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. Interpret the results and compare the widths of the confidence intervals.

A random sample of 35 home theater systems has a mean price of ​$125.00.  Assume the population standard deviation is ​$19.60

Answer 1

Mean () = 125
Sample size (n) = 35
Standard deviation (s) = 19.6
Confidence interval(in %) = 90
z @ 90.0% = 1.645
Since we know that

Required confidence interval =
Required confidence interval = (125.0-5.4499, 125.0+5.4499)
Required confidence interval = (119.5501, 130.4499)
There is 90% probability that the population mean falls under range (119.5501, 130.4499). Also 90% confidence intervals are wider than 95% confidence interval
Mean () = 125
Sample size (n) = 35
Standard deviation (s) = 19.6
Confidence interval(in %) = 95
z @ 95.0% = 1.96
Required confidence interval =
Required confidence interval = (125.0-6.4935, 125.0+6.4935)
Required confidence interval = (118.5065, 131.4935)
There is 95% probability that the population mean falls under range (118.5065, 131.4935)
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