# Deskbody versus socialbody - hypothesis testing

Using AIU's large database of survey responses (Database Attached) (keep in mind this database is your sample), you will begin testing hypotheses. Complete all of the following:

1. Test a hypothesis to see whether the average overall job satisfaction (in the population of all workers in the USA) is equal to 4.5 with a = .05.

a. State the null hypothesis, the alternative hypothesis, and the significance level.

b. Using the data in our database, calculate the test statistic.

c. What is the critical level for the significance level?

d. What is your conclusion? Do we accept or reject the null hypothesis?

You may use Excel for the calculations, but you need to answer all four parts of this question.

2. Propose a hypothesis test for the mean intrinsic job satisfaction, similar to the test from problem 1, and answer parts a, b, c, and d of problem 1 for this hypothesis test. You may use Excel for the calculations, but you need to answer the four questions.

3. We believe that half of the population would have an extrinsic job satisfaction of 5.0 or greater. Answer parts a, b, c, and d of problem 1 for this hypothesis test of a proportion. You may use Excel for the calculations, but you need to answer the four questions.

4. We believe that the variance of the overall job satisfaction is equal to 1.0 Answer parts a, b, c, and d of problem 1 for this hypothesis test of a variance. You may use Excel for the calculations, but you need to answer the four questions.

5. We will call a "deskbody" a person whose intrinsic job satisfaction level is higher than their extrinsic job satisfaction level (i.e. happy with their job more than their office). We will call a "socialbody" a person whose extrinsic job satisfaction level is higher than their intrinsic job satisfaction level (i.e. happy with the office more than their job). We believe that there are equal deskbodies and socialbodies in the work force.

a. State an appropriate null hypothesis and its alternative hypothesis.

b. In our database, what percent of the employees are deskbodies? Are socialbodies?

c. What did you do with the employees who had equal intrinsics and extrinsics?

d. What do you suggest as a good test statistic (i.e. a way to calculate part b of problem 1)?

6. Determine the required sample size if you need to estimate the number of workers in the United States who are highly satisfied with their job and you want the estimate to be within 2 percentage points with a 96% confidence interval.

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#### Solution Preview

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1. Test a hypothesis to see whether the average overall job satisfaction (in the population of all workers in the USA) is equal to 4.5 with a = .05.

a. State the null hypothesis, the alternative hypothesis, and the significance level.

Null: Ho: Average of overall job satisfaction is equal to 4.5

Alternative H1: Average off overall job satisfaction is not equal to 4.5

b. Using the data in our database, calculate the test statistic.

Calculate average for overall job satisfaction 4.3302

Calculate standard deviation for overall job satisfaction 1.3642

Standard Error of the mean standard deviation/(n)^0.5 0.0804

Since N>30 and we use z-test

the test statistic is z value where z=(xbar - muHo)/Standard error -2.1122

c. What is the critical level for the significance level?

Find the value of Z for 5% significance 1.96

d. What is your conclusion? Do we accept or reject the null hypothesis?

Since t statistic -2.1122 lies outside the acceptable region i.e. -1.96 to +1.96. We reject the null. Thus, the avergae overall job satisfaction is significantly different from 4.5

You may use Excel for the calculations, but you need to answer all four parts of this question.

2. Propose a hypothesis test for the mean intrinsic job satisfaction, similar to the test from problem 1, and answer parts a, b, c, and d of problem 1 for this hypothesis test. You may use Excel for the calculations, but you need to answer the four questions.

a. State the null hypothesis, the alternative hypothesis, and the significance level.

Null: Ho: Average of intrinsic job satisfaction is equal to 4.5

Alternative H1: Average off intrinsic job satisfaction is not equal to 4.5

b. Using the data in our database, ...

#### Solution Summary

This posting conducts a series of hypothesis test to understand the job satisfaction level of the employees. Different types of hypothesis tests are illustrated by using the database such as test for difference in mean, test for difference in proportion, test for variance, etc. An easy step-by-step method is presented from writing hypothesis statement to identifying the appropriate test, calculating the test statistics and making inferences. It could be a good learning experience for the students to understand the intricacies of hypothesis testing.