Question

5. A car dealer claims that the average wait time for an oil change is less than 30 minutes. The population of wait times is normally distributed and 26 customers are sampled. The sample mean is 28.7 minutes and the standard deviation of the sample is 2.5 minutes. Test the claim at the .05 significance level (α=.05) using the traditional method.

Answer 1

Step 1:

Ho: = 30

Ha: < 30

Null hypothesis states that average wait time for an oil change is equal to  30 minutes

Alternative hypothesis states that average wait time for an oil change is less than 30 minutes

Step 2: Test statistics

n = 26

sample mean = 28.7

sample sd = 2.5

Assuming that the data is normally distributed and as the population sd is not given, we will calculate t stat

t = -2.651

Step 3:

df = 26-1 = 25

level of significance= 0.05

Left tailed test

t critical = - 1.708

As the t stat (-2.651) falls in the rejection area, we reject the Null hypothesis.