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 61 type I ovens has a mean repair cost of $80.58. The population standard deviation for the repair of type I ovens is known to be $17.46. A sample of 64 type II ovens has a mean repair cost of $73.27. The population standard deviation for the repair of type II ovens is known to be $14.59. Conduct a hypothesis test of the technician's claim at the 0.1 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.

Answer 1

Step 1

The test hypothesis is

This is a one-sided test because the alternative hypothesis is formulated to detect the difference from the hypothesized mean on the upper side

Step 2

Now, the value of test static can be found out by following formula:

Using Excel's function =T.DIST.RT(t0,n-1),

Step 3

the P-value for t0 = 2.5446 in an upper-tailed t-test with 123 degrees of freedom can be computed as

.

Step 4

Since P = 0.006088804325722095 < 0.1, we reject the null hypothesis H_0 in favor of the alternative hypothesis H_1 at \alpha = 0.1.

Degrees of freedom on the t-test statistic are n1 + n2 - 2 = 61 + 64 - 2 = 123

This implies that

Since  ,

we reject the null hypothesis H_0 in favor of the alternative hypothesis H_1 at \alpha = 0.1.

Step 5

There is sufficient evidence to support the claim