Homework: Chapter 10 Homework Score: 3.33 of 4 pts 5 of 5 (5 complete) HW Score:
ID: 3375011 • Letter: H
Question
Homework: Chapter 10 Homework Score: 3.33 of 4 pts 5 of 5 (5 complete) HW Score: 93.89%, 18.7 10.4.37-T Question Economists theorize that the recent recession has affected men more than women because men are typically employed in industries that have been hit hard recession. Women, on the other hand, are typically employed in services which are considered more recession resistant. A sample of 165 men and a sampl women were drawn. In those samples, 18 men were unemployed, and 9 of the women were unemployed. Complete parts a and b below a Perform a hypothesis test using ? 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? B. Ho:P1-P2#0 H1 P1 P2 20 O c. Ho Pi-P2 50 H1 : p1-p2 #0 select your answer and then click Check Answer 5 Clear AllExplanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P1> P2
Alternative hypothesis: P1 < P2
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a two-proportion z-test.
Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).
p = (p1 * n1 + p2 * n2) / (n1 + n2)
p = 0.07941
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = 0.02938
z = (p1 - p2) / SE
z = 1.49
zcritical = 1.645
Rejection region is z > 1.645.
where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.
Interpret results. Since the z-value (1.49) is less than the critical value, we cannot reject the null hypothesis.
Since we have a one-tailed test, the P-value is the probability that the z-score is greater than 1.49.
Thus, the P-value = 0.068.
Interpret results. Since the P-value (0.068) is greater than the significance level (0.05), we cannot reject the null hypothesis.
Do not reject H0, There is not enough evidence to conclude that the unemployement rate is higher for men than women.
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