help predict GPA.

Tutorial for Final Exam Preparation

Final Assignment

$20.00