Score: <1 point> Week 2 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 Mean 52 Variance 316 Observations 25 Hypothesized Mean Di 0 df 24 t Stat 1.968903827 P(T<=t) one-tail 0.03030785 t Critical one-tail 1.71088208 P(T<=t) two-tail 0.060615701 t Critical two-tail 2.063898562 Ho 45 0 25 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? Interpretation: <1 point> 2 Female Mean 38 Variance 334.6667 Observations 25 Hypothesized Mean D 0 df 24 t Stat -1.91321 P(T<=t) one-tail 0.033862 t Critical one-tail 1.710882 P(T<=t) two-tail 0.067724 t Critical two-tail 2.063899 Ho 45 0 25 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? 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: Q3 Ho Female Male Female 45 45 45 45 45 45 45 45 45 45 45 34 41 23 22 23 42 24 24 69 36 34 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 45 45 45 45 45 45 45 45 45 45 45 57 23 50 24 75 24 24 23 22 35 24 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 45 77 1.087 1.149 45 45 55 65 1.052 1.157 1.145 1.140 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? Score: <1 point> Week 2 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 Mean 52 Variance 316 Observations 25 Hypothesized Mean D 0 df 24 t Stat 1.968903827 P(T<=t) one-tail 0.03030785 t Critical one-tail 1.71088208 P(T<=t) two-tail 0.060615701 t Critical two-tail 2.063898562 Ho 45 0 25 Conclusion: Do not reject Ho; mean equals 45 Is this a 1 or 2 tail test? 2 tail - why? Alternative is two tailed P-value is: 0.060615701 Is P-value > 0.05? Yes Why do we not reject Because p-value > 0.05 Ho? Interpretation: The mean is not significantly different than 45 <1 point> 2 Female Mean 38 Variance 334.6667 Observations 25 Hypothesized Mean D 0 df 24 t Stat -1.91321 P(T<=t) one-tail 0.033862 t Critical one-tail 1.710882 P(T<=t) two-tail 0.067724 t Critical two-tail 2.063899 Ho 45 0 25 Conclusion: Do not reject Ho; mean equals 45 Is this a 1 or 2 tail test? 2 tail - why? Alternative is two tailed P-value is: 0.067724 Is P-value > 0.05? Yes Why do we not reject Ho? p-value > 0.05 Because The mean is not significantly different than 45 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: Mean for male - mean for female = 0 Ha: Mean for male - mean for female =/= 0 Test to use: two sample t-test assuming equal variance Place B43 in Outcome range box. t-Test: Two-Sample Assuming Equal Variances Male Mean Variance Observations Pooled Variance Hypothesized Me df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail Female 52.256 37.196 346.5242333333 307.77456667 25 25 327.1494 0 48 2.9437906008 0.0024919964 1.6772241961 0.0049839928 2.0106347576 P-value is: 0.004983993 Is P-value < 0.05? Yes Reject or do not reject Ho: Reject If the null hypothesis was rejected, 0.832629718 what of effect size measure: Meaning is the effect size value: Large effect Interpretation: There is a significant difference between population mean salaries between genders b. Since the one and two sample t-test results provided different outcomes, which is the proper/correct apporach to comparing salary equality? Why? As we are comparing between two samples so its better to apply the two sample test than two one sample test. The two sample test accounts the joint variance and thus is better. <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: Mean for male - mean for female = 0 Q3 Ho Female Male Female 45 45 45 45 45 45 45 45 45 45 45 34 41 23 22 23 42 24 24 69 36 34 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 45 45 45 45 45 45 45 45 45 45 45 57 23 50 24 75 24 24 23 22 35 24 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 45 77 1.087 1.149 45 45 55 65 1.052 1.157 1.145 1.140 Ha: Mean for male - mean for female =/= 0 Statistical test to use: two sample t-test assuming equal variance Place B75 in Outcome range box. t-Test: Two-Sample Assuming Equal Variances Male Mean Variance Observations Pooled Variance Hypothesized Me df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail 1.0574 0.0084004167 25 0.0074744033 0 48 0.1733934143 0.4315356801 1.6772241961 0.8630713602 2.0106347576 Female 1.05316 0.00654839 25 What is the p-value: 0.86307136 Is P-value < 0.05? No Reject or do not reject Ho: Do not reject If the null hypothesis was rejected, what of effect size measure: Meaning is the effect size value: Interpretation: There is no significant difference between population mean compas between genders 4 Since performance is often a factor in pay levels, is the average Performance Rating the same for both genders? <1 point> Ho: Ha: Mean for male - mean for female = 0 Mean for male - mean for female =/= 0 Test to use: two sample t-test assuming equal variance Place B106 in Outcome range box. t-Test: Two-Sample Assuming Equal Variances Male Mean Variance Observations Pooled Variance Hypothesized Me df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail 87.6 75.25 25 130 0 48 1.054295244 0.1485129687 1.6772241961 0.2970259373 2.0106347576 Female 84.2 184.75 25 What is the p-value: 0.297026 Is P-value < 0.05? No Do we REJ or Not reject the null? o not reject D If the null hypothesis was rejected,of effect the effect size Meaning what is size measure: Interpretation: There is no significant difference between population mean Performance Ratings between genders <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? The compas should be used because it is the considering the salary grade mispoint and thus is a better measure than salary. As there is no significant difference between population average compas therefore no evidence of gender bias for pay till this point can be seen. Score: <1 point> Week 2 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 Mean 52 Variance 316 Observations 25 Hypothesized Mean D 0 df 24 t Stat 1.968903827 P(T<=t) one-tail 0.03030785 t Critical one-tail 1.71088208 P(T<=t) two-tail 0.060615701 t Critical two-tail 2.063898562 Ho 45 0 25 Conclusion: Do not reject Ho; mean equals 45 Is this a 1 or 2 tail test? 2 tail - why? Alternative is two tailed P-value is: 0.060615701 Is P-value > 0.05? Yes Why do we not reject Because p-value > 0.05 Ho? Interpretation: The mean is not significantly different than 45 <1 point> 2 Female Mean 38 Variance 334.6667 Observations 25 Hypothesized Mean D 0 df 24 t Stat -1.91321 P(T<=t) one-tail 0.033862 t Critical one-tail 1.710882 P(T<=t) two-tail 0.067724 t Critical two-tail 2.063899 Ho 45 0 25 Conclusion: Do not reject Ho; mean equals 45 Is this a 1 or 2 tail test? 2 tail - why? Alternative is two tailed P-value is: 0.067724 Is P-value > 0.05? Yes Why do we not reject Ho? p-value > 0.05 Because The mean is not significantly different than 45 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: Mean for male - mean for female = 0 Ha: Mean for male - mean for female =/= 0 Test to use: two sample t-test assuming equal variance Place B43 in Outcome range box. t-Test: Two-Sample Assuming Equal Variances Male Mean Variance Observations Pooled Variance Hypothesized Me df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail Female 52.256 37.196 346.5242333333 307.77456667 25 25 327.1494 0 48 2.9437906008 0.0024919964 1.6772241961 0.0049839928 2.0106347576 P-value is: 0.004983993 Is P-value < 0.05? Yes Reject or do not reject Ho: Reject If the null hypothesis was rejected, 0.832629718 what of effect size measure: Meaning is the effect size value: Large effect Interpretation: There is a significant difference between population mean salaries between genders b. Since the one and two sample t-test results provided different outcomes, which is the proper/correct apporach to comparing salary equality? Why? As we are comparing between two samples so its better to apply the two sample test than two one sample test. The two sample test accounts the joint variance and thus is better. <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: Mean for male - mean for female = 0 Q3 Ho Female Male Female 45 45 45 45 45 45 45 45 45 45 45 34 41 23 22 23 42 24 24 69 36 34 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 45 45 45 45 45 45 45 45 45 45 45 57 23 50 24 75 24 24 23 22 35 24 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 45 77 1.087 1.149 45 45 55 65 1.052 1.157 1.145 1.140 Ha: Mean for male - mean for female =/= 0 Statistical test to use: two sample t-test assuming equal variance Place B75 in Outcome range box. t-Test: Two-Sample Assuming Equal Variances Male Mean Variance Observations Pooled Variance Hypothesized Me df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail 1.0574 0.0084004167 25 0.0074744033 0 48 0.1733934143 0.4315356801 1.6772241961 0.8630713602 2.0106347576 Female 1.05316 0.00654839 25 What is the p-value: 0.86307136 Is P-value < 0.05? No Reject or do not reject Ho: Do not reject If the null hypothesis was rejected, what of effect size measure: Meaning is the effect size value: Interpretation: There is no significant difference between population mean compas between genders 4 Since performance is often a factor in pay levels, is the average Performance Rating the same for both genders? <1 point> Ho: Ha: Mean for male - mean for female = 0 Mean for male - mean for female =/= 0 Test to use: two sample t-test assuming equal variance Place B106 in Outcome range box. t-Test: Two-Sample Assuming Equal Variances Male Mean Variance Observations Pooled Variance Hypothesized Me df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail 87.6 75.25 25 130 0 48 1.054295244 0.1485129687 1.6772241961 0.2970259373 2.0106347576 Female 84.2 184.75 25 What is the p-value: 0.297026 Is P-value < 0.05? No Do we REJ or Not reject the null? o not reject D If the null hypothesis was rejected,of effect the effect size Meaning what is size measure: Interpretation: There is no significant difference between population mean Performance Ratings between genders <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? The compas should be used because it is the considering the salary grade mispoint and thus is a better measure than salary. As there is no significant difference between population average compas therefore no evidence of gender bias for pay till this point can be seen