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 34 type I ovens has a mean repair cost of $70.86, with a standard deviation of $12.35. A sample of 48 type II ovens has a mean repair cost of $67.84, with a standard deviation of $21.72. 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: Compute the value of the test statistic.

Step 2: Determine the decision rule for rejecting the null hypothesis H0.

Step 3: Make the decision for the hypothesis test.

Answer 1

Step 1:

Test statistic is:
t= (70.86-67.84)/4.1323 = 0.7308

So,

The value of the test statistic = 0.7308

Step 2:

= 0.10

ndf = n1 + n2 - 2 = 34 + 48 - 2 = 80

From Table, critical value of t = 1.2922

Rejection Region:
Reject H0 if t > 1.2922

Step 3:

Since calculated value of t = 0.7308 is less than critical value of t = 1.2922, the difference is not significant. Fail to reject null hypothesis.

Conclusion:

The data do not support the claim that the mean repair cost of type I oven is greater than the mean repair cost of type II oven.