Question

Because of the expense involved, car crash tests often use small samples. When five Mercedes cars are crashed under standard conditions, the repair costs have a sample mean of $767.40 with sample standard deviation of $284.73. Assume a normal distribution. According to past research, the mean of all Mercedes repair costs is $1000. Use a .05 significance level to test the local Mercedes garage’s claim that the mean of repairs for all Mercedes cars is less than $1000.

A) State the null and alternate hypothesis:

B) Name the Test

C) Determine the P-value: ___________ Write as a decimal.

D) Determine whether to Reject H0 or Fail to Reject H0 , and TELL WHY by relating P-value to α:

E) Interpret the result in a complete sentence with wording related to the problem:

Answer 1

We conduct T-test for One population mean as :

Hence, there is not enough evidence to conclude that the mean of repairs for all Mercedes cars is less than $1000 at 5% level of significance.