Question

Imagine you are the manager of a non-profit business, and you are looking to hire a recent college graduate. You list the position as paying $20,000/year. After interviewing candidates you decide that some will be offered the expected salary, while some will be offered more because of experience and interviewing skills. Others will be offered less than expected until they can demonstrate competence and their salary will increase when they are fully qualified.

Using Microsoft^® Excel^®, run a chi square Goodness of Fit test to determine whether these observed starting salaries are significantly different. What do the findings tell you?

Write a 75- to 100-word summary to describe your results.

Paste your Microsoft^® Excel^® output below your summary.

	Expected Salaries	Observed Salaries
Applicant 1	$20,000	$17,500
Applicant 2	$20,000	$20,000
Applicant 3	$20,000	$22,000
Applicant 4	$20,000	$20,500
Applicant 5	$20,000	$20,000

Answer 1

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

H0​:p1​=0.2,p2​=0.2,p3​=0.2,p4​=0.2,p5​=0.2

Ha​: Some of the population proportions differ from the values stated in the null hypothesis

This corresponds to a Chi-Square test for Goodness of Fit.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, the number of degrees of freedom is df=5−1=4, so then the rejection region for this test is R={χ2:χ2>9.488}.

(3) Test Statistics

The Chi-Squared statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that χ2=525>χc2​=9.488, it is then concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that some of the population proportions differ from those stated in the null hypothesis, at the α=0.05 significance level.

Here is the excel input:

The output is:

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