Chapter 9, Problem 47PS

CarMD reports that after two years of flat U.S. car repair costs, 2016 saw an increase. Once of the most common problems that trigger the “check engine� light is the catalytic converter. Repairing the catalytic converter had a mean repair cost of $\text{\$1,190}$ in 2016.

Suppose a sample of 100 catalytic converter repairs completed in the last month was selected. The sample mean repair cot was $\text{\$1,125}$ with the sample standard deviation of $\text{\$250}\text{.}$

a. Is There evidence that the population mean repair cost is less than  $\text{\$1,190?}$ (Use a 0.005 level of significance.)

b. Determine the p-value and interpret its meaning.