Can a student keep up their grade performance at the next level? Is a strong GPA at the Bachelors level a good predictor of a strong GPA at the Masters level, or are GPAs naturally going to decline since graduate school is tougher, or will GPAs automatically be higher in graduate school because of the 3.00 requirement to graduate and the treatment of a C as subpar instead of average? Using the sample of 200 students (in the data file), conduct a hypothesis test for paired samples and test if there is a difference in the mean GPA from the Bachelors to the Masters programs. Use a .05 significance level.
To conduct a hypothesis test for paired samples and test if there is a difference in the mean GPA from the Bachelors to the Masters programs, you need to follow these steps:
1. Formulate the null hypothesis (H0) and alternative hypothesis (H1):
- Null hypothesis (H0): There is no difference in the mean GPA from the Bachelors to the Masters programs.
- Alternative hypothesis (H1): There is a difference in the mean GPA from the Bachelors to the Masters programs.
2. Determine the significance level (α): In this case, the significance level is given as 0.05.
3. Collect the data: You mentioned having a sample of 200 students in a data file. Ensure that you have the GPA values for each student in both the Bachelors and Masters programs.
4. Calculate the difference in GPA for each student: Subtract the Bachelors GPA from the Masters GPA for each student in your sample.
5. Calculate the sample mean (x̄) and standard deviation (s) of the differences.
6. Conduct the hypothesis test using a t-test for paired samples: Assuming the data is normally distributed, you can use the t-distribution for the test since the sample size is relatively large (200 students). Calculate the t-statistic using the formula:
t = (x̄ - μ) / (s / √n)
- x̄: Sample mean of the differences
- μ: Hypothesized population mean difference (0, in this case)
- s: Sample standard deviation of the differences
- n: Sample size (number of students)
7. Determine the critical value: Look up the critical value corresponding to the significance level and degrees of freedom. In this paired t-test, the degrees of freedom would be (n - 1), where n is the sample size.
8. Compare the calculated t-statistic to the critical value: If the calculated t-statistic falls in the rejection region (beyond the critical value), reject the null hypothesis. Otherwise, fail to reject the null hypothesis.
9. Interpret the result: If the null hypothesis is rejected, you can conclude that there is a statistically significant difference in the mean GPA between the Bachelors and Masters programs. If the null hypothesis is not rejected, you cannot conclude a significant difference.
Note: Since the data file containing the GPA values is not provided, you would need to use appropriate statistical software or programming language to calculate the required statistics and conduct the hypothesis test.