Question

A technician compares repair costs for two types of microwave ovens (type I and type II). He believes that the repair cost for type I ovens is greater than the repair cost for type II ovens. A sample of 37 type I ovens has a mean repair cost of $⁢70.68. The population standard deviation for the repair of type I ovens is known to be $⁢19.05. A sample of 40 type II ovens has a mean repair cost of $⁢64.02. The population standard deviation for the repair of type II ovens is known to be $⁢19.68. Conduct a hypothesis test of the technician's claim at the 0.01 level of significance. Let μ1 be the true mean repair cost for type I ovens and μ2 be the true mean repair cost for type II ovens.

Step 1 of 5 :  State the null and alternative hypotheses for the test.

Step 2 of 5 : Compute the value of the test statistic. Round your answer to two decimal places.

Step 3 of 5 : Find the p-value associated with the test statistic. Round your answer to four decimal places.

Step 4 of 5 : Make the decision for the hypothesis test: Reject Null Hypothesis or Fail to Reject Null Hypothesis

Step 5 of 5 : State the conclusion of the hypothesis test: There is sufficient evidence to support the claim or There is not sufficient evidence to support the claim.

PLEASE DO NOT ANSWER UNLESS YOU ARE CONFIDENT YOUR ANSWER WILL BE CORRECT.

Answer 1

To test :

Test statistic :

where ,

The value of the test statistic :

We reject H0 if the

Now ,

Hence we accept the null hypothesis or H0 .

There is not sufficient evidence to support the claim that the repair cost for type I ovens is greater than the repair cost for type II ovens