Question

Problem 22 on Chapter 10.4

The director of the IRS has been flooded with complaints that people must wait more than 45 minutes before seeing an IRS representative. To determine the validity of these complaints, the IRS randomly selects 400 people entering IRS offices across the country and records the times that they must wait before  seeing an IRS representative. The average waiting time for the sample is 55 minutes with a standard deviation of 15 minutes.

Answer the following questions by using and uploading the Excel template for Testing a Hypothesis.

a. What is the population being studied?

b. Are the complaints substantiated by the data at alpha level of 0.10?

Answer 1

a) The population being studied are all people who come to see IRS representatives

b)

Step 1:

Ho :     45 minutes

Ha. :     45 minutes

Null hypothesis states that the wait time before seeing IRS representative is less than or equal to 45 minutes.

Step 2:

Population mean   = 45 minutes

sample size n = 400

sample mean = 55 minutes

sample deviation s = 15 minutes

level of significance = 0.10

Test Statistics

z = 13.333

This is the a Right tailed test because as per the complaints the wait time is greater than 45 minutes.

The z-critical value for a right-tailed test, for a significance level of =0.10 is zc=1.28

Graphically

Since the Z value (13.333) is greater than Z critical value (1.28) we reject the Null hypothesis. The average wait time before seeing IRS representative is not less than or equal to 45 minutes.  

We have sufficient evidence to support the claim that mean wait time is more than 45 minutes