STAT 222

Unit 3 Statistics Test
MA 222
Spring 2020
Pat Jones oversees retail technology at a national chain of discount department stores and
hypermarkets. The company is rolling out new self-checkout systems so customers can scan and
pay for their items without having to interact with a cashier. Pat wants to know if shoppers
around the world like this service and decides to test a sample from the store in Durham, North
Carolina. Pat looks at the usage data of the self-checkout systems for the first full two weeks of
June and makes a list of how many customers use the system each day:
115 103 115 109 113 86 113
87 99 99 107 92 113 97
Pat believes that if there are at least 100 users per day on average, then shoppers must like it. So
even though it’s been a while since Pat took statistics, Pat runs a hypothesis test on the data
based on this belief.
Tracey Hudson works in the analytics group at the company and stops by Pat’s office to find out
how the new self-checkout system is working out. Pat tells Tracey, “Things are going great! I
took a sample and ran a two-tailed hypothesis test. I used a 10% level of significance, so my test
would have a lot of power. Even though my sample mean was less than 100, my z-score was
1.65 and the sample mean fell within the zone of acceptance. That means that there are at least
100 people using self-checkout per day on average and that shoppers clearly like the system.”
Tracey is puzzled. “Something doesn’t seem right. How confident are you in your results?”
“I’m 99.9% confident that the system gets at least 100 users on average per day!” Pat exclaims.
“How can you doubt me?”
• Answer the following questions to the best of your ability.
• Show all your work. Use a calculator so you don’t make basic math errors.
• After you’ve completed your calculations, round your numbers to two decimal places.
• Do not look on the Internet for help with any part of this test.
• Do not discuss this test with anyone inside or outside of class.
• Your answers are due in Blackboard on or before Sunday, April 26, at 11:59 pm.
• Take pictures of your work and upload the pictures to Blackboard. Do not wait until
the last minute in case you have technical problems.
1. Tracey realizes that Pat has made several serious statistical mistakes with the hypothesis test.
Briefly describe at least three of Pat’s mistakes.
2. Tracey wants to help. Using Pat’s raw data, mu, and level of significance, Tracey runs a new,
correct hypothesis test on the collected data based on Pat’s belief.
a. What assumptions does Tracey need to make before running the test?
b. State your null and alternative hypotheses.
c. What does Tracey find? RUN THE TEST THREE TIMES, USING EACH OF
THE THREE METHODS (one method per test). Draw pictures, show your work,
and state the conclusion of each test.
3. Using Pat’s raw data, what is Tracey 99.9% confident of? Show your work and state Tracey’s
conclusion.
4. Even though Tracey runs the hypothesis test correctly, Tracey recognizes that there are
problems with the internal and external validity of Pat’s study. Identify the validity problems
that you think Tracey notices, explain how each problem relates to internal or external
validity, and briefly discuss what could be done to improve the validity of the study.
5. Out of curiosity, Tracey pulls a larger sample of 31 days, which yielded a sample standard
deviation (s) of 9.4 customers.
a. How large a sample size is needed for Tracey to be 98% confident that the sample
average x-bar is within 2 customers of mu?
b. How many more days does Tracey need to sample?