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 for the population mean. Which interval is wider? If convenient, use technology to construct the confidence intervals. A random sample of 38 gas grills has a mean price of $631.80. Assume the population standard deviation is $59.40. The 90% confidence interval is (1, 1). (Round to one decimal place as needed.) The 95% confidence interval is (1, 1). (Round to one decimal place as needed.) Which interval is wider? Choose the correct answer below. The 95% confidence interval The 90% confidence interval

Explanation / Answer

Here it is given mean=631.80 and sd=59.40

Also n=38

so t value for 90 and 95 are 1.6871 and 2.0262 respectively

So for 90% E=t*sd/sqrt(n)=16.26

Hence CI=mean+/-E=631.80+/-16.26=(615.54,648.06)

Similary E for 95%=19.52

Hence CI=(612.28 ,651.32)

Hence we can see 95% CI is wider

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