Question 1206985
using pooled standard error, i get z = -1.156.


using un-pooled standard error, i get z = -1.161.


the two-tailed alpha is equal to .055.
that would be a tail of alpha/2 = .0275 on the left and a tail of alpha/2 = .0275 on the right.


at .055 two tailed alpha, the critical z-score is plus or minus 1.9189.


z-score of -1.156 and -1.161 are less than -1.9189, so the results are not significant regardless if you used pooled or un-pooled standard error.


answers to your questions:


A.  test statistic is z = -1.156 (pooled standard error is assumed).


B.  the rejection region for the test is z = (-infinity,-1.9189) union (1.9189,infinity).

C.  the p-value of the test is .2476.
that's a two-tailed p-value, meaning half is on the left tail and half is on the right tail.


here's what the results look like on a z-score calculator.


<img src = "http://theo.x10hosting.com/2024/042001.jpg">