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. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals.
A random sample of 40 home theater systems has a mean price of $140.00 Assume the population standard deviation is $19.50.
The 90% confidence interval is?
The 95% confidence interval is?
n= 40, = 140, = 19.50
We are using TI-83 calculator as folllows,
c= 90 %
134.93 < < 145.07
The 90% confidence interval is ( 134.93 , 145.07)
c= 95 %
133.96 < < 146.04
The 95% confidence interval is ( 133.96 , 146.04)
With 90% confidence, it can be said that the population mean price lies in the first interval. With 95% confidence, it can be said that the population mean price lies in the second interval. The 95% confidence interval is wider than the 90%.
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