5. Under federal law some people under the age of 25 are eligible for grants for

Question

5. Under federal law some people under the age of 25 are eligible for grants for attending college. Writers of the law expected that 65% of those eligible would enroll in the program. Officials worry that the actual percentage enrolled is below this figure. They intend to select a pilot survey of 250 eligible persons in order to investigate this issue.

(a) State the appropriate hypotheses. Define p (in words) in this case.

(b) Of the 250 eligible persons sampled, a total of 158 had enrolled in the program. Compute the sample proportion and hence the p-value.

(c) Provide a conclusion (in context please).

Explanation / Answer

Ho : p = 0.65

H1 : p is differnt from 0.65

b)

p = 158/250 0.632

Z = 0.632 - 0.65 / srqt ( [0.65*0.35] / 250 )

Z = -0.60

p value : 0.2743

since p value is greater than alpha (0.05) we fail to reject Ho

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