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 or the population mean. Which interval is wider? If convenient, use technology to construct the confidence intervals. A random sample of 37 gas grills has a mean price of $630.30. Assume the population standard deviation is S56.40 The 90% confidence interval is () (Round to one decimal place as needed.) The 95% confidence interval is CD. Round to one decimal place as needed.) Which interval is wider? Choose the correct answer below. The 95% confidence interval The 90% confidence interval O

Explanation / Answer

Ans:

Given that

sample mean=630.30

population standard deviation=56.4

sample size,n=37

standard error of mean=56.4/sqrt(37)=9.272

z value for 90% Confidence interval is 1.645

90% confidence interval for mean

=630.30+/-1.645*9.272

=630.30+/-15.3

=(615.0, 645.6)

z value for 95% CI is 1.96

95% conffidence interval of mean

=630.3+/-1.96*9.272

=630.3+/-18.2

=(612.1, 648.5)

95% confidence interval is wider(as z multiplir is higher for 95%,hence margin of error higher and CI will be wider)

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