A random sample of 88 observations produced a mean x 258 an

A random sample of 88 observations produced a mean x = 25.8 and a standard deviation s = 2.4. a Find a 95% confidence interval for Mu. b. Find a 90% confidence interval for Mu. c. Find a 99% confidence interval for Mu. a. The 95% confidence interval is (Use integers or decimals for any numbers in the expression. Round to two decimal places as needed b. The 90% confidence interval is (Use integers or decimals for any numbers in the expression. Round to two decimal places as needed C. The 99% confidence interval is (Use integers or decimals for any numbers in the expression. Round to two decimal places as needed

Solution

(a) Given a=0.05, Z(0.025) = 1.96 (from standard normal table)

So 95% confidence interval is

xbar+/-Z*s/vn

--> 25.8 +/- 1.96*2.4/sqrt(88)

--> (25.30, 26.30)

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(b) Given a=0.1, Z(0.05) = 1.645 (from standard normal table)

So 90% confidence interval is

xbar+/-Z*s/vn

--> 25.8 +/- 1.645*2.4/sqrt(88)

--> (25.38, 26.22)

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(c) Given a=0.01, Z(0.005) = 2.58 (from standard normal table)

So 99% confidence interval is

xbar+/-Z*s/vn

--> 25.8 +/- 2.58*2.4/sqrt(88)

--> (25.14, 26.46)