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 58 type I ovens has a mean repair cost of $88.52, with a standard deviation of $23.72. A sample of 49 type II ovens has a mean repair cost of $86.20, with a standard deviation of $14.32. 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 three decimal places.

Step 4 of 4: Make the decision for the hypothesis test.

Answer 1

Answer:

Given,

n1 = 58

1 = $88.52,

1 = $23.72

n2 = 49

2 = $86.20

2 = $14.32

significance level = 0.05

Now hypothesis can be given as follows

Null hypothesis Ho : 1 = 2

Alternative hypothesis H1 : 1 > 2

Now to give the test statistic

z = (1 - 2) / sqrt( / n1 + / n2)

substitute the values

= (88.52 - 86.20) / sqrt((23.72^2/58 + 14.32^2/49))

= 0.6226

z = 0.62

Now here we can say that at 95%confidence interval, Zc value is 1.64

So we can say that z < Zc i.e., 0.62 < 1.64 . So we fail to reject the null hypothesis Ho.

Hence the repair cost of the type 1 oven is same as that of the repair cost of type II oven.