You are given the sample mean and the population standard deviation. Use this in

Question

You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals Which interval is wider? If convenient, use technology to construct the confidence intervals. A random sample of 47 gas grills has a mean price of exist627 50. Assume the population standard deviation is exist57 70 The 90% confidence interval is () (Round to one decimal place as needed) The 95% confidence interval is () (Round to one decimal place as needed) Which interval is wider? Choose the correct answer below The 90% confidence interval The 95% confidence interval

Explanation / Answer

A X% confidence interval is given by the following formula:

Z for 90% is 1.28

Z for 95% is 1.96

Hence,

A 90% confidence interval is Xbar +/- Z*Sigma/sqrt(N) = 627.5 +/- 1.28*57.70/sqrt(47) = 616.727 to 638.273
A 95% confidence interval is Xbar +/- Z*Sigma/sqrt(N) = 627.5 +/- 1.96*57.70/sqrt(47) = 611.004 to 643.996

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