Question

it is in the interest to a Harley Davidson dealer to know the average gas mileage of a 1999 Harley Davidson XLT. A random sample of 17 XLTs were taken from a normally distributed population and found to have a mean of 52 miles per gallon and a standard of 4.1 miles per gallon. Construct a 95% interval for the mean gas mileage of any 1999 Harley Davidson XLT. Interpret your result.

Answer 1

Given that, sample size (n) = 17, sample mean = 52 miles per gallon and sample standard deviation (s) = 4.1 miles per gallon

Degrees of freedom = 17 - 1 = 16

t-critical value at significance level of 0.05 and 16 degrees of freedom is,

The 95% confidence interval for the population mean is,

Therefore, required confidence interval is (49.8919, 54.1081).

Interpretation : we are 95% confident that, the true mean gas mileage of any 1999 Harley Davidson XLT is between 49.8919 and 54.1081 miles per gallon.