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 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 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 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 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 Performance Service Gender Raise Degree 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 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 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 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 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 44 46 47 49 50 6 9 21 29 60 65 62 60 66 76 77 76 72 1.052 1.140 1.087 1.052 1.157 1.134 1.149 1.134 1.074 57 57 57 57 57 67 67 67 67 45 39 37 41 38 36 49 43 52 90 75 95 95 80 70 100 95 95 16 20 5 21 12 12 10 13 5 0 0 0 0 0 0 0 0 0 5.2 3.9 5.5 6.6 4.6 4.5 4 6.3 5.4 1 1 1 0 0 1 1 1 0 Gender1 Grade 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 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 The ongoing question that the weekly assignments will focus on is: Are males and females Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal wo 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 - Salary in thousands Performance Rating - Appraisal rating (Empl Gender: 0 = male, 1 = female Raise - percent of last raise Degree (0= BS\\BA 1 = MS) Compa - salary divided by midpoint M M M M M M M M M E E E E E F F F F on is: Are males and females paid the same for equal work (under the Equal Pay Act)? ach grade comprise equal work. thousands g - Appraisal rating (Employee evaluation score) , 1 = female vided by midpoint Week 2 1 Testing means 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 nul Below are 2 one-sample t-tests comparing male and female average salaries to the overall sample mea (Note: a one-sample t-test in Excel can be performed by selecting the 2-sample unequal variance t-tes Based on our sample, how do you interpret the results and what do these results suggest about the pop Males Ho: Mean salary = 45 Ha: Mean salary =/= 45 Note: While the results both below are actually from Excel's t-Test: Two-Sample Assuming Unequal V having no variance in the Ho variable makes the calculations default to the one-sample t-test outcome Male Ho Mean 52 45 Variance 316 0 Observations 25 25 Hypothesized Mean Difference 0 df 24 t Stat 1.9689038266 P(T<=t) one-tail 0.0303078503 t Critical one-tail 1.7108820799 P(T<=t) two-tail 0.0606157006 t Critical two-tail 2.0638985616 Conclusion: Do not reject Ho; mean equals 45 Is this a 1 or 2 tail test? - why? P-value is: Is P-value > 0.05? Why do we not reject Ho? 2 tail test Ha: 45 0.0606157006 yes because P-value > 0.05 Interpretation: The mean salary of the population is 45 thousand. The mean salary of males and the mean salary of fem 2 Based on our sample data set, perform a 2-sample t-test to see if the population male and female avera (Since we have not yet covered testing for variance equality, assume the data sets have statistically eq Ho: the mean salary of male employees = the mean salary of female empl the mean salary of male employees the mean salary of female emplo Ha: Test to use: two-sample t-test with an assumption of equal variances Place B43 in Outcome range box. Two-Sample t-Test (with an assumption of equal variances) Male Mean Variance Observations Pooled Variance Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail 52 316 25 325.3333333333 0 48 2.7442189608 0.0042530089 1.6772241966 0.0085060177 2.0106347219 P-value is: Is P-value < 0.05? yes Reject or do not reject Ho: reject Ho Female 38 334.6666666667 25 0.0085060177 If the null hypothesis was rejected, what is the effect size value: 0.7761823345 Meaning of effect size measure: Because the effect size is large, it indicates that there is a significant dif Interpretation: There is enough evidence to suggest that the mean salary of male empl b. Since the one and two tail t-test results provided different outcomes, which is the proper/correct appo The two-tail test the the correct approaoch when comparing salary equality. In order to determine sig 3 Based on our sample data set, can the male and female compas in the population be equal to each othe Ho: the mean compa of male employees = the mean compa of female emplo Ha: the mean compa of male employees the mean compa of female empl Statistical test to use: two-sample t-test with an assumption of equal variances Place B75 in Outcome range box. Two-Sample t-Test (with an assumption of equal variances) Female Male Mean Variance Observations Pooled Variance Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail What is the p-value: Is P-value < 0.05? Reject or do not reject Ho: If the null hypothesis was rejected, what is the effect size value: Meaning of effect size measure: 1.05624 0.0070206067 25 0.0059844917 0 48 -0.5703690595 0.2855439182 1.6772241966 0.5710878365 2.0106347219 1.06872 0.0049483767 25 0.5710878365 no do not reject Ho does not apply does not apply Interpretation: There is not enough evidence to suggest the the mean compa of male 4 Since performance is often a factor in pay levels, is the average Performance Rating the same for both Ho: Ha: the mean performance rating of male employees = the mean performa the mean performance rating of male employees the mean performa Test to use: two-sample t-test with an assumption of equal variances Place B106 in Outcome range box. Two-Sample t-Test (waith an assumption of equal variances) Male Mean Variance Observations Pooled Variance Female 87.6 75.25 25 130 84.2 184.75 25 Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail 0 48 1.054295244 0.1485129687 1.6772241966 0.2970259374 2.0106347219 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 is the effect size value: Meaning of effect size measure: Interpretation: 0.2970259374 no do not reject Ho does not apply does not apply There is not enough evidence to suggest t 5 If the salary and compa mean tests in questions 2 and 3 provide different results about male and fema 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? The salary mean test results suggest that the difference between male and female mean salaries is stat difference between mail and feamle mean compas is not significant. The compa mean test results are grade, which reduces bias. The overall conclusion is that males and females are paid the same for equ es you will be testing. jecting or not rejecting the null hypothesis. aries to the overall sample mean. -sample unequal variance t-test and making the second variable = Ho value -- see column S) e results suggest about the population means for male and female average salaries? Females Ho: Mean salary = 45 Ha: Mean salary =/= 45 o-Sample Assuming Unequal Variances, the one-sample t-test outcome - we are tricking Excel into doing a one sample test for us. Female Ho Mean 38 45 Variance 334.6666666667 0 Observations 25 25 Hypothesized Mean D 0 df 24 t Stat -1.9132063573 P(T<=t) one-tail 0.0338621184 t Critical one-tail 1.7108820799 P(T<=t) two-tail 0.0677242369 t Critical two-tail 2.0638985616 Conclusion: Do not reject Ho; mean equals 45 Is this a 1 or 2 tail test? 2 tail test - why? Ha: 45 P-value is: 0.0677242369 Is P-value > 0.05? yes Why do we not reject Ho? because P-value > 0.05 ales and the mean salary of females are significantly different from the mean of the population. pulation male and female average salaries could be equal to each other. e data sets have statistically equal variances.) he mean salary of female employees he mean salary of female employees f equal variances es that there is a significant difference between the mean salaries of male and female employees. t the mean salary of male employees is significantly different from the mean salary of female employees. hich is the proper/correct apporach to comparing salary equality? Why? ality. In order to determine significance, the one-tail test is not appropriate. opulation be equal to each other? (Another 2-sample t-test.) he mean compa of female employees he mean compa of female employees f equal variances st the the mean compa of male employees is significantly different from the mean compa of female employees. mance Rating the same for both genders? mployees = the mean performance rating of female employees mployees the mean performance rating of female employees f equal variances ot enough evidence to suggest that the mean performance rating of male employees is significantly different from the mean perfor nt results about male and female salary equality, ut salary equity? Why? nd female mean salaries is statistically significant. The compa mean test results suggest the the he compa mean test results are more appropriate because this measure disregards the impact of males are paid the same for equal work. Ho Female 45 45 45 45 45 45 45 45 45 45 45 34 41 23 22 23 42 24 24 69 36 34 45 45 45 45 45 45 45 45 45 45 45 57 23 50 24 75 24 24 23 22 35 24 45 77 45 45 55 65 ifferent from the mean performance ratin og female employees. Q3 Male Female 1.017 0.870 1.157 0.979 1.134 1.149 1.052 1.175 1.043 1.134 1.043 1.096 1.025 1.000 0.956 1.000 1.050 1.043 1.043 1.210 1.161 1.096 1.000 1.074 1.020 0.903 1.122 0.903 0.982 1.086 1.075 1.052 1.140 1.187 1.000 1.041 1.043 1.119 1.043 1.043 1.000 0.956 1.129 1.043 1.087 1.149 1.052 1.157 1.145 1.140