Question

Test the claim that the mean GPA of night students is significantly different than 3.5 at the 0.05 significance level.

The null and alternative hypothesis would be: H 0 : p = 0.875 H 1 : p ≠ 0.875 H 0 : p = 0.875 H 1 : p < 0.875 H 0 : p = 0.875 H 1 : p > 0.875 H 0 : μ = 3.5 H 1 : μ < 3.5 H 0 : μ = 3.5 H 1 : μ > 3.5 H 0 : μ = 3.5 H 1 : μ ≠ 3.5

The test is: left-tailed right-tailed two-tailed

Based on a sample of 65 people, the sample mean GPA was 3.49 with a standard deviation of 0.07

The test statistic is: (to 2 decimals)

The positive critical value is: (to 2 decimals)

Based on this we: Reject the null hypothesis Fail to reject the null hypothesis

Answer 1

As we are trying to test whether the mean GPA of night students is significantly different than 3.5 , therefore the null and the alternate hypothesis here are given as:

Ho : μ 3.5

1:11メ3.5

As we are testing it from both sides, this is a two tailed test.

The test statistic here is computed as:

_ μ0 3.49-3.5 07ー-=-1.15 ˇ丽 7t

Therefore -1.15 is the test statistic value here.

As this is a two tailed test for n - 1 = 64 degrees of freedom, we get form the t distribution tables that:

P( -1.998 < t₆₄ < 1.998 ) = 0.95

Therefore 2.00 is the required positive critical value here.

As the test statistic value here is < critical value, therefore the test is not significant and we cannot reject the null hypothesis here. Therefore fail to reject the null hypothesis .