In a survey of 180 females who recently completed high school. 75% were enrolled

Question

In a survey of 180 females who recently completed high school. 75% were enrolled in college. In a survey of 175 males who recently completed high school. 64% were enrolled in college. At alpha = 0.07. can you reject the claim that there is no difference in the proportion of college enrollees between the two groups? Assume the random samples are independent. Complete parts (a) through (e). D. H_a: p_1 greaterthanorequal p_2 H_0: p_1 lessthanorequalto H_a: p_1 > p_2 E.H_a: p_1=p_2 H_0: p_1=p_2 H_a=p_1 notequalto p_2 F. H_a: p_1 p_2 H_1: p_1 lessthanorequalto p_2 (b) Find the critical value(s) and identify the rejection region(s). The critical value(s) is(are) ___. (Use a comma to separate answers as needed. Type an integer or a decimal. Round to two decimal places as needed.) Identify the rejection region(s). Select the correct choice below and fill in the answer box(es) within your choice. (Round to two decimal places as needed.) A. x > ___ B. ___

Explanation / Answer

a) Option E. H0: p1 = p2
Ha: p1 p2

b) For 0.07 significance level,
z < -1.81 and z > 1.81

c) For two sample proportion test,
Pooled sample proportion.p = (p1 * n1 + p2 * n2) / (n1 + n2) = (0.75*180 + 0.64*175)/(180+175) = 0.695775
Standard error.SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] } = sqrt{0.696*(1-0.696)*[(1/180)+(1/175)]} = 0.048842
test statistic, z = (p1-p2)/SE = (0.75 - 0.64)/0.048842 = 2.25

d) Since 2.25 > 1.81(critical value),
Reject H0 because the test statistic is in the rejection region

e) D. At the 7% significance level, there is sufficient evidence to reject the claim

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