True or False: As the sample size increases, the standard error of the sampling distribution of ¯y increases. Explain your answer.

4.54.* A junior college admits students only if they score above 500 on a standardized achievement test. Applicants from Region A have a mean of 550 and a standard deviation of 120 on this test, and applicants fromRegionB have a mean of 600 and a standard deviation of 120. Both distributions are approximately normal, and both regions have the same size.

(a) Find the proportion not admitted for students from each region.

(b) Of the students who are not admitted, what proportion are from Region A?

(c) A state legislator proposes that the college lower the cutoff point for admission to 300, thinking that the proportion of the students who are not admitted who are from Region A would decrease. If this policy is implemented, determine the effect on the answer to (b), and comment.