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 43 type I ovens has a mean repair cost of $70.15. The population standard deviation for the repair of type I ovens is known to be $20.62. A sample of 57 type II ovens has a mean repair cost of $65.36. The population standard deviation for the repair of type II ovens is known to be $22.21. Conduct a hypothesis test of the technician's claim at the 0.05 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.

Step 5 of 5: State the conclusion of the hypothesis test.

Answer 1

Step 1: H0: the repair cost for type I ovens is not greater than the repair cost for type II ovens

i.e. H0: μ1 = μ2

H1: the repair cost for type I ovens is greater than the repair cost for type II ovens (Right tail test)

i.e. Ha: μ1 > μ2

Step 2:

Step 3: P-Value: 0.1330

tep 4: Here P-value > alpha 0.05 so we accept null hypothesis

Step 5: Thus we conclude that the repair cost for type I ovens is not greater than the repair cost for type II ovens i.e. μ1 = μ2