Question

B. Critical Values

C. P value and interpret the result

Answer within 15 minutes

Economists theorize that the recent recession has affected men more than women because mon are typically employed in industries that have been hit hardest by the recession Women, on the other hand, are typically employed in services which are considered more recession resistant. A sample of 170 men and a sample of 145 women were drawn. In those samples, 21 men were unemployed, and 11 of the women were unemployed. Complete parts a and b below. a. Perform a hypothesis test using a = 0.05 to determine if the unemployment rate for men is higher than the rate for women. Let population 1 be men and population 2 be women. What are the correct null and alternative hypotheses? A Ho: P - P20 3. Ho: PP, 50 H: P.-P-0 H: P1-P2 > 0 O c. Ho: P1 - P2 <0 OD. Ho: P1 P2 - 0 H₂ : P1 P2 20 He: P.-P20 What is the best statistic? 2.-(Round to two decimal places as needed.)

Answer 1

For sample 1, we have that the sample size is Ni = 170, the number of favorable cases is X1 = 21, so then the sample proportion is p1 = * = *1 = 0.1235 For sample 2, we have that the sample size is N2 = 145, the number of favorable cases is X2 = 11, so then the sample proportion is p2 = * = * = 0.0759 The value of the pooled proportion is computed as p = Ni+X 0.1016 Also, the given significance level is a = 0.05. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: 21+11 170+145 Ho: Pi = P2 Ha: Pı > P2 This corresponds to a right-tailed test, for which a z-test for two population proportions needs to be conducted (2) Rejection Region Based on the information provided, the significance level is a = 0.05, and the critical value for a right-tailed test is ze = 1.64. The rejection region for this right-tailed test is R = {2:2>1.64}

(3) Test Statistics The Z-statistic is computed as follows: 1 - 2 0.1235 - 0.0759 1.396 (1-5)(1/nı +1/n2) 0.1016. (1 – 0.1016)(1/170 +1/145) (4) Decision about the null hypothesis Since it is observed that z = 1.396<%= 1.64, it is then concluded that the null hypothesis is not rejected. Using the P-value approach: The p-value is p = 0.0814, and since p=0.0814 > 0.05, it is concluded that the null hypothesis is not rejected. (5) Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population proportion p1 is greater than p2, at the 0.05 significance level.