for MathematicsEx
Attahed is week 2 assignment for Statistic for Managers. I enclosed data sheet and questions sheet.
And the following is the answers I already submitted which he gave me a zero:
Week 2 Testing means Q3 Salary Compa Performance Rating
In questions 2 and 3, be sure to include the null and alternate hypotheses you will be testing. Ho Female Male Female Female Male Female Male Female Male
In the first 3 questions use alpha = 0.05 in making your decisions on rejecting or not rejecting the null hypothesis. 45 34 1.017 1.096 23 24 1.000 1.043 90 85
45 41 0.870 1.025 22 24 0.956 1.043 80 70
1 Below are 2 one-sample t-tests comparing male and female average salaries to the overall sample mean. 45 23 1.157 1.000 23 25 1.000 1.086 100 90
(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) 45 22 0.979 0.956 24 27 1.043 0.870 90 80
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? 45 23 1.134 1.000 24 28 1.043 0.903 80 95
Males Females 45 42 1.149 1.050 23 28 1.000 0.903 65 80
Ho: Mean salary = 45 Ho: Mean salary = 45 45 24 1.052 1.043 24 47 1.043 1.175 95 90
Ha: Mean salary =/= 45 Ha: Mean salary =/= 45 45 24 1.175 1.043 24 40 1.043 1.000 60 80
45 69 1.043 1.210 24 43 1.043 1.075 90 80
Note: While the results both below are actually from Excel's t-Test: Two-Sample Assuming Unequal Variances, 45 36 1.134 1.161 23 47 1.000 0.979 75 90
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. 45 34 1.043 1.096 22 49 0.956 1.020 95 90
Male Ho Female Ho 45 57 1.000 1.187 24 58 1.043 1.017 100 85
Mean 52 45 Mean 38 45 45 23 1.074 1.000 34 66 1.096 1.157 75 100
Variance 316 0 Variance 334.6666667 0 45 50 1.020 1.041 36 60 1.161 1.052 80 95
Observations 25 25 Observations 25 25 45 24 0.903 1.043 34 64 1.096 1.122 70 90
Hypothesized Mean Difference 0 Hypothesized Mean Difference 0 45 75 1.122 1.119 35 56 1.129 0.982 90 95
df 24 df 24 45 24 0.903 1.043 41 60 1.025 1.052 100 90
t Stat 1.968903827 t Stat -1.913206357 45 24 0.982 1.043 42 65 1.050 1.140 100 75
P(T<=t) one-tail 0.03030785 P(T<=t) one-tail 0.033862118 45 23 1.086 1.000 57 62 1.187 1.087 65 95
t Critical one-tail 1.71088208 t Critical one-tail 1.71088208 45 22 1.075 0.956 50 60 1.041 1.052 75 95
P(T<=t) two-tail 0.060615701 P(T<=t) two-tail 0.067724237 45 35 1.052 1.129 55 66 1.145 1.157 95 80
t Critical two-tail 2.063898562 t Critical two-tail 2.063898562 45 24 1.140 1.043 69 76 1.210 1.134 55 70
Conclusion: Do not reject Ho; mean equals 45 Conclusion: Do not reject Ho; mean equals 45 45 77 1.087 1.149 65 77 1.140 1.149 90 100
Is this a 1 or 2 tail test? 2 tail test Is this a 1 or 2 tail test? 2 tail test 75 76 1.119 1.134 95 95
- why? Ha: µ ≠ 45 - why? Ha: µ ≠ 45 77 72 1.149 1.074 95 95
P-value is: 0.060615701 P-value is: 0.067724237 45 55 1.052 1.145
Is P-value > 0.05? Yes Is P-value > 0.05? Yes 45 65 1.157 1.140
Why do we not reject Ho? P-value > 0.05 Why do we not reject Ho? P-value > 0.05
As the P-value is greater than the significance level, α = 0.05, we do not reject the Ho. The P-value gives the probability of rejecting a true null hypothesis.
Interpretation: There is no evidence to suggest, at 95% level of confidence, that the mean salary of the male employees is significantly different from the mean salary of the population, which is 45 thousands.
There is no evidence to suggest, at 95% level of confidence, that the mean salary of the female employees is significantly different from the mean salary of the population, which is 45 thousands.
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: Mean salary of male employees = Mean salary of female employees
Ha: Mean salary of male employees ≠ Mean salary of female employees
Statistical test to use: Two-Sample t-Test Assuming Equal Variances
t-Test: Two-Sample Assuming Equal Variances
Male Female
Mean 52 38
Variance 316 334.6666667
Observations 25 25
Pooled Variance 325.3333333
Hypothesized Mean Difference 0
df 48
t Stat 2.744218961
P(T<=t) one-tail 0.004253009
t Critical one-tail 1.677224197
P(T<=t) two-tail 0.008506018
t Critical two-tail 2.010634722
P-value is: 0.008506018
Is P-value < 0.05? Yes
Reject or do not reject Ho: Reject Ho
If the null hypothesis was rejected, what is the effect size value: 0.776182335
Meaning of effect size measure: The effect size is large. The large effect size indicates that there is considerable difference between the mean salaries of male and female employees.
Interpretation: There is sufficient evidence to suggest, at 0.05 significance level, that the mean salary of the male employees is significantly different from the mean salary of the female employees.
b. Since the one and two tail t-test results provided different outcomes, which is the proper/correct apporach to comparing salary equality? Why?
The two sample t-test is the proper/correct approach to comparing salary equality among male and female employees.
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 compa of male employees = Mean compa of female employees
Ha: Mean compa of male employees ≠ Mean compa of female employees
Statistical test to use: Two-Sample t-Test Assuming Equal Variances
t-Test: Two-Sample Assuming Equal Variances
Male Female
Mean 1.05624 1.06872
Variance 0.007020607 0.004948377
Observations 25 25
Pooled Variance 0.005984492
Hypothesized Mean Difference 0
df 48
t Stat -0.57036906
P(T<=t) one-tail 0.285543918
t Critical one-tail 1.677224197
P(T<=t) two-tail 0.571087836
t Critical two-tail 2.010634722
What is the p-value: 0.571087836
Is P-value < 0.05? No
Reject or do not reject Ho: Do Not Reject Ho
If the null hypothesis was rejected, what is the effect size value: Not Applicable
Meaning of effect size measure: Not Applicable
Interpretation: There is no evidence to suggest, at 0.05 significance level, that the mean compa of the male employees is significantly different from the mean compa of the female employees.
4 Since performance is often a factor in pay levels, is the average Performance Rating the same for both genders?
Ho: Mean performance rating of male employees = Mean performance rating of female employees
Ha: Mean performance rating of male employees ≠ Mean performance rating of female employees
Statistical test to use: Two-Sample t-Test Assuming Equal Variances
t-Test: Two-Sample Assuming Equal Variances
Male Female
Mean 87.6 84.2
Variance 75.25 184.75
Observations 25 25
Pooled Variance 130
Hypothesized Mean Difference 0
df 48
t Stat 1.054295244
P(T<=t) one-tail 0.148512969
t Critical one-tail 1.677224197
P(T<=t) two-tail 0.297025937
t Critical two-tail 2.010634722
What is the p-value: 0.297025937
Is P-value < 0.05? No
Do we REJ or Not reject the null? Do Not Reject Ho
If the null hypothesis was rejected, what is the effect size value: Not Applicable
Meaning of effect size measure: Not Applicable
Interpretation: There is no evidence to suggest, at 0.05 significance level, that the mean performance rating of the male employees is significantly different from the mean performance rating of the female employees.
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 salary mean test output implies that there is a statistically significant difference between the male and female mean salaries. The compa mean test output implies that there is no significant difference between the male and female mean compas. Compa is the more appropriate variable as it is a measure of salary which removes the impact of grade and thus reduces chances of bias due to grade.
The overall conclusion is that, males and females paid the same for equal work.
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