A technician compares repair costs for two types of microwave ovens (type I and

Question

A technician compares repair costs for two types of microwave ovens (type I and type II). He believes that the repair cost tor type | ovens is greater than the repair cost for type II ovens. A sample of 37 type I ovens has a mean repair cost of $86.72. The population standard deviation for the repair of type l ovens is Known to be $22.35. A sample of 31 type II ovens has a mean repair cost of $79.50. The population standard deviation for the repair of type II ovens is known to be $ 17.27. Conduct a hypothesis test of the technician's claim at the 0.05 level of significance. Let mu_1 be the true mean repair cost for type I ovens and mu_2 be the true mean repair cost for type II ovens. Find the p-value associated with the test statistic. Round your answer to four decimal places.

Explanation / Answer

Statistical software output for this problem is:

Two sample Z hypothesis test:
1 : Mean of population 1 (Std. dev. = 22.35)
2 : Mean of population 2 (Std. dev. = 17.27)
1 - 2 : Difference between two means
H0 : 1 - 2 = 0
HA : 1 - 2 > 0

Hypothesis test results:

Therefore,

p = 0.0666

Difference n1 n2 Sample mean Std. err. Z-stat P-value 1 - 2 37 31 7.22 4.8084997 1.5015078 0.0666

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