# Hypotheses

Using the large database of survey responses (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

Using the large database of survey responses (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.

Let M = average overall job satisfaction = SUM(OVERALL) / N-1

where N = sample size = 288

Ho: M = 4.5

Ha: M≠4.5

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

The sample average overall job satisfaction is M = SUM(OVERALL) / N-1 = 4.33

(refer to EXCEL for calculation)

The standard deviation of overall job satisfaction is

SD = SUM(OVERALL - M)2 / N = 1.364

Then the standard error is

SE = SD / SQRT(N) = 1.364 / SQRT(288) = 0.08

Then compute t = (4.5 - M) / SD = (4.5 - 4.33) / 0.08 = 2.11

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

This is a two-tailed test, so the critical value for the significance level = 0.05 is 97.5% t value with degree of freedom = n-1 = 287

From a t-table, the critical value t* = 1.97

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

Since the computed t = 2.11, which is greater than the critical value t* = 1.97

We have to reject the null hypothesis at the 0.05 significance level.

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.

Let Mi = average overall job satisfaction = SUM(INTRINSIC) / N-1

Ho: Mi = 4.5

Ha: Mi ≠4.5

b. Using the data ...

#### Solution Summary

Using the large database of survey responses (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.