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 69 type I ovens has a mean repair cost of $⁢86.44, with a standard deviation of $⁢12.97. A sample of 65 type II ovens has a mean repair cost of $⁢80.47, with a standard deviation of $⁢11.66. 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: State the null and alternative hypotheses for the test

Step2: Compute the value of the test statistic. Round your answer to two decimal places

Step 3: Determine the decision rule for rejecting the null hypothesis Ho. Round the numerical portion of your answer to two decimal places

Step 4: Make the decision for the hypothesis test

Answer 1

since sample size n1,n2>30 we can use z approximation:

step 1":

null hypothesis: Ho:μ1-μ2			=	0
Alternate hypothesis: Ha:μ1-μ2			>	0

Step2: Compute the value of the test statistc =2.81 (please try 2.80 if this comes wrong)

Step 3: reject Ho if z>1.64

(please try t>1.66 if t distribution is to be used)

Step 4: reject the null.