Confidence Intervals and Chi Square discussion

Business & Finance
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Question description


Week 4 Confidence Intervals and Chi Square  (Chs 11 - 12)   Let's look at some other factors that might influence pay. <Note: use right click on row numbers to insert rows to perform analysis below any question>
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 populaton 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 - M or 0 7 5 3 2 5 3 25            
COUNT - F or 1 8 2 2 3 7 3 25            
total 15 7 5 5 12 6 50            
7.5 3.5 2.5 2.5 6 3 25 <Highlighting each cell with show how the value          
7.5 3.5 2.5 2.5 6 3 25 is found: row total times column total divided by          
15 7 5 5 12 6 50 grand total.>          
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)?            
Males Mean St error Low to High            
52 3.65878 44.4483 59.5517 Results are mean +/-2.064*standard error        
Females 38 3.62275 30.5226 45.4774 2.064 is t value for 95% interval          
<Reminder: standard error is the sample standard deviation divided by the square root of the sample size.>            
3 Based on our sample data, can we conclude that males and females are distributed across grades in a similar pattern within the population?            
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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