Statistics question

Question

Test the claim that the mean GPA of night students is smaller than 2.2 at the 0.005 significance level.The null and alternative hypothesis would be:

The test is:

Based on a sample of 60 people, the sample mean GPA was 2.18 with a standard deviation of 0.04The p-value is:  (to 2 decimals)Based on this we:

Answer 1

The null hypothesis assumes nothing, usually that translates into NO difference between groups wrt(with respect to) the variable of interest, but in this case, the problem states: Test ... the mean GPA of night students is smaller than 2.2, so, in this case the null hypothesis would be:

H_o; Mean GPA _{night students} is NOT< 2.2( or you could say Mean GPA _{night students} ≥2.2)

The alternative hypothesis is what you hope the data will 'prove', usually that translates into there IS a difference between groups wrt the variable of interest, but for this problem H_a: Mean GPA _{night students}< 2.2 .

Note: this should be the same variable as the one in the null hypothesis.

With an n=60, you can use the standard normal z-test to test this hypothesis. Plug the numbers into the formula to calculate the test, and look up that value in the correct tables to get the p-value associated with that value, which are likely to be found at the back of your textbook.