Week 2Testing means – T-testsIn questions 2, 3, and 4be sure to include the null and alternate hypotheses you will betesting.In the first 4 questionsuse alpha = 0.05 in making your decisions on rejecting or not rejecting thenull hypothesis.1Below are 2 one-samplet-tests comparing male and female average salaries to the overall samplemean.(Note: a one-samplet-test in Excel can be performed by selecting the 2-sample unequal variancet-test and making the second variable = Ho value – a constant.)Note: These values are not the same as the datathe assignment uses. The purpose is toanalyze the results of t-tests rather than directly answer our equal payquestion.Based on these results,how do you interpret the results and what do these results suggest about thepopulation means for male and female average salaries?MalesFemalesHo: Mean salary =45.00Ho: Mean salary =45.00Ha: Mean salary =/=45.00Ha: Mean salary =/=45.00Note: While the resultsboth below are actually from Excel’s t-Test: Two-Sample Assuming UnequalVariances,having no variance inthe Ho variable makes the calculations default to the one-sample t-testoutcome – we are tricking Excel into doing a one sample test for us.MaleHoFemaleHoMean5245Mean3845Variance3160Variance334.6670Observations2525Observations2525Hypothesized Mean Difference0Hypothesized Mean Difference0df24df24t Stat1.968903827t Stat-1.91321P(T<=t) one-tail0.03030785P(T<=t) one-tail0.03386t Critical one-tail1.71088208t Critical one-tail1.71088P(T<=t) two-tail0.060615701P(T<=t) two-tail0.06772t Critical two-tail2.063898562t Critical two-tail2.0639Conclusion: Do not reject Ho; mean equals 45Conclusion: Do notreject Ho; mean equals 45Note:the Female results are done for you, please complete the male results.Is this a 1 or 2 tail test?1 tailIs this a 1 or 2 tail test?2 tail- why?- why?Ho contains =P-value is:P-value is:0.06772Is P-value < 0.05 (one tail test) or 0.025 (two tail test)?Is P-value < 0.05(one tail test) or 0.025 (two tail test)?NoWhy do we not reject the null hypothesis?Why do we not rejectthe null hypothesis?P-value greater than(>) rejection alphaInterpretation of test outcomes:2Based on our sample dataset, perform a 2-sample t-test to see if the population male and femaleaverage salaries could be equal to each other.(Since we have not yetcovered testing for variance equality, assume the data sets havestatistically equal variances.)Ho:Male salary mean = Femalesalary mean Ha:Male salary mean =/=Female salary mean Test to use:t-Test: Two-SampleAssuming Equal Variances P-value is:Is P-value < 0.05 (one tailtest) or 0.025 (two tail test)?Reject or do not reject Ho:If the null hypothesiswas rejected, calculate the effect size value:If calculated, what is the meaning of effect size measure:Interpretation:b.Is the one or two samplet-test the proper/correct apporach to comparing salary equality? Why?3Based on our sample dataset, can the male and female compas in the population be equal to each other?(Another 2-sample t-test.)Again, please assumeequal variances for these groups.Ho:Ha:Statistical test to use:What is the p-value:Is P-value < 0.05 (one tailtest) or 0.025 (two tail test)?Reject or do not reject Ho:If the null hypothesiswas rejected, calculate the effect size value:If calculated, what is the meaning of effect size measure:Interpretation:4Since performance isoften a factor in pay levels, is the average Performance Rating the same forboth genders?NOTE: do NOT assumevariances are equal in this situation.Ho:Ha:Test to use:t-Test: Two-SampleAssuming Unequal Variances What is the p-value:Is P-value < 0.05(one tail test) or 0.025 (two tail test)?Do we REJ or Not reject the null?If the null hypothesis was rejected, calculatethe effect size value:If calculated, whatis the meaning of effect size measure:Interpretation:5If the salary and compamean tests in questions 2 and 3 provide different results about male andfemale salary equality,which would be moreappropriate to use in answering the question about salary equity? Why?What are your conclusionsabout equal pay at this point?
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