A NAPA Auto Parts supplier wants information about how long

A NAPA Auto Parts supplier wants information about how long car owners plan to keep their cars. A random sample of 41 car owners results in a mean of 7 years with a standard deviation of 3.75 years. Find a 95% confidence interval for the true population mean. Identify the point estimate for mean and margin of error.

*Must provide calculator command, point estimate, confidence interval, and margin of error*

Solution

a) Point estimate of the population mean = Xbar = 7 years

point estimate of the mean: 7 years

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b) Confidence interval for population mean is
Xbar +/- Margin of error (E)
Margin of error = confidence coefficient*SD/sqrt n
Degrees of freedom = n-1 = 41-1 = 40
Critical value of t for 40 d.f for 95% confidence is 2.021
E = 2.021*3.75/sqrt 41 = 1.18
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c) The CI is
7 + 1.18
lower limit is 7 - 1.18 = 5.82
upper limit is 7 + 1.18 = 8.18
The CI is (5.82, 8.18)