in a survey of 230 males ages 18 to 24, 36% were enrolled in college. In a surve
ID: 3321603 • Letter: I
Question
in a survey of 230 males ages 18 to 24, 36% were enrolled in college. In a survey of 220 females ages 18 to 24, 41% were enrolled in college. These sample are random and independent. At -o 09, can you support the claim that the proportion of males ages 18 to 24 who enrolled in college is less than the proportion of females ages 18 to 24 who enrolled in college? 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). Choose the correct answer below. 0 (c) Find the standardized test statistic. :- (Round to two decimal places as needed ) Click to select your answer(s). eExplanation / Answer
H0 : pmean = pgirls
Ha : pmen < pwomen
Here for alpha = 0.09 and one tailed test
Z(critical) = -1.34 (for one tailed test
Rejection region
Z < Z(critical ) option C is coorrect
(c) Pooled estimate p = (230 * 0.36 + 220 * 0.41)/ (230 + 220) = 0.3844
Standard error of proportion = se0 = sqrt [p * (1-p) * (1/n1 + 1/n2) ] = sqrt [0.3844 * 0.6156 * (1/230 + 1/220)]
= 0.04587
Here test statistic
Z = (pmen - pwomen)/se0 = (0.36 - 0.41)/ 0.04587 = -1.09
SO here Z > Z(critical)
so failed to reject the null and claim that there is no difference in enrolled of men in college with respect to woemn.
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