Score: <1 point> Week 4 Confidence Intervals and Chi Square (Chs 11 - 12) For questions 3 and 4 below, be sure to list the null and alternate hypothesis statements. Use .05 for your significance level in making your decisions. For full credit, you need to also show the statistical outcomes - either the Excel test result or the calculations you performed. 1 Using our sample data, construct a 95% confidence interval for the population's mean salary for each gender. Interpret the results. How do they compare with the findings in the week 2 one sample t-test outcomes (Question 1)? Mean St error t value Low to High Males Females Interpretation: <1 point> 2 Using our sample data, construct a 95% confidence interval for the mean salary difference between the genders in the population. How does this compare to the findings in week 2, question 2? Difference St Err. T value Low to High Yes/No Can the means be equal? Why? How does this compare to the week 2, question 2 result (2 sampe t-test)? a. Why is using a two sample tool (t-test, confidence interval) a better choice than using 2 one-sample techniques when comparing two samples? <1 point> 3 We found last week that the degree values within the population do not impact compa rates. This does not mean that degrees are distributed evenly across the grades and genders. Do males and females have athe same distribution of degrees by grade? (Note: while technically the sample size might not be large enough to perform this test, ignore this limitation for this exercise.) What are the hypothesis statements: Ho: Ha: Note: You can either use the Excel Chi-related functions or do the calculations manually. Data input tables - graduate degrees by gender and grade level OBSERVED A B C D E F Total M Grad Fem Grad Male Und Female Und If desired, you can do manual calculations per cell here. A B C D E F M Grad Fem Grad Male Und Female Und Sum = EXPECTED M Grad Fem Grad Male Und Female Und For this exercise - ignore the requirement for a correction factor for cells with expected values less than 5. Interpretation: What is the value of the chi square statistic: What is the p-value associated with this value: Is the p-value <0.05? Do you reject or not reject the null hypothesis: If you rejected the null, what is the Cramer's V correlation: What does this correlation mean? What does this decision mean for our equal pay question: <1 point> 4 Based on our sample data, can we conclude that males and females are distributed across grades in a similar pattern within the population? What are the hypothesis statements: Ho: Ha: A OBS COUNT - m OBS COUNT - f B C D E Do manual calculations per cell here (if desired) A B C D E F M F F Sum = EXPECTED What is the value of the chi square statistic: What is the p-value associated with this value: Is the p-value <0.05? Do you reject or not reject the null hypothesis: If you rejected the null, what is the Phi correlation: What does this correlation mean? What does this decision mean for our equal pay question: <2 points> 5. How do you interpret these results in light of our question about equal pay for equal work? Score: <1 point> Week 4 Confidence Intervals and Chi Square (Chs 11 - 12) For questions 3 and 4 below, be sure to list the null and alternate hypothesis statements. Use .05 for your significance level in making your decisions. For full credit, you need to also show the statistical outcomes - either the Excel test result or the calculations you performed. Using our sample data, construct a 95% confidence interval for the population's mean salary for each gender. Interpret the results. How do they compare with the findings in the week 2 one sample t-test outcomes (Question 1)? Mean St error t value Low to High Males Females 1 Interpretation: <1 point> Using our sample data, construct a 95% confidence interval for the mean salary difference between the genders in the population. How does this compare to the findings in week 2, question 2? 2 Difference St Err. T value Low to High Yes/No Can the means be equal? Why? How does this compare to the week 2, question 2 result (2 sampe t-test)? a. Why is using a two sample tool (t-test, confidence interval) a better choice than using 2 one-sample techniques when comparing two samples? <1 point> We found last week that the degree values within the population do not impact compa rates. This does not mean that degrees are distributed evenly across the grades and genders. Do males and females have athe same distribution of degrees by grade? (Note: while technically the sample size might not be large enough to perform this test, ignore this limitation for this exercise.) 3 What are the hypothesis statements: Ho: Ha: Note: You can either use the Excel Chi-related functions or do the calculations manually. Data input tables - graduate degrees by gender and grade level A B C D E F Total OBSERVED M Grad Fem Grad Male Und Female Und If desired, you can do manual calculations per cell here. A B C D E F M Grad Fem Grad Male Und Female Und Sum = EXPECTED M Grad Fem Grad Male Und Female Und For this exercise - ignore the requirement for a correction factor for cells with expected values less than 5. Interpretation: What is the value of the chi square statistic: What is the p-value associated with this value: Is the p-value <0.05? Do you reject or not reject the null hypothesis: If you rejected the null, what is the Cramer's V correlation: What does this correlation mean? What does this decision mean for our equal pay question: <1 point> 4 Based on our sample data, can we conclude that males and females are distributed across grades in a similar pattern within the population? What are the hypothesis statements: Ho: Ha: A OBS COUNT - m OBS COUNT - f B C D E Do manual calculations per cell here (if desired) A B C D E F M F Sum = EXPECTED F What is the value of the chi square statistic: What is the p-value associated with this value: Is the p-value <0.05? Do you reject or not reject the null hypothesis: If you rejected the null, what is the Phi correlation: What does this correlation mean? What does this decision mean for our equal pay question: <2 points> 5. How do you interpret these results in light of our question about equal pay for equal work? ID Salary Compa Midpoint Age 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 66.1 25.9 35.2 55.3 49.6 78.3 42.3 22.8 78 23.3 23.6 60.8 40.6 21.7 21.8 37.4 57 33.5 23 36 76 43.7 25.3 48.9 25.8 23.3 42.3 75.2 80.9 49 24.2 27.5 63.6 28.6 22.4 23.6 24.3 63 34.8 24.3 42.8 23 75.4 60.7 57.9 62.2 62.2 70.1 61.7 61.4 1.159 0.834 1.135 0.971 1.033 1.168 1.058 0.990 1.164 1.014 1.025 1.067 1.014 0.943 0.949 0.934 1.000 1.081 1.000 1.162 1.135 0.911 1.098 1.019 1.122 1.013 1.057 1.122 1.208 1.020 1.054 0.886 1.115 0.922 0.976 1.026 1.057 1.105 1.123 1.057 1.071 0.998 1.125 1.065 1.206 1.091 1.091 1.230 1.083 1.077 57 31 31 57 48 67 40 23 67 23 23 57 40 23 23 40 57 31 23 31 67 48 23 48 23 23 40 67 67 48 23 31 57 31 23 23 23 57 31 23 40 23 67 57 48 57 57 57 57 57 34 52 30 42 36 36 32 32 49 30 41 52 30 32 32 44 27 31 32 44 43 48 36 30 41 22 35 44 52 45 29 25 35 26 23 27 22 45 27 24 25 32 42 45 36 39 37 34 41 38 Performance Service Gende Raise Degree Gender Rating r 1 85 80 75 100 90 70 100 90 100 80 100 95 100 90 80 90 55 80 85 70 95 65 65 75 70 95 80 95 95 90 60 95 90 80 90 75 95 95 90 90 80 100 95 90 95 75 95 90 95 80 8 7 5 16 16 12 8 9 10 7 19 22 2 12 8 4 3 11 1 16 13 6 6 9 4 2 7 9 5 18 4 4 9 2 4 3 2 11 6 2 5 8 20 16 8 20 5 11 21 12 0 0 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1 0 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 1 1 0 1 0 0 1 0 0 5.7 3.9 3.6 5.5 5.7 4.5 5.7 5.8 4 4.7 4.8 4.5 4.7 6 4.9 5.7 3 5.6 4.6 4.8 6.3 3.8 3.3 3.8 4 6.2 3.9 4.4 5.4 4.3 3.9 5.6 5.5 4.9 5.3 4.3 6.2 4.5 5.5 6.3 4.3 5.7 5.5 5.2 5.2 3.9 5.5 5.3 6.6 4.6 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 M M F M M M F F M F F M F F F M F F M F M F F F M F M F M M F M M M F F F M F M M F F M F M M F M M Gr E B B E D F C A F A A E C A A C E B A B F D A D A A C F F D A B E B A A A E B A C A F E D E E E E E The ongoing question that the weekly assignments w Note: to simplfy the analysis, we will assume that jo The column labels in the table mean: ID - Employee sample number Salary - S Age - Age in years Performan Service - Years of service (rounded) Gender - 0 Midpoint - salary grade midpoint Raise - pe Grade - job/pay grade Degree (0= Gender1 (Male or Female) Compa - s will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)? obs within each grade comprise equal work. Salary in thousands nce Rating - Appraisal rating (employee evaluation score) 0 = male, 1 = female ercent of last raise 0= BS\\BA 1 = MS) salary divided by midpoint Sal Compa 24 24.2 23.4 23.4 22.6 22.9 1.045 1.053 1.018 1.017 0.983 0.995 23.1 23.3 1.003 1.011 22.7 23.5 23 24 0.985 1.023 1.002 1.042 35.5 1.145 34.7 35.5 35.2 1.119 1.146 1.136 40.4 42.7 53.4 51.5 49.8 68.3 1.01 1.068 1.112 1.072 1.037 1.198 65.4 78.4 75.9 24 23.3 24.1 27.5 1.148 1.17 1.133 1.044 1.012 1.049 0.887 27.1 27.7 40.8 43.9 41 48.7 49.4 64.4 64.5 58.9 57.9 59 0.875 0.895 1.019 1.097 1.025 1.014 1.029 1.13 1.132 1.033 1.016 1.035 63.3 56.8 58 62.4 63.8 79 77 74.8 76 1.111 0.996 1.017 1.094 1.12 1.179 1.149 1.116 1.135 G 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 Mid 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 Age 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 EES 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 SR 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 G 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 Raise 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 Deg 1 1 1 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 0 1 1 1 0 0 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 SUMMARY OUTPUT SUMMARY OUTPUT Regression Statistics Multiple R 0.705018 R Square 0.49705 Adjusted R 0.413225 Standard E 0.056125 Regression Statistics Multiple R 0.993129 R Square 0.986305 Adjusted R 0.984022 Standard E 2.435282 Observatio Observatio 50 ANOVA 50 ANOVA df Regressio Residual SS MS F Significance F 7 0.13075 0.018679 5.929623 7.8E-005 42 0.132302 0.00315 Regressio Residual SS MS F Significance F 7 17938.42 2562.632 432.1034 5.3E-037 42 249.0852 5.9306 Total 49 0.263052 Total 49 18187.51 Intercept df Coefficients Standard Error t Stat P-value Lower 95%Upper 95% Lower 95.0% Upper 95.0% 0.948624 0.081717 11.60868 1.1E-014 0.783713 1.113535 0.783713 1.113535 Mid Age EES SR G Raise 0.0035 0.000553 -0.00185 -0.00042 0.064665 0.014655 0.000649 0.001446 0.001025 0.001828 0.01834 0.013909 Deg 0.001468 0.01611 5.390013 0.382293 -1.80085 -0.22881 3.525963 1.053639 3.0E-006 0.704172 0.078911 0.820124 0.001035 0.298072 t Critical tw 2.010635 0.00481 0.003471 0.000223 0.00327 0.101676 0.042724 0.002189 -0.00237 -0.00392 -0.00411 0.027654 -0.01341 0.00481 0.003471 0.000223 0.00327 0.101676 0.042724 0.0911 0.927847 -0.03104 0.033979 -0.03104 0.033979 t-Test: Two-Sample Assuming Equal Variances Variable 1 Variable 2 Mean 1.06684 1.04836 Variance 0.004302 0.006481 Observatio 25 25 Pooled Var 0.005391 Hypothesiz 0 df 48 t Stat 0.889835 P(T<=t) one0.188996 t Critical o 1.677224 P(T<=t) two0.377993 0.002189 -0.00237 -0.00392 -0.00411 0.027654 -0.01341 Intercept Coefficients Standard Error t Stat P-value Lower 95%Upper 95% Lower 95.0% Upper 95.0% -4.87145 3.545701 -1.3739 0.17676 -12.027 2.284059 -12.027 2.284059 Mid Age EES SR G Raise 1.228416 0.036828 -0.08216 -0.07785 2.914508 0.676329 0.028171 0.06274 0.044484 0.079309 0.795761 0.603509 43.60516 0.586996 -1.8469 -0.98159 3.662545 1.120662 1.3E-036 0.560349 0.071815 0.331925 0.000694 0.268799 1.171563 -0.08979 -0.17193 -0.2379 1.308599 -0.5416 1.285268 0.163442 0.007615 0.082203 4.520418 1.894259 1.171563 -0.08979 -0.17193 -0.2379 1.308599 -0.5416 1.285268 0.163442 0.007615 0.082203 4.520418 1.894259 Deg 0.034504 0.699007 0.049362 0.960865 -1.37615 1.445158 -1.37615 1.445158 %