D) Silver Gym's aerobic class grew so large that the class had to be split in half and offered on two different nights. Silver also hired a new aerobic leader to handle the Tuesday night class, whereas an existing staff member continued to handle the Thursday night class. Concerned about customer satisfaction with the new leader, Silver Gym's management decided to secure a leader-approval rating from each class after four weeks. Results are shown in the table below:
Mean Approval Rating
Standard Deviation 38
Did the new leader of the Tuesday night class receive a lower approval rating than the leader of the Thursday night class? Set up and test = 0.05. at  as your hypotheses.
Please see the attachments.
H0: There is no significant difference in the mean approval rating (µ1=µ2)
H1: Tuesday night class receive a lower approval rating than the leader of the Thursday night class (µ1<µ2).
The test statistic used is independent sample t test with where
The solution provides step by step method for the calculation of test statistic for independent sample t test . Formula for the calculation and Interpretations of the results are also included.