Question: A simple random sample of size n is drawn from a population. The sample mean, x, is 54.8 and the sample standard deviation is10.5. (a)

A simple random sample of size n is drawn from a population. The sample mean, x̄, is 54.8 and the sample standard deviation is10.5.

(a) Construct the 90% conﬁdence interval for the population mean if the sample size, n, is 30.

(b) Construct the 90% conﬁdence interval for the population mean if the sample size, n,is 51.How does increasing the sample size affect the width of the interval?

(c) Construct the 99% conﬁdence interval for the population mean if the sample size, n, is 30. Compare the results to tho se obtained in part (a). How does increasing the level of conﬁdence affect the conﬁdence interval?

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