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 he 90% and 95% confidence intervals or the population mean n er ret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals. A random sample of 35 home theater systems has a mean price of $113.00. Assume the population standard deviation is $18.60. Construct a 90% confidence interval for the population mean. The 90% confidence interval is (DD (Round to two decimal places as needed.) Construct a 95% confidence interval for the population mean The 95% confidence interval is CD (Round to two decimal places as needed.)

Explanation / Answer

Mean is 113 and s is 18.6

for 35 sample size, the standard error SE is s/sqrt(N)=18.6/sqrt(35)=3.144

a) For 90% confidence, the z value is 1.65 thus the lower limit is mean-z*SE=113-3.144*1.65=107.81

the upper limit is mean+z*SE=113+3.144*1.65=118.19

b) For 95% confidence, the z value is 1.86 thus the lower limit is mean-z*SE=113-3.144*1.96=106.84. the upper limit is =113+3.144*1.96=119.16

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