Question

You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If​convenient, use technology to construct the confidence intervals.

A random sample of 50 home theater systems has a mean price of ​$130.00. Assume the population standard deviation is $15.50.

Construct a​ 90% confidence interval for the population mean.

The​ 90% confidence interval is __,__

Answer 1

Solution :

At 90%

Z_/2 = 1.645

Margin of error = E = Z_/2* ( /n)

= 1.645 * (15.50 / 50)

= 3.61

At 90% confidence interval estimate of the population mean is,

- E < < + E

130 - 3.61 < < 130 + 3.61

126.39 < < 133.61

(126.39 133.61,)

At 95%

Z_/2 = 1.96

Margin of error = E = Z_/2* ( /n)

= 1.96 * (15.50 / 50)

= 4.30

At 95% confidence interval estimate of the population mean is,

- E < < + E

130 - 4.30 < < 130 + 4.30

125.70 < < 134.30

(125.70 , 134.30)