Question: A simple random sample of size n is drawn. The sample mean,x, is found to be 35.1,and the sample standard deviation,s, is found to be

A simple random sample of size n is drawn. The sample mean,x, is found to be 35.1,and the sample standard deviation,s, is found to be 8.7.

(a) Construct a 90% conﬁdence interval for µ if the sample size, n, is 40.

(b) Construct a 90% conﬁdence interval for µ if the sample size,n, is 100. How does increasing the sample size affect the margin of error,E?

(c) Construct a 98% conﬁdence interval for µ if the sample size, n, is 40. Compare the results to those obtained in part (a). How does increasing the level of conﬁdence affect the margin of error,E?

(d) If the sample size is n = 18, what conditions must be satisﬁed to compute the conﬁdence interval?

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