Question

So i have a question that involves two-sample hypothesis testing. The question will be posted as a comment.

Answer 1

part a) is a breeze,\[H_o: \mu_1-\mu_2=0\]\[H_a: \mu_1>\mu_2\]if you label that mu1 is for exclusive breaststrokers and mu2 is for individual medley

Answer 2

now for part b), what i think is correct is that the rejection region should look like this,\[RR=\left\{ T:\left| T \right| \ge C\right\}=.01\]and if this is correct, then my problem is that i don't understand what kind of n i have for the Bernoulli distribution that this problem is most likely distributed as.
Do i add the individual sample sizes, take an average, i'm unsure

Answer 3

for part c), i believe that the appropriate test statistic is a T statistic, considering that the sigma is unknown

Answer 4

Judging by the sample sizes, I think you're intended to use the Z statistic.

As for the rejection region ... the null hypothesis is rejected if the calculated Z falls to the left or right of the critical values, \(-Z_{\alpha/2}\) and \(Z_{\alpha/2}\) respectively.

Since \(\alpha=0.01\), we have \(\pm Z_{0.005}=\pm 2.575\).

This means the RR would be \(\left\{Z:|Z|>2.575\right\}\).