Score: Week 2 <1 point> 1 Testing means - T-tests In questions 2 and 3, be sure to include the null and alternate hypotheses you will be testing. In the first 3 questions use alpha = 0.05 in making your decisions on rejecting or not rejecting the null hypothesis. 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 -- see column S) Based on our sample, 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 Ho: Mean salary = 45 Ha: Mean salary =/= 45 Ha: Mean salary =/= 45 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 334.6667 0 Observations 25 25 Observations 25 25 Hypothesized Mean Difference 0 Hypothesized Mean Difference 0 df 24 df 24 t Stat 1.9689038266 t Stat -1.913206 P(T<=t) one-tail 0.0303078503 P(T<=t) one-tail 0.033862 t Critical one-tail 1.7108820799 t Critical one-tail 1.710882 P(T<=t) two-tail 0.0606157006 P(T<=t) two-tail 0.067724 t Critical two-tail 2.0638985616 t Critical two-tail 2.063899 Conclusion: Do not reject Ho; mean equals 45 Conclusion: Do not reject Ho; mean equals 45 Is this a 1 or 2 tail test? Is this a 1 or 2 tail test? - why? - why? P-value is: P-value is: Is P-value > 0.05? Is P-value > 0.05? Why do we not reject Ho? Why do we not reject Ho? Interpretation: <1 point> 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: Ha: Test to use: Place B43 in Outcome range box. P-value is: Is P-value < 0.05? Reject or do not reject Ho: If the null hypothesis was rejected, what of effect size measure: Meaning is the effect size value: Interpretation: b. Since the one and two sample t-test results provided different outcomes, which is the proper/correct apporach to comparing salary equality? Why? <1 point> 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.) Ho: Ha: Statistical test to use: Place B75 in Outcome range box. What is the p-value: Is P-value < 0.05? Reject or do not reject Ho: If the null hypothesis was rejected, what of effect size measure: Meaning is the effect size value: Interpretation: <1 point> 4 Since performance is often a factor in pay levels, is the average Performance Rating the same for both genders? Ho: Ha: Test to use: Place B106 in Outcome range box. What is the p-value: Is P-value < 0.05? Do we REJ or Not reject the null? If the null hypothesis was rejected, what of effect size measure: Meaning is the effect size value: Interpretation: <2 points> 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? Q3 Ho Female 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 34 41 23 22 23 42 24 24 69 36 34 57 23 50 24 75 24 24 23 22 35 24 77 Male 1.017 0.870 1.157 0.979 1.134 1.149 1.052 1.175 1.043 1.134 1.043 1.000 1.074 1.020 0.903 1.122 0.903 0.982 1.086 1.075 1.052 1.140 1.087 Female 1.096 1.025 1.000 0.956 1.000 1.050 1.043 1.043 1.210 1.161 1.096 1.187 1.000 1.041 1.043 1.119 1.043 1.043 1.000 0.956 1.129 1.043 1.149 45 45 55 65 1.052 1.157 1.145 1.140 See comments at the right of the data set. ID Salary Compa Midpoint Age 8 10 11 14 15 23 26 31 35 36 37 42 3 18 20 39 7 13 22 24 45 17 48 28 43 19 25 40 2 32 34 16 27 41 5 30 1 4 12 33 38 44 46 47 49 50 6 9 21 29 23 22 23 24 24 23 24 24 24 23 22 24 34 36 34 35 41 42 57 50 55 69 65 75 77 24 24 25 27 28 28 47 40 43 47 49 58 66 60 64 56 60 65 62 60 66 76 77 76 72 45.00 1.000 0.956 1.000 1.043 1.043 1.000 1.043 1.043 1.043 1.000 0.956 1.043 1.096 1.161 1.096 1.129 1.025 1.050 1.187 1.041 1.145 1.210 1.140 1.119 1.149 1.043 1.043 1.086 0.870 0.903 0.903 1.175 1.000 1.075 0.979 1.020 1.017 1.157 1.052 1.122 0.982 1.052 1.140 1.087 1.052 1.157 1.134 1.149 1.134 1.074 1.062 23 23 23 23 23 23 23 23 23 23 23 23 31 31 31 31 40 40 48 48 48 57 57 67 67 23 23 23 31 31 31 40 40 40 48 48 57 57 57 57 57 57 57 57 57 57 67 67 67 67 41.76 32 30 41 32 32 36 22 29 23 27 22 32 30 31 44 27 32 30 48 30 36 27 34 44 42 32 41 24 52 25 26 44 35 25 36 45 34 42 52 35 45 45 39 37 41 38 36 49 43 52 35.72 Performance Service Gender Raise Degree Gender1 Grade Rating 90 80 100 90 80 65 95 60 90 75 95 100 75 80 70 90 100 100 65 75 95 55 90 95 95 85 70 90 80 95 80 90 80 80 90 90 85 100 95 90 95 90 75 95 95 80 70 100 95 95 85.9 9 7 19 12 8 6 2 4 4 3 2 8 5 11 16 6 8 2 6 9 8 3 11 9 20 1 4 2 7 4 2 4 7 5 16 18 8 16 22 9 11 16 20 5 21 12 12 10 13 5 8.96 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5.8 4.7 4.8 6 4.9 3.3 6.2 3.9 5.3 4.3 6.2 5.7 3.6 5.6 4.8 5.5 5.7 4.7 3.8 3.8 5.2 3 5.3 4.4 5.5 4.6 4 6.3 3.9 5.6 4.9 5.7 3.9 4.3 5.7 4.3 5.7 5.5 4.5 5.5 4.5 5.2 3.9 5.5 6.6 4.6 4.5 4 6.3 5.4 0 0 0 0 0 1 1 0 1 1 1 0 0 1 1 1 0 1 0 1 0 0 1 1 1 1 0 0 0 0 1 0 1 0 1 0 0 1 0 1 0 1 1 1 0 0 1 1 1 0 F F F F F F F F F F F F F F F F F F F F F F F F F M M M M M M M M M M M M M M M M M M M M M M M M M A A A A A A A A A A A A B B B B C C D D D E E F F A A A B B B C C C D D E E E E E E E E E E F F F F The ongoing question that the weekly assignments wi Note: to simplfy the analysis, we will assume that jobs The column labels in the table mean: ID - Employee sample number Age - Age in years Service - Years of service (rounded) Midpoint - salary grade midpoint Grade - job/pay grade Gender1 (Male or Female) Salary - S Performan Gender: 0 Raise - pe Degree (0= Compa - s will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)? s within each grade comprise equal work. Salary in thousands nce Rating - Appraisal rating (Employee evaluation score) 0 = male, 1 = female ercent of last raise = BS\\BA 1 = MS) salary divided by midpoint