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Sparr Investments, Inc., specializes in tax-deferred investment opportunities for its clients. Recently Sparr offered a payroll deduction investment program for the employees of a particular company. Sparr estimates that the employees are currently averaging $100 or less per month in tax-deferred investments. A sample of 40 employees will be used to test Sparr’s hypothesis about the current level of investment activity among the population of employees. Assume the employee monthly tax-deferred investment amounts have a standard deviation of $75 and that a .05 level of significance will be used in the hypothesis test. a. What is the Type II error in this situation? b. What is the probability of the Type II error if the actual mean employee monthly investment is $120? c. What is the probability of the Type II error if the actual mean employee monthly investment is $130? d. Assume a sample size of 80 employees is used and repeat parts (b) and (c).

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

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Section
BuyFindarrow_forward

STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 9.6, Problem 53E
Textbook Problem
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Sparr Investments, Inc., specializes in tax-deferred investment opportunities for its clients. Recently Sparr offered a payroll deduction investment program for the employees of a particular company. Sparr estimates that the employees are currently averaging $100 or less per month in tax-deferred investments. A sample of 40 employees will be used to test Sparr’s hypothesis about the current level of investment activity among the population of employees. Assume the employee monthly tax-deferred investment amounts have a standard deviation of $75 and that a .05 level of significance will be used in the hypothesis test.

  1. a. What is the Type II error in this situation?
  2. b. What is the probability of the Type II error if the actual mean employee monthly investment is $120?
  3. c. What is the probability of the Type II error if the actual mean employee monthly investment is $130?
  4. d. Assume a sample size of 80 employees is used and repeat parts (b) and (c).

a.

To determine

Write the Type II error in the given situation.

Explanation of Solution

The hypotheses are given below:

Null hypothesis:

H0:μ100

Alternative hypothesis:

Ha:μ

b.

To determine

Find the probability of making a Type II error if μ=$120.

c.

To determine

Find the probability of making a Type II error if μ=$130.

d.

To determine

Find the probability of making a Type II error if μ=$120 and μ=$130.

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Chapter 9 Solutions

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