Week 4 Confidence Intervals and Chi Square (Chs 11 – 12) Let’s look at some other factors that might influence pay.
For question 3 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 One question we might have is if the distribution of graduate and undergraduate degrees independent of the grade the employee?
(Note: this is the same as asking if the degrees are distributed the same way.)
Based on the analysis of our sample data (shown below), what is your answer?
Ho: The population correlation between grade and degree is 0.
Ha: The population correlation between grade and degree is > 0
Perform analysis:
OBSERVED A B C D E F Total
COUNT – 0 (Deg) 7 5 3 2 5 3 25
COUNT – 1 (Deg) 8 2 2 3 7 3 25
Total 15 7 5 5 12 6 50
EXPECTED
7.5 3.5 2.5 2.5 6 3 25
7.5 3.5 2.5 2.5 6 3 25
15 7 5 5 12 6 50
By using either the Excel Chi Square functions or calculating the results directly as the text shows, do we reject or not reject the null hypothesis? What does your conclusion mean?
2 Using our sample data, we can 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)?
3 Based on our sample data, can we conclude that males and females are distributed across grades in a similar pattern within the population?
Ho: The population correlation between grade and degree is 0.
Ha: The population correlation between grade and degree is > 0
4 Using our sample data, construct a 95% confidence interval for the population’s mean service difference for each gender. Do they intersect or overlap? How do these results compare to the findings in week 2, question 2?
5 How do you interpret these results in light of our question about equal pay for equal work?
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