GENERATING A RANDOM SAMPLE USING TECHNOLOGY

We already know, how to generate random samples by rolling number cubes. We can also generate random samples by using technology.

Here, we are going to see, how to generate samples using technology (Graphing calculator). 

Example :

Each of the 200 students in a school will have a chance to vote on one of two names, Tigers or Bears, for the school’s athletic teams. A group of students decides to select a random sample of 20 students and ask them for which name they intend to vote. How can the group choose a random sample to represent the entire population of 200 students ?

Solution : 

One way to identify a random sample is to use a graphing calculator to generate random integers.

Step 1 :

Press MATH , scroll right and select PRB, then select 5 : randInt(.

Step 2 : 

Enter the least value, comma, greatest possible value. 

In this specific case, the students enter randInt (1, 200), because there are 200 students in school. 

Step 3 :

Hit ENTER 20 times to generate 20 random numbers.

The group gets a list of all the students in the school and assigns a number to each one. The group surveys the students with the given numbers.

Discussion : 

Of the 20 students surveyed, 9 chose Tigers. The percent choosing Tigers was .

What might the group infer ?

The group might infer that the name Bears will probably win, or that both names are almost equally likely to win.

Explore Activity

We can simulate multiple random samples to see how much statistical measures vary for different samples of size 20.

Let us assume that the 200 students are evenly divided among those voting for Tigers and those voting for Bears. We can generate random numbers and let each number represent a vote.

Let numbers from 1 to 100 represent votes for Tigers, and numbers from 101 to 200 represent votes for Bears.

For each simulated sample, use randInt(1, 200) and generate 20 numbers.

Perform the simulation 10 times and record how many numbers from 1 to 100 are generated.

How many of the samples indicated that there were 9 or fewer votes for Tigers ?

We have to check the results of the students.

Combine your results with those of your classmates. Make a dot plot showing the number of numbers from 1 to 100 generated in each simulation.

We have to check the results of the students.

Reflect

Question :

Suppose you wanted to simulate a random sample for the situation in the above Explore Activity without using technology. One way would be to use marbles of two different colors to represent students choosing the different names. Describe how you could perform a simulation.

Solution :

Let white represent a vote for Tigers and black represent a vote for Bears. Place 100 white marbles and 100 black marbles in a bag. Draw one without looking, record the color, replace the marble and repeat till you’ve drawn 20 marbles.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.