As with the compa-ratio lecture example, we want to examine salary variation within the groups
Week 2: Identifying Significant Differences - part 1
To Ensure full credit for each question, you need to show how you got your results. This involves either showing where the data you used is located or showing the excel formula in each cell. Be sure to copy the appropriate data columns from the data tab to the right for your use this week.
As with our examination of compa-ratio in the lecture, the first question we have about salary between the genders involves equality - are they the same or different?
What we do, depends upon our findings.
1As with the compa-ratio lecture example, we want to examine salary variation within the groups - are they equal?Use Cell K10 for the Excel test outcome location.
aWhat is the data input ranged used for this question:
b Which is needed for this question: a one- or two-tail hypothesis statement and test ?
Answer:
Why:
c. Step 1:Ho:
Ha:
Step 2:Significance (Alpha):
Step 3:Test Statistic and test:
Why this test?
Step 4:Decision rule:
Step 5:Conduct the test - place test function in cell k10
Step 6:Conclusion and Interpretation
What is the p-value:
What is your decision: REJ or NOT reject the null?
Why?
What is your conclusion about the variance in the population for male and female salaries?
2Once we know about variance quality, we can move on to means: Are male and female average salaries equal?Use Cell K35 for the Excel test outcome location.
(Regardless of the outcome of the above F-test, assume equal variances for this test.)
aWhat is the data input ranged used for this question:
b Does this question need a one or two-tail hypothesis statement and test?
Why:
c. Step 1:Ho:
Ha:
Step 2:Significance (Alpha):
Step 3:Test Statistic and test:
Why this test?
Step 4:Decision rule:
Step 5:Conduct the test - place test function in cell K35
Step 6:Conclusion and Interpretation
What is the p-value:
What is your decision: REJ or NOT reject the null?
Why?
What is your conclusion about the means in the population for male and female salaries?
3Education is often a factor in pay differences.
Do employees with an advanced degree (degree = 1) have higher average salaries? Use Cell K60 for the Excel test outcome location.
Note: assume equal variance for the salaries in each degree for this question.
aWhat is the data input ranged used for this question:
b Does this question need a one or two-tail hypothesis statement and test?
Why:
c. Step 1:Ho:
Ha:
Step 2:Significance (Alpha):
Step 3:Test Statistic and test:
Why this test?
Step 4:Decision rule:
Step 5:Conduct the test - place test function in cell K60
Step 6:Conclusion and Interpretation
What is the p-value:
Is the t value in the t-distribution tail indicated by the arrow in the Ha claim?
What is your decision: REJ or NOT reject the null?
Why?
What is your conclusion about the impact of education on average salaries?
4Considering both the compa-ratio information from the lectures and your salary information, what conclusions can you reach about equal pay for equal work?
Why - what statistical results support this conclusion?
Hint
Statistics2)a. Sheet1!A1:B26B. two tailed test, the direction of hypothesis is not mentionedc.Step 1: Ho: there is no significant difference in the mean salary of male and female. u1 = u2Ha: there is a significant difference in the mean salary of male and female. u1 =/= u2Step 2: Significance (Alpha): 0.05Step 3: t test for 2 samples assuming equal variances2
samples (Males and females) are inde...
B. two tailed test, the direction of hypothesis is not mentioned
c.
Step 1:Ho: there is no significant difference in the mean salary of male and female. u1 = u2
Ha: there is a significant difference in the mean salary of male and female. u1 =/= u2
Step 2:Significance (Alpha): 0.05
Step 3:t test for 2 samples assuming equal variances
2
samples (Males and females) are independent of each other and I want to
test mean difference between them. Also equal variances between them is
assumed.
Step 4:Decision rule:Reject the null hypothesis if p<5%. Else if p>5%, fail to reject hO.
Step 6:
P-value: 0.009
Reject HO
Since p<5%
there is a significant difference in the POPULATION mean salary of male and female. u1 =/= u2.