Question

The IRS claims that the mean wait time for callers during a recent tax filing season was at most 7 minutes. A random sample of 11 callers has a mean wait time of 8.7 minutes and a standard deviation of 2.7 minutes. IS there enough evidence to reject the claim at alpha = 0.10? Notice that the sample size is < 30. That will determine whether you use the t-test or the z-test.

State if it is a one-tailed or two-tailed test and draw your distribution and designate your rejection region using critical values.

Answer 1

Solution:

Null hypothesis H0: mean = 7

Alternate hypothesis Ha: mean <7

Sample size = 11, sample mean = 8.7

Sample standard deviation = 2.7

Test stat = (8.7-7)/2.7/Sqrt(11) = 2.09

As sample size is less than 30 and population standard deviation is also unknown so we will use t test. And this is one tailed test

P-value = 0.032

At alpha=0.1, we can reject the null hypothesis, as p-value is less than alpha value and we have significant evidence to accept the alternate hypothesis.