Problem 22 on Chapter 10.4 The

Problem 22 on Chapter 10.4

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

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

a. What is the population being studied?

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

Answer:

a) Thepopulation being studied are all people who come to see IRSrepresentatives

b)

Step 1:

Ho :     45 minutes

Ha. :    45 minutes

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

Step2:

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 complaintsthe wait time is greater than 45 minutes.

The z-critical value for a right-tailed test, for a significancelevel 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 beforeseeing IRS representative is not less than or equal to 45minutes.  

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


 
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