Question: A study of the GPAs of students at UC Berkeley found that the average GPA was a 3.0 with an SD of 0.3. You wish to test whether students in Stat 2 have a larger average GPA. You take a simple random sample of 10 students from the Stat 2 class and find that the average was a 3.1 with an SD of 0.4. Test the hypothesis at the 5% significance level.

1. Identify the appropriate hypothesis test to use. Use a one sample t-test
2. State the null and alternative hypotheses. The difference is just chance error. Average GPA of stat 2 students is the same as the average GPA of all students at Cal.
3. Compute the test statistic . Use SD+ of V10/9 x 0.4 \(\approx \) 0.42; Degrees of Freedom = 10 - 1 = 9. t-statistic = 0.75.
4. What do you conclude from this test ? Looking at the t-Distribution table, the t-value associated to 5% significance is 1.83. The t-statistic is 0.75 < 1.83. Therefore, we fail to reject the null hypothesis. The difference can be explained by chance.

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