Thirty GPAs from a randomly selected sample of statistics students at a college are given in the accompanying table. Assume that the population distribution is approximately Normal. The technician in charge of records claimed that the population mean GPA for the whole college is 2.85. Aone-sided test with a significance level of 0.05 had previously been performed on the data and the null hypothesis was rejected. Use the data to find a95% confidence interval for the mean GPA. If atwo-sided alternative had been used with a significance level of0.05, would the hypothesized mean of 2.85 have beenrejected?

2.83 3.39 3.17 2.57 3.46 2.75 3.02 3.51 2.66 3.92

2.81 2.67 3.55 3.01 2.77 3.42 2.41 3.15 3.44 3.14

3.13 3.09 3.17 2.94 3.49 3.57 2.56 3.18 3.29 3.05

First, find the 95% confidence interval for the mean GPA.

The confidence interval is to .

(Round to two decimal places as needed. Use ascending order.)

Next, test the two-sided alternative with a significance level of 0.05. Determine the null and alternative hypotheses. Choose the correct answer below.

a. Ho:u=2.85 b. Ho:u=2.85 c. Ho:u=2.85

Ha:u2.85 Ha:u<2.85 Ha:u>2.85

d. Ho:u2.85 e. Ho:u<2.85 f. Ho:u>2.85

Ha:u=2.85 Ha:u2.85 Ha:u2.85

The test statistic is .

(Two decimal places.)

The p value is .

(Three decimal places.)

Interpret the results of the test.

Since the p-value is (less than or equal to, greater than) the significance level, (do not reject, reject) Ho. There is (insufficient, sufficient) evidence to conclude that the mean GPA for statistics students is different from 2.85 at a significance level of 0.05.