Download Lesson 7.1.1 Distributions of Sample Proportions

 STATWAY® STUDENT HANDOUT | 1 Lesson 7.1.1 Distributions of Sample Proportions
STUDENT NAME DATE INTRODUCTION The population proportion of all blue M&M’s, that is, the fraction of all M&M’s in the world that are blue, is an example of a parameter. The proportion of blue M&M’s in a sample is an example of a statistic. Statistics are often used to estimate parameters or to test claims made about population parameters. In this activity we will gather multiple samples from a population. In each sample we will find a sample proportion. For example, we may find a sample proportion of blue M&M’s in a Halloween M&M’s package. However, another child’s Halloween M&M’s package may have a different sample proportion of blue M&M’s. Different samples may produce different sample proportions. These proportions are just a small part of the collection of all sample proportions. A sampling distribution is the distribution of values for all of the sample proportions. Population Sample Collection of all M&M’s 25 M&M’s Parameter Statistic Proportion of blue candy in the population, ! Proportion of blue candy in sample, ! TRY THESE You have been given a cup that contains a random sample of 25 M&M’s candies. 1 Count the colors of candies in your sample and fill in the chart below: Blue Brown Green Orange Red Number of candies Proportion of candies © 2013 THE CARNEGIE FOUNDATION FOR THE ADVANCEMENT OF TEACHING A PATHWAY THROUGH STATISTICS, VERSION 2.5, STATWAY® -­‐ STUDENT HANDOUT Yellow Total STATWAY® STUDENT HANDOUT | 2 Lesson 7.1.1 Distributions of Sample Proportions 2 In the table on the board, record the number of blue candies and the proportion of blue candies in your sample. Plot the proportion of blue candies in your sample on the dotplot on the board. 3 Plot the numbers and proportions gathered by the entire class on the dotplots below. Numbers of Blue Candies
frequency
12
10
8
6
4
2
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
0
number of blue candies
Proportions of Blue Candies
frequency
12
10
8
6
4
2
1.00
0.96
0.92
0.88
0.84
0.80
0.76
0.72
0.68
0.64
0.60
0.56
0.52
0.48
0.44
0.40
0.36
0.32
0.28
0.24
0.20
0.16
0.12
0.08
0.04
0.00
0
proportion of blue candies
4 Did everyone have the same proportion of blue candies? © 2013 THE CARNEGIE FOUNDATION FOR THE ADVANCEMENT OF TEACHING A PATHWAY THROUGH STATISTICS, VERSION 2.5, STATWAY® -­‐ STUDENT HANDOUT STATWAY® STUDENT HANDOUT | 3 Lesson 7.1.1 Distributions of Sample Proportions A sampling distribution of sample proportions is the distribution of all possible sample proportions from samples of a given size (the same size). Your class just constructed a dotplot that is only part of the entire sampling distribution of sample proportions. 5 What does the distribution of sample proportions look like? What is its shape? Where is its center? How much spread does it appear to have? Write a description of the distribution that you see. 6 A distribution of sample proportions holds a lot of clues about an unknown population parameter. The unknown parameter in our case is the true proportion of blue candies in the population of all M&M’s candies. What is your best guess for this population parameter? Population All M&M’s candies. Unknown Population Parameter The proportion of all M&M’s that are blue. We give this parameter the symbol !. The cups of 25 M&M’s. Samples Known Sample Statistics Sampling Distribution for the Unknown Population Parameter Distribution of Sample Statistics The proportions of blue candies in each cup. We give each of these statistics the symbol !. The distribution of sample statistics from all possible samples of a given size. The distribution in our dotplot. Since every cup contained 25 M&M’s, this distribution is part of a sampling distribution for the population parameter. © 2013 THE CARNEGIE FOUNDATION FOR THE ADVANCEMENT OF TEACHING A PATHWAY THROUGH STATISTICS, VERSION 2.5, STATWAY® -­‐ STUDENT HANDOUT STATWAY® STUDENT HANDOUT | 4 Lesson 7.1.1 Distributions of Sample Proportions YOU NEED TO KNOW In the space below, write definitions that describe each of these concepts. CONCEPT WHAT I THINK IT MEANS Population Sample Parameter Statistic Distribution of Sample Proportions: NEXT STEPS In Part 2 of this lesson, you will continue simulating part of a sampling distribution of the sample proportions of blue M&M’s. You are going to use a computer to do the simulation. Counting out candies is time consuming and inefficient. Computers can help us do a better job of simulating a distribution of sample proportions. We will now use a computer applet to simulate more sample proportions. To do this simulation, you will need a value for the population proportion, p, of all M&M’s that are blue, and you will need a sample size, n. © 2013 THE CARNEGIE FOUNDATION FOR THE ADVANCEMENT OF TEACHING A PATHWAY THROUGH STATISTICS, VERSION 2.5, STATWAY® -­‐ STUDENT HANDOUT