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### Chapter 5

Section 1 – Part 2

Samples: Good & Bad

- What makes a sample bad?
- What type of “bad” sampling did we discuss previously?

Sampling Design

- Choosing a sample by chance avoids bias by giving all individuals an equal chance to be chosen
- refers to the method used to choose the sample from the population

Simple Random Sample

- every individual has an equal chance of being selected
- Draw names out of a hat; limited uses for small populations
- Table of Random Digits; limited uses for small populations
- Computer - generated software, calculators; large populations

Examples

- Suppose we were to take an SRS of 100 BHS students – put each students’ name in a hat. Then randomly select 100 names from the hat. Each student has the same chance to be selected!
- Not only does each student has the same chance to be selected – but every possible group of 100 students has the same chance to be selected! Therefore, it has to be possible for all 100 students to be seniors in order for it to be an SRS!

Random Digit Table

- Label – Assign a numerical label to every individual in the population. Be sure that all labels have the same number of digits. EX: If you have 20 individuals in the population you must assign everyone a two-digit number, 00-19 or 01-20. If you have 8 individuals in your population you can assign one-digit numbers, 0-7 or 1-8
- Table- Choose a line to begin with and use random digits to select labels at random.

Example

- The AP Institute needs to select 5 educators to write this years AP exam out of the 100 College Statistics Professors.
- We will start by assigning each professor a number from 00-99. Use the random number table below to select the 5 educators that will write the exam this year.
1 9 2 2 3 9 5 0 3 4 0 5 7 5 6 2 8 7 1 3 9 6 4 0 9 1 2 5 3 1 4 2 5 4 4 8 2 8 5 3 7 3 6 7 6 4 7 1 5 0 9 9 4 0 0 0 1 9 2 7 2 7 7 5 4 4 2 6 4 8 8 2 4 2 5

Find the professors that are associated with these numbers, and call them to tell them they have been selected.

SRS with Technology

- Using a calculator
- Press Math
- Select PRB
- Choose 5 r and Int(Fill in the range, # of individuals to be chosen then close)
- Example (1, 30 , 5) for 30 individuals, choose 5
- Enter

Does SRS work?

- Class Activity
- Everyone convert your height into inches
- When called on, everyone will give me your height
- Everyone will take a sample of 6 people. Use your calculator to select your 6 classmates. Find out their height, and average it.

- How does your mean compare to that of population?
- How could you have gotten closer to the population mean?

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