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 54 type I ovens has a mean repair cost of $80.93. The population standard deviation for the repair of type I ovens is known to be $16.07. A sample of 35 type II ovens has a mean repair cost of $74.68. The population standard deviation for the repair of type II ovens is known to be $16.90. 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. Reject, or fail to reject null hypothesis

Answer 1

Let be the the population mean repair cost for type I ovens .

Let be the the population mean repair cost for type II ovens.

Given:

For: = $80.93, ₁ = $16.07, n₁ = 54

For: = $74.68, = $16.90, n₂ = 35

(1) The Hypothesis:

H0: = : The population mean repair cost for type I ovens is equal to the population mean repair cost for type II ovens.

Ha: > : The population mean repair cost for type I ovens is greater the population mean repair cost for type II ovens.

This is a Right tailed test.

(2) The Test Statistic:

(3) The p Value:    The p value (Right Tail) for Z = 1.73, is; p value = 0.0418

(4) The Decision Rule: Reject H0 if the P value is <

The Decision:   Since P value (0.0418) is < (0.05), We Reject H0.

(5) The Conclusion: There is sufficient evidence at the 95% significance level to conclude that the population mean repair cost for type I ovens is greater the population mean repair cost for type II ovens.