Posted by **rose** on Wednesday, December 5, 2012 at 2:51am.

8. Suppose that the IQ score for a person selected from a certain group of people

is approximately N(; 100). Let X1;X2; : : : ;Xn be a random sample of such IQ

scores.

(a) How large should n be so that a 90% con dence interval for with maximum

error " = 1 is [ x 1:645(10)=

p

n ; x + 1:645(10)=

p

n ]?

(b) Verify your answer empirically. In particular, simulate 50 random samples

of size n from the normal distribution N(110; 100). Do approximately 90%

of these samples yield a con dence interval that contains = 110?

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