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 40 type I ovens has a mean repair cost of $83.73. The population standard deviation for the repair of type I ovens is known to be $10.60. A sample of 31 type II ovens has a mean repair cost of $77.38. The population standard deviation for the repair of type II ovens is known to be $17.35. Conduct a hypothesis test of the technician's claim at the 0.05 level of significance. Let μ1μ1 be the true mean repair cost for type I ovens and μ2 be the true mean repair cost for type II ovens.

1

State the null and alternative hypotheses for the test.

2

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

3  

Find the p-value associated with the test statistic. Round your answer to four decimal places.

4    

Make the decision for the hypothesis test.

5    

State the conclusion of the hypothesis test.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ1 = μ2
Alternative Hypothesis, Ha: μ1 > μ2

Pooled Variance
sp = sqrt(s1^2/n1 + s2^2/n2)
sp = sqrt(112.36/40 + 301.0225/31)
sp = 3.5383

Test statistic,
z = (x1bar - x2bar)/sp
z = (83.73 - 77.38)/3.5383
z = 1.79

P-value Approach
P-value = 0.0367

As P-value < 0.05, reject the null hypothesis.

There is sufficient evidence to conclude that the repair cost for type I ovens is greater than the repair cost for type II ovens