S W You are the head of an agency seeking funding for a program to reduce unemployment among teenage males. Nationally, the unemployment rate for this group is 18%. A random sample of 323 teenage males in your area reveals an unemployment rate of 21.7%. Is the difference significant? Can you demonstrate a need for the program? Should you use a one-tailed test in this situation? Why? Explain the result of your test of significance as you would to a funding agency.

Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

Solutions

Chapter
Section
Chapter 7, Problem 7.16P
Textbook Problem
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S W You are the head of an agency seeking funding for a program to reduce unemployment among teenage males. Nationally, the unemployment rate for this group is 18%. A random sample of 323 teenage males in your area reveals an unemployment rate of 21.7%. Is the difference significant? Can you demonstrate a need for the program? Should you use a one-tailed test in this situation? Why? Explain the result of your test of significance as you would to a funding agency.

Expert Solution
To determine

To find:

The significant difference between the given statements.

Explanation of Solution

Given:

The given information is,

You are the head of an agency seeking funding for a program to reduce unemployment among teenage males. Nationally, the unemployment rate for this group is 18%. A random sample of 323 teenage males in your area reveals an unemployment rate of 21.7%.

The five step model for hypothesis testing is:

Step 1. Making assumptions and meeting test requirements.

Step 2. Stating the null hypothesis.

Step 3. Selecting the sampling distribution and establishing the critical region.

Step 4. Computing test statistics.

Step 5. Making a decision and interpreting the results of the test.

Formula used:

For large samples with single sample proportions, the Z value is given by,

Z(obtained)=PsPuPu(1Pu)/N

Where, Ps is the sample proportion,

Pu is the population proportion and,

N is the sample size.

Calculation:

From the given information, the sample size is 323, sample proportion is 21.7% and the population proportion is 18%.

As the presence of significant difference is to be tested, a two-tailed test is applied.s

Follow the steps for two-tailed hypothesis testing as,

Step 1. Making assumptions and meeting test requirements.

Model:

Random sampling.

Level of measurement is interval ratio.

Sampling distribution is Normal.

Step 2. Stating the null hypothesis.

The statement of the null hypothesis is that the proportion of unemployed males from the sample are not significantly different from the proportion of unemployed males from the populations.

Thus, the null and the alternative hypotheses are,

H0:Pu=0.18

H1:Pu0.18

Step 3. Selecting the sampling distribution and establishing the critical region.

Since, the sample is large, Z distribution can be used.

The information given is in the form of proportions, the test for proportion can be used.

Thus, the sampling distribution is Z distribution.

The level of significance is α=0.05.

And area of critical region is Z(critical)=±1

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