Question

a university is interested in promoting graduates of its honors program by establishing that the mean gpa of these graduates exceeds 3.50. a sample of 36 honors students is taken and is found to have a mean gpa equal to 3.60. the population standard deviation is assumed to equal 0.40. at a 5% significance level, the decision is to .

Answer 1

To determine the decision, we need to conduct a hypothesis test with the following hypotheses:

Null hypothesis: the mean GPA of honors graduates is not greater than 3.50.

Alternative hypothesis: the mean GPA of honors graduates is greater than 3.50.

We can set up the test using a one-sample t-test with a level of significance of 0.05. The test statistic is calculated as:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

t = (3.60 - 3.50) / (0.40 / sqrt(36))

t = 2.25

The degrees of freedom for the t-test is 35 (sample size - 1). Using a t-distribution table with 35 degrees of freedom and a significance level of 0.05, the critical value is 1.690.

Since the calculated t-value (2.25) is greater than the critical value (1.690), we reject the null hypothesis. Therefore, we can conclude that the mean GPA of honors graduates is greater than 3.50 with 95% confidence level.

Explanation: