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# Null hypothesis - Testing

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A stock analyst wants to determine whether there is a difference in the mean rate of return for
three types of stock: utility, retail, and banking stocks. The following sample information is
collected.

Rates of Return
Utility Retail Banking
14.3 11.5 15.5
18.1 12 12.7
17.8 11.1 18.2
17.3 11.9 14.7
19.5 11.6 18.1
13.2

a. Using the .05 level of significance, is there a difference in the mean rate of return among the
three types of stock?

b. Suppose the null hypothesis is rejected. Can the analyst conclude there is a difference
between the mean rates of return for the utility and the retail stocks? Explain.

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## Hypothesis testing for overall job satisfaction

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?
Provide answer to 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. Provide answer to 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. Provide answer to 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. Provide answer to 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?

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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