Week 2 Testing means – T-tests               In questions 2, 3, and 4 be sure to include the null and alternate hypotheses you will be testing.       In the first 4 questions use alpha = 0.05 in making your decisions on rejecting or not rejecting the null hypothesis.                   1 Below are 2 one-sample t-tests comparing male and female average salaries to the overall sample mean.     (Note: a one-sample t-test in Excel can be performed by selecting the 2-sample unequal variance t-test and making the second variable = Ho value – a constant.)   Note:  These values are not the same as the data the assignment uses.  The purpose is to analyze the results of t-tests rather than directly answer our equal pay question.   Based on these results, how do you interpret the results and what do these results suggest about the population means for male and female average salaries?                     Males       Females         Ho: Mean salary = 45.00     Ho: Mean salary = 45.00       Ha: Mean salary =/= 45.00     Ha: Mean salary =/= 45.00                         Note: While the results both below are actually from Excel’s t-Test: Two-Sample Assuming Unequal Variances,    having no variance in the Ho variable makes the calculations default to the one-sample t-test outcome – we are tricking Excel into doing a one sample test for us.     Male Ho     Female Ho     Mean 52 45   Mean 38 45     Variance 316 0   Variance 334.667 0     Observations 25 25   Observations 25 25     Hypothesized Mean Difference 0     Hypothesized Mean Difference 0       df 24     df 24       t Stat 1.968903827     t Stat -1.91321       P(T<=t) one-tail 0.03030785     P(T<=t) one-tail 0.03386       t Critical one-tail 1.71088208     t Critical one-tail 1.71088       P(T<=t) two-tail 0.060615701     P(T<=t) two-tail 0.06772       t Critical two-tail 2.063898562     t Critical two-tail 2.0639       Conclusion: Do not reject Ho; mean equals 45 Conclusion: Do not reject Ho; mean equals 45 Note: the Female results are done for you, please complete the male results.         Is this a 1 or 2 tail test?       Is this a 1 or 2 tail test? 2 tail       – why?       – why? Ho contains =     P-value is:       P-value is: 0.06772     Is P-value < 0.05 (one tail test) or 0.25 (two tail test)?     Is P-value < 0.05 (one tail test) or 0.25 (two tail test)? No     Why do we not reject the null hypothesis?     Why do we not reject the null hypothesis? P-value greater than (>) rejection alpha                     Interpretation of test outcomes:                                 2 Based on our sample data set, perform a 2-sample t-test to see if the population male and female average salaries could be equal to each other.   (Since we have not yet covered testing for variance equality, assume the data sets have statistically equal variances.)                     Ho:  Male salary mean = Female salary mean         Ha:  Male salary mean =/= Female salary mean         Test to use: t-Test: Two-Sample Assuming Equal Variances                                                                                                                                                                                                                                                                                                         P-value is:                 Is P-value < 0.05 (one tail test) or 0.25 (two tail test)?                 Reject or do not reject Ho:               If  the null hypothesis was rejected, calculate the effect size value:               If calculated, what is the meaning of effect size measure:                                   Interpretation:                                 b. Is the one or two sample t-test the proper/correct apporach to comparing salary equality?  Why?                                       3 Based on our sample data set, can the male and female compas in the population be equal to each other? (Another 2-sample t-test.)   Again, please assume equal variances for these groups.           Ho:                 Ha:                 Statistical test to use:                                                                                                                                                                                                                                                                                                                 What is the p-value:                 Is P-value < 0.05 (one tail test) or 0.25 (two tail test)?                 Reject or do not reject Ho:               If  the null hypothesis was rejected, calculate the effect size value:               If calculated, what is the meaning of effect size measure:                                    Interpretation:                                  4 Since performance is often a factor in pay levels, is the average Performance Rating the same for both genders?   NOTE: do NOT assume variances are equal in this situation.         Ho:                 Ha:                                   Test to use: t-Test: Two-Sample Assuming Unequal Variances                                                                                                                                                                                                                                                                                                                             What is the p-value:               Is P-value < 0.05 (one tail test) or 0.25 (two tail test)?                 Do we REJ or Not reject the null?                                 If  the null hypothesis was rejected, calculate the effect size value:               If calculated, what is the meaning of effect size measure:                                   Interpretation:                                                 5 If the salary and compa mean tests in questions 2 and 3 provide different results about male and female salary equality,      which would be more appropriate to use in answering the question about salary equity?  Why?                                         What are your conclusions about equal pay at this point?