In: Statistics and Probability
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 40 type I ovens has a mean repair cost of $83.73, with a standard deviation of $10.60. A sample of 31 type II ovens has a mean repair cost of $77.38, with a standard deviation of $17.35. 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 4 : State the null and alternative hypotheses for the test.
Step 2 of 4: Compute the value of the test statistic. Round your answer to two decimal places.
Step 3 of 4: Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to two decimal places.
Step 4 of 4: Make the decision for the hypothesis test. Fail or reject to fail.