A report states 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 $3,927 in 2012. 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 $3,850 with the sample standard deviation of $400. Complete parts (a) and (b) below.
a. Is there evidence that the population mean cost is less than $3,927? (Use a 0.05 level of significance.)
State the null and alternative hypotheses.
Find the test statistic for this hypothesis test.
The critical value(s) for the test statistic is(are) ___ ?
Is there sufficient evidence to reject the null hypothesis using a = 0.05?