In a survey of 240 males ages 18 to 24, 40% were enrolled in college. In a surve

Question

In a survey of 240 males ages 18 to 24, 40% were enrolled in college. In a survey of 230 females ages 18 to 24, 49% were enrolled in college. These sample are random and independent. At = 0.05, 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? (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). Choose the correct answer below Click to select your answer(s). here to search

Explanation / Answer

The statistical software output for this problem is:

Two sample proportion summary hypothesis test:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions
H0 : p1 - p2 = 0
HA : p1 - p2 < 0

Hypothesis test results:

Hence,

b) Critical value = -1.65

Rejection region: z < -1.65

c) Test statistic = -1.96

d) Since test statistic < Critical value, reject Ho

Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. Z-Stat P-value p1 - p2 96 240 112.7 230 -0.09 0.045847162 -1.9630441 0.0248

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