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1.11 You are going to use the random number generator to generate different types of samples from the data.

This table displays six sets of quiz scores (each quiz counts 10 points) for an elementary statistics class.

Instructions: Use the Random Number Generator to pick samples.

1. Create a stratified sample by column. Pick three quiz scores randomly from each column.

â—¦ Number each row one through ten.

â—¦ On your calculator, press Math and arrow over to PRB.

â—¦ For column 1, Press 5:randInt( and enter 1,10). Press ENTER. Record the number. Press ENTER 2 more

times (even the repeats). Record these numbers. Record the three quiz scores in column one that correspond

to these three numbers.

â—¦ Repeat for columns two through six.

â—¦ These 18 quiz scores are a stratified sample.

2. Create a cluster sample by picking two of the columns. Use the column numbers: one through six.

â—¦ Press MATH and arrow over to PRB.

â—¦ Press 5:randInt( and enter 1,6). Press ENTER. Record the number. Press ENTER and record that number.

â—¦ The two numbers are for two of the columns.

â—¦ The quiz scores (20 of them) in these 2 columns are the cluster sample.

3. Create a simple random sample of 15 quiz scores.

â—¦ Use the numbering one through 60.

â—¦ Press MATH. Arrow over to PRB. Press 5:randInt( and enter 1, 60).

â—¦ Press ENTER 15 times and record the numbers.

â—¦ Record the quiz scores that correspond to these numbers.

â—¦ These 15 quiz scores are the systematic sample.

4. Create a systematic sample of 12 quiz scores.

â—¦ Use the numbering one through 60.

â—¦ Press MATH. Arrow over to PRB. Press 5:randInt( and enter 1, 60).

â—¦ Press ENTER. Record the number and the first quiz score. From that number, count ten quiz scores and

record that quiz score. Keep counting ten quiz scores and recording the quiz score until you have a sample

of 12 quiz scores. You may wrap around (go back to the beginning).

Step by step solution

01

Step-1 (a) Explanation

In order to select the three numbers from each column of the given table, first mark each row from 1 to 10. To get the three numbers from the first column, use a TI-83. To open the randInt() function of the calculator, click on the MATH button and then scroll to the PRB option and then press 5. Enter 1,10 in the function and press the enter button three times to select three numbers. See the screenshot below:

As can be seen in the screenshot above, both the first column and the second column of the table have numbers below them $8^{\text{th}},1^{\text{st}}\text{and}{4}^{\text{th}}$. Each row will select 3 random numbers. The numbers will be 8,5 and 9. Similarly, repeat the above process to have 3 random numbers for each of columns 2,3,4,5, and 6.

02

Step-2 (b) Explanation

Cluster sampling:

During cluster sampling, the investigator divides the population into several clusters and then selects several clusters at random. The investigator then studies all the members of these clusters.

03

Step-3(c) Create a simple random sample of 15 quiz scores.

Simple random sampling:

A simple random sampling is one in which each individual unit of the population has an equal chance of being included in the sample. In order to select the sample, the researcher uses a variety of techniques like a random number table, the lottery method, etc.

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Step-4(d) A systematic sample of 15 quiz scores will be created.

Systematic sampling:

To perform this type of sampling, the investigator first randomly selects the starting point from the population and then collects data from$n^{\text{th}}$Population data from the listing.

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