CHAPTER 1.2

CHAPTER 1 GETTING STARTED

PART 2 – Random Samples

OBJECTIVE(S):

·  Students will learn the definition of a simple random sample.

·  Students will learn how to generate a sample using a random number table and the random number generator in your calculator.

·  Students will learn the definition of a simulation and how to use random numbers to conduct a simulation.

·  Students will learn the definitions of the five basic sampling techniques.

Simple Random Sample -

a.

b.

EXAMPLE 5: SIMPLE RANDOM SAMPLE

Is open space around metropolitan areas important? Players of the Colorado Lottery might think so, because some of the proceeds of the game go to fund open space and outdoor recreational space. To play the game, you pay one dollar and choose any six different numbers from the group of number 1 through 42. If your group of six numbers matches the winning group of six numbers selected by simple random sampling, then you are a winner of a grand prize of at least 1.5 million dollars.

a.  Is the number 25 as likely to be selected in the winning group of six numbers as the number 5?

b.  Could all the winning numbers be even?

c.  Your friend always plays the numbers

1 2 3 4 5 6

Could she ever win?

EXAMPLE 6: RANDOM-NUMBER TABLE

Use a random-number table to pick a random sample of 30 cars from a population of 500 cars.

SOLUTION:

Again, we assign each car a different number between ___ and ____, inclusive. Then we use the random-number table to choose the sample. Table 1 in the Appendix has ____ rows and ____ blocks of five digits each;

You can read the digits by beginning anywhere in the table. You can start at the beginning of any row or block. Let’s begin at row 15, block 5. If we need more digits, we’ll move on to row 16, and so on. The digits begin with are

Since the highest number assigned to a car is ______, and this number has ______digits, we regroup our digits into blocks of 3:

To construct our random sample, we use the first _____ car numbers we encounter in the random-number table when we start at row 15, block 5. We skip the first three groups - ______, ______, and ______. Why?

The next group of three digits is ______, which corresponds to _____. Car number ____ is the first car included in our sample, and the next is car number ______. We skip the next ______groups and then include car number ______and ______. To get the rest of the cars in the sample, we continue to the n0065t line and use the random-number table in the same fashion. What do we do if we encounter a number we’ve used before?

When we use the term ______, we have very specific criteria in mind for selecting the sample. One proper method for selecting a simple random sample is to use a computer-based or calculator-based random number generator or to use a table of random numbers as we have done in the example. The term ______should not be confused with ______.

How to draw a random sample:

  1. Number all members of the population ______.
  2. Use a table, calculator, or computer to select ______from the numbers assigned to the population members.
  3. Create the sample by using population members with numbers corresponding to those randomly selected.

Simulation -

EXAMPLE 7: SIMULATION

Use a random-number table to simulate the outcomes of tossing a balanced (that is, fair) penny 10 times.

a.)  How many outcomes are possible when you toss a coin once?

b.)  There are several ways to assign numbers to the two outcomes. Because we assume a fair coin, assign an even digit to the outcome heads and an odd digit to the outcome tails. Then, starting at row 2, and block 3 of Table 1 in the Appendix, list the first 10 single digits.

c.)  What are the outcomes associated with the 10 digits?

d.)  If you start in a different block and row of Table 1 in the Appendix, will you get the same sequence of outcomes?

Sampling with Replacement -

Stratified Sampling -

Systematic Sampling –

Cluster Sampling –

Convenience Sampling -