# Chapter 1. Simple Random Sample

## Introduction

Statistical Applets

Set the population size, then set the sample size n and click the SAMPLE button to take a sample. Click RESET to move all the balls back from the Sample area into the "Population hopper".

Click the "Quiz Me" button to complete the activity.

A sample selected in such a way that every sample of the desired size is equally likely to be chosen is called a simple random sample (SRS). This applet lets you randomly sample a population of lotto balls, where the population size can be set anywhere between 1 and 144.

### Question 1.1

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2
Correct.
To calculate the population mean, add up the values of each of the balls in the population (1, 2, 3, 4, 5, 6, 7, 8, 9, and 10), and divide by the number of balls in the population (10). Try again.
Incorrect.

### Question 1.2

2
Correct.
The average sample mean should be equal to the population mean. Try again.
Incorrect.

### Question 1.3

Take three random samples of 3 balls each from your population of 10 balls. After taking each sample, enter the sample's mean below (accurate to one decimal place):

Sample 1: Ho78jnU6U9Yzazz+zh1GTOUFhH5hiy+EE47TnyCiWiqAE7PZnF2XUmMz1j5Fbzer

3
First generate a sample of 3 balls from a population of 10. Then calculate the mean of that sample and enter it in the blank.
Incorrect. The correct mean is shown above in green.
Great job.

### Question 1.4

Sample 2: Ho78jnU6U9Yzazz+zh1GTOUFhH5hiy+EE47TnyCiWiqAE7PZnF2XUmMz1j5Fbzer

3
First generate a sample of 3 balls from a population of 10. Then calculate the mean of that sample and enter it in the blank.
Incorrect. The correct mean is shown above in green.
Great job.

### Question 1.5

Sample 3: Ho78jnU6U9Yzazz+zh1GTOUFhH5hiy+EE47TnyCiWiqAE7PZnF2XUmMz1j5Fbzer

3
First generate a sample of 3 balls from a population of 10. Then calculate the mean of that sample and enter it in the blank.
Incorrect. The correct mean is shown above in green.
Great job.

### Question 1.6

Pon80uY6Fcvulg/gc3WjjEIewMO2enLE8c8qeN9pQnmtTPZIiWFL8ZqqdQZ2NQz3VvNzf+X73fs5dGV+2ubYAEEfbb2c5P5WFl9yLNSJtSTB2syjLurPBh0JS+9M4opopeuv3ZBeEYW5R+6S8t4ecSSA5RrKVcpT0BIatpU4/Zq2KMOmrUt+V2CCUcva0LLG8OtEzcfNQ5kquImRltufbr1JVvZt5bfWroT+m8OkGXmOaFJK
The actual average sample mean will almost never be exactly equal to the theoretical average sample mean, because random samples are (as their name implies) random. However, the distribution of sample means should always be centered around the theoretical average, and over the course of many samples, the average sample mean should approach the theoretical value.