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You are given the sample mean and the population standard deviation. Use this information to construct...

Question

You are given the sample mean and the population standard deviation. Use this information to construct...

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 60 home theater systems has a mean price of ​$113.00. Assume the population standard deviation is ​$17.90. Construct a​ 90% confidence interval for the population mean

Answers

Solution :

Given that,

(a)

At 90%

Z\alpha/2 = 1.645

Margin of error = E = Z\alpha/2* (\sigma /\sqrtn)

= 1.645 * (17.90 / \sqrt 60)

= 3.80

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

\bar x - E < \mu < \bar x + E

113 - 3.80 < \mu < 113 + 3.80

109.2 < \mu < 116.80

(109.2  , 116.80)

(ii)

At 95%

Z\alpha/2 = 1.96

Margin of error = E = Z\alpha/2* (\sigma /\sqrtn)

= 1.96 * (17.90 / \sqrt 60)

=4.53

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

\bar x - E < \mu < \bar x + E

113 - 4.53 < \mu < 113 + 4.53

108.47 < \mu < 117.53

(109.2  , 116.80)


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