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Section 1.3 Simple Random Sampling

Definition 1.3.1. random sampling.
using chance (an objective device) to select individuals from a population to be included in the sample
Definition 1.3.2. simple random sample.
every sample of a certain size is equally likely (and every subject has an equal chance of being selected)
Definition 1.3.3. \(N\).
population size
Definition 1.3.4. \(n\).
sample size
Definition 1.3.5. frame.
list of all individuals in a population being studied
Definition 1.3.6. sampling without replacement.
once selected, an individual cannot be chosen again
Definition 1.3.7. sampling with replacement.
once selected, individuals are placed back in the population and can be chosen again

Subsection Generating Random Numbers on the TI-84 Plus Calculator

There are several ways to generate random numbers on your calculator. One simple way is to use the randInt function.

Computation 1.3.8. Generate Random Integers.

To generate a random integer between 1 and 10:

  1. Press the math button and use the cursor to highlight the PROB tab.
  2. Select 5:randInt(
  3. Fill out the StatWizard so it looks like below
    		lower:1
		upper:10
		n:
		Paste
    Highlight Paste and press enter.
  4. Press enter to execute the function you previously pasted into the command window.
Computation 1.3.9. List of Random Integers.

To generate a list of 4 random integers between 1 and 10:

  1. Press the math button and use the cursor to highlight the PROB tab.
  2. Select 5:randInt(
  3. Fill out the StatWizard so it looks like below
    		lower:1
		upper:10
		n:4
		Paste
    Highlight Paste and press enter.
  4. Press enter to execute the function you previously pasted into the command window.
Computation 1.3.10. List of Random Integers with No Repeats.

To generate a list of 10 random integers between 1 and 20 with no repeats:

  1. Press the math button and use the cursor to highlight the PROB tab.
  2. Select 8:randIntNoRep(
  3. Fill out the StatWizard so it looks like below
    		lower:1
		upper:20
		n:10
		Paste
    Highlight Paste and press enter.
  4. Press enter to execute the function you previously pasted into the command window.

Reading Questions Four Tickets for Friends

Sophia has 10 friends that she would like to invite to a concert, but only 4 tickets to give away.

Mike, Jamie, Adam, Yvette, Ashley, Monica, Cherie, Julie, Willard, Bruce

1.
Which of the following would produce a simple random sample of the 4 friends that she will bring with her:
  1. List each persons name on a piece of paper, place them in a hat and draw 4. Answer
    yes
  2. List the names in alphabetical order and take the first 4 names. Answer
    no
  3. Ask one of her friends who she should bring. Answer
    no
  4. Number the friends from 1 to 10 and use a random number generator to produce 4 numbers between 1 and 10 which correspond to the 10 friends. Answer
    yes
2.
Use the TI graphing calculator to obtain a random sample of the 4 friends that she will bring with her and give their names. Solution

Thus she would invite Mike, Yvette, Ashley and Julie.

We can also have the calculator sort the list in ascending order:

In this case, she would invite Mike, Jamie, Monica and Willard.

Reading Questions Employee Survey

The owner of a private food store is concerned with employee morale. She decides to survey the employees to learn about work environment and job satisfaction.

1 Archer 9 Foushi 16 Kemp 23 Oliver
2 Bolcerek 10 Gow 17 Lathus 24 Orsini
3 Bryant 11 Grove 18 Lindsey 25 Salazar
4 Carlisle 12 Hall 19 Massie 26 Ullrich
5 Cole 13 Hills 20 McGuffin 27 Vaneck
6 Dimas 14 Houston 21 Musa 28 Weber
7 Ellison 15 Kats 22 Nickas 29 Zavodny
8 Everhart

1.
Obtain a simple random sample of size 6 from the above table using the TI graphing calculator. Solution
Thus the randomly selected employees are: Bolcerek, Carlisle, Musa, Vaneck, Weber, and Zavodny.
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