CarMD reports that the cost of repairing a hybrid vehicle is falling even while typical repairs on conventional vehicles are getting more expensive. The most common hybrid repair, replacing the hybrid inverter assembly, had a mean repair cost of $ 2,826 in 2013. (Data extracted from 2014 CarMD Vehicle Health Index, available at corp.carmd.com.) Industry experts suspect that the cost will continue to decrease given the increase in the number of technicians who have gained expertise on fixing gas–electric engines in recent months. Suppose a sample of 100 hybrid inverter assembly repairs completed in the last month was selected. The sample mean repair cost was $ 2,700 with the sample standard deviation of $ 500.
a. Is there evidence that the population mean cost is less than $ 2,826? (Use a 0.05 level of significance.)
b. Determine the p- value and interpret its meaning.