Question

The owner of Luke's Cooling company believes that the average time to install a new blower motor on a residential furnace is 12.5 minutes. Assume that installation time is normally distributed, and that ? = 2.7 minutes. The company owner goes through the times for a random sample of 26 furnace blower motor installations, and finds that the average installation time was 11.44 minutes. Using a significance level of ? = .05, is the company owner’s belief correct? Conduct a complete and appropriate hypothesis test.

Step 1 (Hypotheses)

H₀:  (Click to select)??nx-bars?p  (Click to select)=??>?<  

H_A:  (Click to select)?x-bar?p?sn  (Click to select)=??>?<  

Step 2 (Decision rule)

Using only the appropriate statistical table in your textbook, the critical value for rejecting H₀is (Click to select)+-± . (report your answer to 2 decimal places, using conventional rounding rules)

Step 3 (Test statistic)

Using the sample data, the calculated value of the test statistic is (Click to select)+-± . (report your answer to 2 decimal places, using conventional rounding rules)

Step 4 (Evaluate the null hypothesis)

Should the null hypothesis be rejected?  (Click to select)yesno

Step 5 (Practical conclusion)

Should the company owner conclude that the average time to install a new furnace blower motor is 12.5 minutes? [no]

Using only the appropriate statistical table in your textbook, what is the p-value of this hypothesis test?  

Answer: ?? (Report your answer to 4 decimal places, using conventional rounding rules)

Answer 1

Step 1. Hypotheses:

Step 2.(Decision Rule)

the critical value for a two-tailed test is zc = 1.96

The rejection region for this two-tailed test is

Step 3 (Test statistic)

The z-statistic is computed as follows:

Step 4 (Evaluate the null hypothesis) YES.

  Since it is observed that, it is then concluded that the null hypothesis is rejected.

Step 5 (Practical conclusion)

Should the company owner conclude that the average time to install a new furnace blower motor is 12.5 minutes? No.

The p-value of this hypothesis test is 0.0453.