Question

The owner of Nick's Heating & 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)x-bars?np??  (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 H₀ is (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? (Click to select)yesno

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

Given
mu = 12.5

xbar = 11.44
s = 2.7
n = 26

The hypothesis is
H0 : the average time to install is 12.5 minutes
H1 : the average time to install is different from 12.5 minutes

we caclulate
degtee of freedom as

df = n-1 = 26-1 = 25
the critical value for df = 25 and alpha = 0.05 is
+- 2.05

the test stat is calculated as

t = (xbar-mu)/(sd/sqrt(n))

= (11.44-12.5)/(2.7/sqrt(26)) = -2.001

as the t stat falls in the region of +- 2.05
hence we fail to reject the null hypothesis in favor of alternate hypothesis

Should the company owner conclude that the average time to install a new furnace blower motor is 12.5 minutes?
yes

The P-Value is .056361.

The result is not significant at p < .01.