1. Unit 3 Examples

2. Susan is shooting free throws in the gym practicing for the game tonight. Her shooting percentage is 70%. She usually gets the chance to shoot about 10 free throws during a game. Simulate her performance tonight using a random number table. Do three trials. Use the average of the three trials to predict how many free throws she will make tonight.
Example 1

3. A person with blood type O-positive blood can receive blood only from other type O donors. About 44% of the US population has type O blood. At a blood drive, how many potential blood donors do you expect to examine in order to get three units of type O blood? Design a simulation to answer this question and do 10 trials.
Example 2

4. Fifty-seven students participating in a lottery for a particularly desirable dorm room – a triple with a fireplace and private bath in the tower. Twenty of the participants were members of the same varsity team. When all three winners were members of the team, the other students cried foul. Use a simulation to determine whether an all-team outcome could reasonably be expected to happen if everyone had a fair shot at the room.
Example 3

5. Bill has $20 and is going to play roulette
Bill has $20 and is going to play roulette. He has a system that he believes will win him money. Every time the wheel is spun he bets $1 on black and $1 on the number 3. The wheel is numbered 00 – 36 with odd numbers being red, even numbers being black and 00 being green. If the wheel lands on black he keeps the $1 he bet and wins another $1. If it lands on red or green, he loses the dollar he bet on black. If it lands on 3 he wins $5 and keeps the $1 he bet on 3. If it lands on any other number, he loses the dollar he bet on 3. Simulate this game and keep track of Bill’s money until he either loses all his money or doubles his money.
Example 4

6. Example 5 Which method of data collection would you use?
A) I want to see if Crest Whitestrips works better than Colgate Clinical White Toothpaste.
Experiment
Example 5

7. Example 5 Which method of data collection would you use?
B) I want to know how many CHHS seniors favor off campus lunch
Survey
Example 5

8. Example 5 Which method of data collection would you use?
) I want to see how many times I would roll a 3 on a fair die if I rolled it 10,000 times.
Simulation
Example 5

9. Example 5 Which method of data collection would you use?
There is a new display at the grocery store for beverages. We want to see if it attracts more men or women.
Observational Study
Example 5

10. My population of interest is members of the Texas A & M band
My population of interest is members of the Texas A & M band. Identify the sampling technique used in the scenario below:
A) All Texas A & M band members are listed in alphabetical order and numbered. I choose a random number 1 – 5. The student with that number becomes the first in my sample. I then select every 5th person on the list until I get to the end.
Systematic Sample
Example 6

11. My population of interest is members of the Texas A & M band
My population of interest is members of the Texas A & M band. Identify the sampling technique used in the scenario below:
B) I separate the Texas A & M band members into 4 grade level lists. Each grade level is alphabetized and numbered. I use a random number generator to select 10 students from each grade level.
Stratified Sampling
Example 6

12. My population of interest is members of the Texas A & M band
My population of interest is members of the Texas A & M band. Identify the sampling technique used in the scenario below:
C) I put section names in a hat, I draw out 3 of them. I survey all the students in each chosen section.
Cluster Sampling
Example 6

13. My population of interest is members of the Texas A & M band
My population of interest is members of the Texas A & M band. Identify the sampling technique used in the scenario below:
D) All members of the Texas A & M band are listed in alphabetical order and numbered. I use a random number generator to select 40 students off the list.
Simple Random Sample
Example 6

14. My population of interest is members of the Texas A & M band
My population of interest is members of the Texas A & M band. Identify the sampling technique used in the scenario below:
E) I stand outside the practice rooms for a week, surveying students who practice between 8:00 and 10:00 am.
Convenience Sampling
Example 6

15. Google wants to survey its employees about new furniture in the meditation area. Identify a form of bias that could result from each plan and a potential problem that it might create. (There may be more than one correct answer.)
A) The intern who drafted the survey put his favorite furniture choice first and made its picture bigger than all the other choices.
Response Bias
Example 7

16. Google wants to survey its employees about new furniture in the meditation area. Identify a form of bias that could result from each plan and a potential problem that it might create. (There may be more than one correct answer.)
B) They send out an to all employees and ask them to respond if they wish.
Voluntary Response Bias
Example 7

17. Google wants to survey its employees about new furniture in the meditation area. Identify a form of bias that could result from each plan and a potential problem that it might create. (There may be more than one correct answer.)
C) Since Google is a big company they decide to send the survey to only the executives, not all the employees.
Undercoverage
Example 7

18. Google wants to survey its employees about new furniture in the meditation area. Identify a form of bias that could result from each plan and a potential problem that it might create. (There may be more than one correct answer.)
D) The survey went out to employees the same week most of them had a deadline for a big project. Only a handful of employees responded.
Nonresponse
Example 7

19. State police set up a roadblock to check cars for up-to-date registration, insurance, and safety inspections. They usually find problems with about 10% of the cars they stop.
Identify the following for the problem:
1) the population
2) the population parameter of interest
3) the sampling frame
4) the sample
5) the sampling method
6) any potential sources of bias or problems
Example 8

20. 100 volunteers who suffer from indigestion are available to test a new indigestion medication. There are 50 men & 50 women.
A) Design a completely randomized, comparative experiment to test the new drug.
B) Design a comparative experiment, blocked on gender, to test the new drug.
Example 9

21. A consumer group wants to test the effectiveness of a new “organic” laundry detergent and make recommendations to customers about how to best use the product. They intentionally get grass stains on 30 white T-shirts in order to see how well the detergent will clean them. They want to try the detergent in cold water and in hot water on both the “regular” and “delicates” wash cycles. Design an appropriate experiment, indicating the number of factors, levels, and treatments. Explain how you would randomize in your experiment.
Example 10

22. P.P. Pumpkineater, the renowned agricultural geneticist, has mutated previous varieties of pumpkins and produced two new strains, ScaryFace and CandleBreath. Because he has limited marketing funds, he must decide which strain is the most “jack-o- lanternable”. Having been in the jack-o-lantern business for a long period of time, he had developed the PPPJOL Test to compare different strains. The plot of land available for planting is on the side of a hill with a number of trees on top and a stream near the bottom. He is quite concerned about the effects of sunlight and water on the growth of the pumpkins. He has 30 seeds of each variety available for testing. Design an experiment that will help P.P. determine which strain to market.
Example 11

23. It is a common belief that people behave strangely when there is a full moon, and that as a result, police and emergency rooms are busier than usual. Design a way you could find out if there is any merit to this belief. Will you use an observational study or an experiment? Why?
Example 12

24. The makers of Frumpies, “the breakfast of rug rats” want to improve their marketing, so they consult you:
A) They first want to know what fraction of children, age 10 – 13, like their celery flavored cereal. What kind of study should they perform?
B) They are thinking of introducing a new flavor, maple- marshmallow Frumpies, and want to know whether children will prefer the new flavor to the old one. Design a completely randomized experiment to investigate this question.
C) They suspect that children who regularly watch the Saturday morning cartoon show starring Frump, the flying teenage warrior rabbit who eats Frumpies in every episode, may respond differently to the new flavor. How would you take that into account in your design?
Example 13