Question

4. Nationally, the unemployment rate for teenage males is 18%. A random sample of 323 teenage males in your area reveals an unemployment rate of 21.7%. Are our local teens more likely to be unemployed?   (20%) This question is an example of statistical research using hypothesis testing. You will need to use the 5 step model of hypothesis testing to test for significance at a=.01.

• State assumptions

• State the null hypothesis and the alternative hypothesis
• State the appropriate hypothesis test for each question and determine your critical scores for testing significance at .01
• Calculate your test statistic making sure you show your formulas
• Interpret your results using complete sentences indicating is significance was determined

Answer 1

(1)

Question:

State assumptions

(i) The data are Simple Random Sample from the population of interest.

(ii) The population isat least 10times as large as the sample

(iii) np = 323 X 0.18 = 58.14 10

(iv) n (1- p) = 323 X (1 - 0.18) = 264.86 10

(2)

Question:

State the null hypothesis and the alternative hypothesis

Answer:
H0:Null Hypothesis: P 0.18 ( our local teens are not more likely to be unemployed )

HA: Alternative Hypothesis: P > 0.18 ( our local teens are more likely to be unemployed ) (Claim)

(3)

Question:

State the appropriate hypothesis test for each question and determine your critical scores for testing significance at .01

Z Test One Population Proportion

= 0.01

One Tail - Right Side Test

From Table, critical value of Z = 2.33

(4)

Question:

Calculate your test statistic making sure you show your formulas

= Sample Proportion = 0.217

p0 = Hypothesized population proportion = 0.18

Test Statistic is given by:

(5)

Sincecalculated value of Z = 1.718 is less than critical value of Z = 2.33, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data do not support the claim that our local teens are more likely to be unemployed.