A professor believes that all Thursday sections are cursed and will always score lower on tests compared to Monday sections. To tests this he collects samples of test scores from these two sections. For Monday's section, the mean test score was 60, the estimated population standard deviation was 5, and the sample size was 20. For Thursday's section the mean test score was 55, the estimated population standard deviation was 7 and the sample size was 20. With alpha equal to 0.05.

Question

What is the appropriate statistical test? I'm not sure if it would be a z-test or an Independent Samples t-test.

I believe it would also be a one tailed test and I have no idea how to get the obtained value. Can anyone help? Sorry for the super long question.

Answer 1

Ho: M = T
Ha: M > T (one-tailed)

I do not want to do an F-test to find out if the SDs are equal.

Z = (mean1 - mean2)/standard error (SE) of difference between means

SEdiff = √(SEmean1^2 + SEmean2^2)

SEm = SD/√n

If only one SD is provided, you can use just that to determine SEdiff.

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability
related to the Z score. Is it ≤ .05?