Question

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 $3,890 with the sample standard deviation of ​$300.

Complete parts​ (a) and​ (b) below.

a. Is there evidence that the population mean cost is less than $3,927​? ​(Use a 0.1 level of​ significance.)

Answer 1

This is the two tailed test .

The null and alternative hypothesis is

H₀ : = 3927

H_a : < 3927

Test statistic = t

= ( - ) / s / n

= (3890 - 3927) / 300 / 100

Test statistic = 1.767

P-value = 0.0804

= 0.1

P-value <

Reject the null hypothesis .

There is sufficient evidence to conclude that the  population mean cost is less than $3,927