1. Comparing Sampling Methods

2. Comparing Sampling Methods
The tumultuous town mayor decides to set an example for the town by buying recycling bins for city hall. He can choose among red, green, or blue bins but wants input from city hall workers.

3. Comparing Sampling Methods
Should he use convenience, systematic, or simple random sampling to get input? Tell which you would use and describe your plan.
I would choose convenience sampling because the decision is not that important and should be made fast and at low cost. I would ask a few workers outside my office for input. Then, I would choose the color that was the most popular.

4. Comparing Sampling Methods
Which sampling method do you use most in your life? Explain.
I use convenience sampling most because it’s easy, free, and quick. If I had a bigger decision to make, I might use a more systematic method of sampling.

5. Comparing Sampling Methods
Different situations call for different sampling methods.
You have studied three sampling methods. For what situations is each type of sampling most effective?

6. Comparing Sampling Methods
Convenience Sampling is best when…
You do not have access to all of the members of the population
You do not have time or resources to use a more accurate sampling method
The members available are representative of the population, or it is not important that the sample be representative

7. Comparing Sampling Methods
Systematic Sampling is best when…
The whole population is available, or a stream of representative members are available
There is no pattern to the arrangement of the population or the stream of members

8. Comparing Sampling Methods
Simple Random Sampling is best when…
The whole population is available
The characteristics of the population are unknown

9. Comparing Sampling Methods
Suppose the new music teacher wants to find out how many students in the school can play a musical instrument. Identify the sampling method in each description. Does each description produce a representative sample? Explain.

10. Comparing Sampling Methods
Survey every 5th student who enters the music room.
Systematic Sampling.
No; students who enter the music room probably play some sort of instrument and are more likely to play a musical instrument than students who do not go in the music room. So the sample has bias toward playing a musical instrument.

11. Comparing Sampling Methods
Survey the students in the school whose names are picked out of a hat.
Simple Random Sampling.
Yes; the random aspect of this method most likely produces a representative sample.

12. Comparing Sampling Methods
Survey the students in the homeroom closest to the music room.
Convenience Sampling.
Yes; students in each homeroom are probably a good representation of the population because students were most likely assigned to a homeroom at random. So the sample is representative.

13. Comparing Sampling Methods
Survey all the students in the next band practice.
Convenience Sampling.
No; students in the band play an instrument, so the sample has bias toward playing a musical instrument.

14. Comparing Sampling Methods
Survey every 10th student who enters the school cafeteria.
Systematic Sampling.
Yes; the order in which students enter the cafeteria is random, in general, so the sample is representative.

15. Comparing Sampling Methods
Suppose workers at an amusement park want to find out how many customers like to ride the roller coaster. Identify the sampling method in each description. Does each description produce a representative sample? Explain.

16. Comparing Sampling Methods
Survey every 8th customer waiting in line for the roller coaster.
Systematic Sampling.
No; customers waiting in line probably like to ride the roller coaster, so the sample has bias toward “yes”.

17. Comparing Sampling Methods
Survey every 12th customer who enters the park.
Systematic Sampling.
Yes; there is usually no pattern in the customers entering the park, so it is a representative sample.

18. Name the sampling method described.
Comparing Sampling Methods
Name the sampling method described.
The drama teacher wants to audition students for a play. She assigns each student a unique number as they enter the room. She then draws 5 numbers from a basket to choose the students.
Simple Random Sampling

19. Comparing Sampling Methods
Suppose you are a city developer. You want to determine how many of each model home there are in a neighborhood of 200 houses. Describe how you would choose a sample of 20 houses using either systematic sampling or simple random sampling. Justify your choice of sampling method.

20. Comparing Sampling Methods
Systematic Sampling
Find the interval
200/20 =10
If there is a pattern to the line of house that repeats every 10 houses, your sample may only include one type of model, regardless of which house you start at.

21. Comparing Sampling Methods
Simple Random Sampling
Assign a unique number from 1 to 200 to each house. Generate 20 numbers between 1 and 200 at random, and sample those houses.
Simple random sampling is the best choice because each type of house is equally likely to be chosen.

22. Comparing Sampling Methods
Suppose you want to determine how many cars exceed the speed limit on a local highway. If about 2,480 cars travel on the highway per day, tell whether you would use systematic sampling or simple random sampling to choose a sample of 100 cars. Justify your choice of sampling method.

23. Comparing Sampling Methods
Systematic Sampling
Find the interval
2480/100 ≈25
Sampling every 25th car means you should have plenty of time to record each car’s speed. There is no pattern to the cars driving on the highway.

24. Comparing Sampling Methods
Simple Random Sampling
Assign a number from 1 to 2,480 to each car that travels on the highway. Generate 100 numbers between 1 and 2,480 at random, and sample those cars.
Recording the speed of exactly those cars that were assigned the numbers you generated may be difficult to do, especially if you need to record the speed of two cars that pass at almost the same time.

25. Comparing Sampling Methods
Systematic sampling is the best choice because it is easier to get the sample, and it produces a representative sample of the cars on the highway.

26. Suppose you are an inspector at a toy factory that makes 600 toys per day. Six machines each make toys and place them on the conveyor belt. Describe how you would choose a sample of at least 75 toys from one day’s production using either convenience or systematic sampling. Justify your choice of sampling method.

27. Comparing Sampling Methods
Convenience Sampling Pros:
It is easy to take a sample of the next 75 toys on the conveyor belt.
Convenience Sampling Cons:
The sample represents only a fraction of the time that the toys are being produced, so it does not give a representative sample of toys from the whole day.
It is difficult to catch toys that are defective if a machine malfunctions at a time other than when the sample is taken.

28. Comparing Sampling Methods
Systematic Sampling Pros:
It generates a sample of toys produced throughout the day.
Systematic Sampling Cons:
You need to spend the entire day to collect the sample.
The machines place the toys on the conveyor belt in the same order each time. So, if you choose an interval that is a multiple of 2, 3, or 4 your sample would not include toys from all of the machines.

29. Comparing Sampling Methods
Use systematic sampling with an interval of 5. This will give a representative sample of 600/5 or 125 toys produced by all six machines throughout the day.

30. Comparing Sampling Methods
You want to know how many students in your school are double-jointed. If there are 400 students in your school, tell whether you would choose a sample of 20 students using either convenience or systematic sampling. Justify your choice of sampling method.

31. Comparing Sampling Methods
The trait of being double-jointed is most likely spread out throughout the school so that any group of students would produce a representative sample. Use convenience sampling because it is quick and produces a representative sample.

32. Comparing Sampling Methods
For what situations is each type of sampling most effective?
Convenience: available members are representative of the population.
Systematic: the population pattern’s interval doesn’t match the sampling interval or there’s no pattern.
Simple random: you need a representative sample and are able to choose randomly.