Week 15: Math 40 Final Exam

Instructions:

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

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Name:

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THE SCENARIO:

You are the Director of Admissions for a large business school. Students must take the GMAT to apply. You want to analyze GPA statistics and determine whether GMAT scores can predict GPA at graduation.

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THE DATA:

GMAT scores (X) and GPA at graduation (Y) for 20 randomly selected students are provided.

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QUESTIONS

1. Descriptive Statistics [4 POINTS]

• Find the mean and standard deviation of the sample GPA.
• Paste Excel descriptive statistics output.

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

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

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

• Determine required sample size for a 95% confidence interval with margin of error ≤ 0.10.
• Assume σ = 0.30.
• Paste PHStat output.

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4. Hypothesis Test (Regression Slope) [14 POINTS]

• Test at α = 0.01:

  H₀: β₁ = 0
  H₁: β₁ ≠ 0

• Include:
  • Test statistic
  • p-value
  • Decision rule
  • Decision
  • Conclusion

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5. Hypothesis Test for Mean GPA

• Test whether mean GPA > 3.2.
• Paste PHStat output.

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6. Repeat Hypothesis Test

• Change α to 0.05.
• Describe what changes (if any) occur.
• Paste PHStat output.

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7. True or False Section

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 rejection region than the first.
• The test statistic measures the distance between the hypothesized mean and the sample mean.
• The null hypothesis is rejected if alpha exceeds the p-value.
• The critical value separates the rejection and non-rejection regions.
• The p-value is the probability of obtaining a test statistic as extreme or more extreme assuming H₀ is true.

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8. Confidence Interval for Proportion [8 POINTS]

• Given 8 out of 20 students are women:
  • Construct a 95% confidence interval.
  • Paste PHStat output.
• Comment on the precision of the interval.

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9. Sample Size for Proportion [4 POINTS]

• Assume p = 0.45
• Determine required sample size for margin of error ≤ 0.05
• Paste PHStat output

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LINEAR REGRESSION SECTION

10. Scatter Plot [4 POINTS]

• Create and paste scatter plot (GMAT vs GPA).

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11. Regression Analysis [4 POINTS]

• Perform regression using PHStat
• Paste full regression output

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12. Regression Output Interpretation [10 POINTS]

State:

• Regression equation
• Slope
• Y-intercept
• Standard error of estimate
• Coefficient of determination (R²)

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13. Hypothesis Test for Regression [8 POINTS]

• Test if a linear relationship exists at α = 0.05

Include:

• Null hypothesis
• Alternative hypothesis
• p-value
• Decision
• Conclusion

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14. Interpretation [6 POINTS]

• Interpret the y-intercept
• Interpret the slope
• Predict GPA when GMAT = 600

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15. Residual Analysis [12 POINTS]

• Paste residual plot

Determine whether assumptions are satisfied:

• Linearity
• Equal variance

Provide justification.

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16. Normality Check [8 POINTS]

• Paste normal probability plot of residuals
• State whether normality assumption is satisfied
• Explain reasoning

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17. Confidence & Prediction Intervals [4 POINTS]

• Determine 95% confidence and prediction intervals for X = 600
• Paste PHStat output

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18. Model Evaluation [4 POINTS]

• Evaluate how good the regression model is for predicting GPA
• Provide justification

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19. Additional Variables

• Suggest at least TWO other independent variables that could improve the model

Tutorial for Math 40 Final Exam