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 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. Make sure to use the five-step model.

I am wondering if my answers to this are correct?

Step 1: Make assumptions and meet test requirements.

Random sampling.

Level of measurement is nominal.

Sampling distribution is normal in shape.

Step 2: State the null hypothesis.

You should use a two-tailed test for this situation because we are testing if there is a difference in the unemployment rate in the population and a program. This is the reason why you should not use a one-tailed test, because we are not exactly looking to see if there is a difference between the population and program in one direction. The unemployment rate could go either direction.

H₀: P_u = 0.18

H₁: P_u ≠ 0.18

Step 3: Select the sampling distribution and establish the critical region.

α = 0.05

Z(critical) = ±1.96

Step 4: Compute the test statistic.

Z(obtained) = 1.73

Step 5: Make a decision and interpret the results of the test.

We fail to reject the null hypothesis because Z(obtained) = 1.63 and does not fall in the critical region (±1.96). We fail to reject the null hypothesis because we cannot find sufficient evidence against it. Therefore, the difference is not significant. We cannot demonstrate a need for the program because the difference is not significant.

To a funding agency: The program does not show a significant difference compared to the population, as we found there is not enough evidence to reject the null hypothesis. Z(obtained) was 1.73, while the critical region was ±1.96, which Z(obtained) falls outside of.

Answer 1

Sample size is N = 323

Sample proportion, = 0.217

Step 1: Assumptions:

Sample is random.

Level of measurement is nominal.

Sampling distribution is normal in shape.

Step 2 :Null and Alternative Hypotheses

Step 3: Critical value

At = 0.05, the critical value for a two-tailed test, = 1.96

Step 4: Test Statistics

Step 5: Decision about the null hypothesis

Since it is observed that z = 1.718 < = 1.96, it is then concluded that the null hypothesis is not rejected.

Therefore, there is not enough evidence to claim that the national unemployment rate is different area unemployment rate, at the = 0.05 significance level.