# Confidence Intervals and Chi Square discussion

**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 | ||||||

EXPECTED | |||||||||||||

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? | |||||||||||||

Interpretation: | |||||||||||||

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.> | |||||||||||||

Interpretation: | |||||||||||||

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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