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 51 type I ovens has a mean repair cost of $87.59, with a standard deviation of $20.27$. A sample of 34 type II ovens has a mean repair cost of $84.62, with a standard deviation of $20.46. Conduct a hypothesis test of the technician's claim at the 0.01 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 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

The statistical software output for this problem is:

Two sample Z summary hypothesis test:
μ₁ : Mean of population 1 (Std. dev. = 20.27)
μ₂ : Mean of population 2 (Std. dev. = 20.46)
μ₁ - μ₂ : Difference between two means
H₀ : μ₁ - μ₂ = 0
H_A : μ₁ - μ₂ > 0

Hypothesis test results:

Difference	n1	n2	Sample mean	Std. err.	Z-stat	P-value
μ1 - μ2	51	34	2.97	4.5131405	0.65807834	0.2552

Hence,

Step - 2: Test statistic = 0.66

Step - 3: Decision Rule: Reject Ho if z > 2.326

Step - 4: Decision: Reject the null hypothesis