Explore Sampling Methods

Explore Sampling Methods

Objectives:

Learning Objective: Students will use the sampling methods to determine the sample size used in studies.

Language Objective: Students will express their reasoning in written form.

Looking Back

Recall the Spud Potato Chips scenario. You hypothesized that the true mean weight of bags of Spud’s might be less than the 28.3 grams advertised on the bags. How would you get a sample of the population of Spud Potato Chip?

Cluster Sampling Method

The most feasible method is to ask other U.S. schools to help with cluster sampling.

On a smaller scale, you could mimic this by cluster sampling from grocery stores in the area. The easiest choice (but least reliable) is convenience sampling.

Pursue the idea of cluster sampling with other schools. To do this, you simply modify random selection techniques to choose your schools. Following are two ways to use

random numbers for selection.

Method 1: Random Number Tables

Such tables can be found on the Internet by typing “random number tables” in the search box. Here is an example of what you might get:

Example: Random Number Table

If you have 100 schools and wish to select 12 of them to help with the study, you assign each school a number between 00 and 99. Then read the table from left to right and select the schools as their numbers appear.

What are the numbers of the 12 schools you will select?

Multiple Choice

To randomly select 25 basketball players from the 300 players in the NBA, I would:

• Number the players from 01-25, read 3 digits at a time from a random table, discarding repeats and numbers over 25, and then stop when I reach 25.

• Number the players from 0-299, read 2 digits at a time from a random table, discarding repeats and numbers over 299, and stop when I reach 25.

• Number the players from 01-299, read 2 digits at a time from a random table, discarding repeats and numbers over 300, and stop when I reach 25.

• Number the players from 001-300, read 3 digits at a time from a random table, discarding repeats, 000 and numbers over 300, and stop when I reach 25.

Multiple Choice

If you have 1,000 schools on the list, number them from 000 to 999 and read the table three digits at a time. What are the first five schools in this sample?

• 24, 19, 83, 72, 41

• 241, 983, 724, 152, 579

• 2419, 8372, 4152, 5761, 0849

Method 2: Random Number Generators

The same task can be accomplished with your graphing calculator or a random number generator found on the Internet.

Stratified Sampling Method

Do you remember what car you liked best when you were in 7th grade? What car do you like best now? Are the cars different because your tastes have matured or because new car styles have been introduced?

To investigate whether students’ tastes vary by grade level, students from every grade level (7–12) must be represented fairly. You decide to use a sample size of 60. Since there are six grade levels, you could randomly select 10 students from each grade.

Notice, however, that the 8th-grade class is much larger than the 12th-grade class. Should both of these grade levels have the same number of students in the sample? One way to fairly represent each grade is to use a stratified sample. Following are sample enrollment numbers.

Example: Use Stratified Sampling

Find you sample size from each grade level.

Multiple Choice

There are three age groups in a competition. The table shows the number of competitors in each age group. John wants to do a survey of the competitors. He uses a stratified sample of exactly 50 competitors according to each age group. Work out the number of competitors in each 16-18 age group that should be in his stratified sample of 50.

• 21

• 11

• 30

• 10

Multiple Choice

There are three age groups in a competition. The table shows the number of competitors in each age group. John wants to do a survey of the competitors. He uses a stratified sample of exactly 50 competitors according to each age group. Work out the number of competitors in each 19-24 age group that should be in his stratified sample of 50.

• 10

• 17

• 21

• 22

Multiple Choice

There are three age groups in a competition. The table shows the number of competitors in each age group. John wants to do a survey of the competitors. He uses a stratified sample of exactly 50 competitors according to each age group. Work out the number of competitors in each 25+ age group that should be in his stratified sample of 50.

• 17

• 18

• 12

• 10

Done

Homework due on Friday.