Question

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 unemployment rate among teenage males in your area significantly higher than that in the population? Can you demonstrate a need for the program at 95% confidence level? Explain the results of your rest of significance as you would to a funding agency.

Answer 1

Let P : Proportion of unemployment among teenage males = 0.18

n = number of teenage males selected in a sample = 323.

p : sample Proportion of unemployment among teenage males = 21.7.% = 0.217

We have to test the hypothesis that

Whether or not unemployment rate among teenage males in sample is higher than in the population.

i.e. Null Hypothesis- Ho : P = 0.18

against

Alternative Hypothesis- Ha : P > 0.18 ( Right-tailed test)

Alpha = level of significance = 0.05

We used one sample proportion test for testing population proportion.

The value of test statistic is

Under Ho : P = 0.18

The value of test statistic is

Critical value:

p-value :

Since the test is right-tailed and value of test statistic is 1.7290

p-value = P ( Z> 1.7290)

from normal probability table

p-value = P ( Z> 1.7290) = 0.0419

Decision :

Since p-value < level of significance alpha, we reject Ho at 5% level of significance.

Conclusion :

There is sufficient evidence to claim that unemployment rate among teenage males in sample is higher than in the population.

You need to demonstrate a need for the program at 95% confidence level.