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 59 type I ovens has a mean repair cost of $70.10, with a standard deviation of $19.40. A sample of 49 type II ovens has a mean repair cost of $63.21, with a standard deviation of $12.29. Conduct a hypothesis test of the technician's claim at the 0.05 level of significance. Let ?1 be the true mean repair cost for type I ovens and ?2 be the true mean repair cost for type II ovens.

Step 1 of 4:

State the null and alternative hypotheses for the test.

H₀: ?₁ (blank) ?₂

H_a: ?₁ (blank) ?₂

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.

Reject H₀ if (blank) (blank) (blank) [NOTE: First blank choices: z or | z | Second blank choices: > or < Third blank: Round answer to 3 decimal places]

Step 4 of 4: Multiple Choice

a) Reject Null Hypothesis

b) Fail to Reject Null Hypothesis

Thank you so much!!

Answer 1

The statistical software output for this problem is:

Two sample Z summary hypothesis test:
?₁ : Mean of population 1 (Std. dev. = 19.4)
?₂ : Mean of population 2 (Std. dev. = 12.29)
?₁ - ?₂ : Difference between two means
H₀ : ?₁ - ?₂ = 0
H_A : ?₁ - ?₂ > 0

Hypothesis test results:

Difference	n1	n2	Sample mean	Std. err.	Z-stat	P-value
?1 - ?2	59	49	6.89	3.0759577	2.2399528	0.0125

Hence,

Step 1:

Ho:

Ha:

Step - 2: Test statistic = 2.24

Step - 3: Decision rule: Reject Ho if z > 1.645

Step - 4: Reject Null Hypothesis