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State Hypothesis And Calculate Chi-Square Test

Question

A psychologist is studying the effects of certain stressors on overall job satisfaction. One stressor is job insecurity, in particular, a person’s belief about the chances of losing his or her job. Using the General Social Survey (GSS) data, the psychologist develops the following table and side-by-side bar chart. The total number of observations n = 765.

Job Satisfaction

Likelihood of Job Loss

Dissatisfied

Mod. Sat.

Very Sat.

Grand Total

Not Likely

62

265

348

675

Fairly Likely

16

17

14

47

Very Likely

12

15

16

43

Grand Total

90

297

378

765

 

The researcher will use the chi-squared test of independence to examine the relationship. The computer output from the test of independence is given below.

Pearson's Chi-squared test data: .Table
X-squared * 39.0459, df = 4, p-value = 6.816e-08

> .TestSexpected # Expected Counts
                  Diss Diss.    Mod Sat.    Very Sat.

Not Likely     79.411765  262.05882   333.52941

Fairly Likely   5.529412    18.24706    23.22353

Very Likely     5.058824   16.69412    21.24706

a). Does there appear to be a relationship just from examining the chart? If so, state what the apparent relationship is. Note: Be specific.
b). State the hypotheses.
c). The expected counts are shown in the output above. Show how the expected count of 79.412 in the upper left of the “Expected Counts” table was calculated. Hint: you will need to use the first table above.
d). Calculate the first (and only the first) term involved in the computation of the chi squared test statistic, assuming the “first term” involves the expected count of 79.412.
e). State the conclusion of the test in the context of the problem, using either the pvalue or rejection region approach, at the 0.05 level.
f). Compute Cramer’s coefficient . Relate this value to your conclusion in (e) and your answer to (a).

Summary

The question belongs to Statistics and it discusses about stating hypothesis and calculating chi-square test for data about job satisfaction and employees who are likely to leave the organization.

Total Word Count 139

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