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. Which interval is​ wider? If​ convenient, use technology to construct the confidence intervals. A random sample of 43 gas grills has a mean price of ​$626.90. Assume the population standard deviation is ​$56.60.

The​ 90% confidence interval is ​. ​(Round to one decimal place as​ needed.)

The​ 95% confidence interval is ​. ​(Round to one decimal place as​ needed.)

Answer 1

A random sample of 43 gas grills has a mean price of ​$626.90. Assume the population standard deviation is ​$56.60

population standard deviation is 56.60
sample size is 43.
standard error of the sample mean is 56.60 / square root(43) = 8.63141

at 90% confidence level, critical z is plus or minus 1.645.

at 95% confidence level, critical z is plus or minus 1.96.

critical raw score will be sample mean plus or minus critical z-score * standard error of the mean.

your sample mean is 626.9.
your standard error of the mean is 8.63141
at 90% confidence level, your critical raw score will be 626.9 plus or minus 1.645 * 8.63141 .

that becomes 626.9 plus or minus 14.19867 rounded to the nearest penny.

at 90% confidence level, the true population mean will be between 612.70133 and 641.09867.

at 95% confidence level, your critical raw score will be 626.9 plus or minus 1.96 * 8.63141 .

that becomes 626.9 plus or minus 16.91756 rounded to the nearest penny.

at 95% confidence level, the true population mean will be between 609.98243 and 643.81755.