You are the head of an agency seeking funding for a program to reduce unemployme

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.

Example of response I want.

Part 2. One sample test of proportions

Pu=.19

Ps=.217

N=323

CI=95%

Step 1. Making Assumptions

Our sample is random (collected using EPSEM techniques).

Our variable is nominal (unemployed or not, so this is a test of proportions).

The sampling distribution is normal (our sample is large enough (>120 for the purposes of hypothesis testing)).

Step 2. Stating the Hypotheses

Research Hypothesis: Unemployment rate among teenage males in your area is significantly higher than that in the population.

Null Hypothesis: Unemployment rate among teenage males in your area is the same as that in the population.

Step 3. Drawing the Sampling Distribution and establishing a critical region.

One tailed test for 95% confidence level.

Zcritical=+1.65

Step 4. Computing the Z obtained. (Note: a different answer may be obtained due to different rounding practices)

Step 5. Placing Z obtained on the distribution and stating the conclusion.

Conclusion: Z obtained is not in the critical region (it is not higher than the Z critical). We fail to reject the null hypothesis with 95% confidence. It appears that unemployment rate among teenage males in your area is the same as that in the population.

I ALSO WANT A GRAPH

Zcritical=+1.65

Explanation / Answer

1)

The sampling distribution is normal (our sample is large enough (>120 for the purposes of hypothesis testing))

2) H0 : P = .217

Ha : P > .217

3) Critical region for 95% confidence interval = 1.64

4)

= sqrt[ P * ( 1 - P ) / n ]

= sqrt [(0.217 * 0.783) / 323]

= 0.02
z = (p - P) / = (.18 - .217)/0.02 = -1.85

5)

we reject the null hypothesis with 95% confidence.

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