Mars, Inc. states that 16% of all milk chocolate M&M’S® produced are green. A group of students took the following samples from a bowl of 500 mixed up M&M’S®. (see attachment) Why can we not realistically calculate the population parameter of interest directly? How could the concept of random sampling be used to investigate the population parameter of interest? What are we interested in finding out about each of the samples of M&M’S®?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Mars, Inc. states that 16% of all milk chocolate M&M’S® produced are green. A group of students took the following samples from a bowl of 500 mixed up M&M’S®. (see attachment)

  1. Why can we not realistically calculate the population parameter of interest directly?
  2. How could the concept of random sampling be used to investigate the population parameter of interest?
  3. What are we interested in finding out about each of the samples of M&M’S®?
Sample #
1234567
8
9
10
11
12
13
Sample Proportions for n = 30
14
15
16
17
18
19
20
Proportion of green M&M's
5/30 = 0.17
6/30 = 0.20
3/30 = 0.10
8/30 = 0.27
3/30 = 0.10
3/30 = 0.10
6/30 = 0.20
5/30 = 0.17
7/30 = 0.23
3/30 = 0.10
3/30 = 0.10
4/30 = 0.13
7/30 = 0.23
5/30 = 0.17
5/30 = 0.17
1/30 = 0.03
6/30 = 0.20
8/30 = 0.27
1/30 = 0.03
5/30 = 0.17
Sample #
12345678
9
10
11
12
13
14
15
16
17
Sample Proportions for n = 60
18
19
20
Proportion of green M&M's
12/60 = 0.20
15/60 = 0.25
14/60 = 0.23
7/60 = 0.12
10/60 = 0.17
10/60 = 0.17
11/60 = 0.28
7/60 = 0.12
8/60 = 0.13
10/60 = 0.17
8/60 = 0.13
11/60 = 0.18
6/60 = 0.10
11/60 = 0.18
12/60 = 0.20
10/60 = 0.17
12/60 = 0.20
11/60 = 0.18
13/60 = 0.22
8/60 = 0.13
Transcribed Image Text:Sample # 1234567 8 9 10 11 12 13 Sample Proportions for n = 30 14 15 16 17 18 19 20 Proportion of green M&M's 5/30 = 0.17 6/30 = 0.20 3/30 = 0.10 8/30 = 0.27 3/30 = 0.10 3/30 = 0.10 6/30 = 0.20 5/30 = 0.17 7/30 = 0.23 3/30 = 0.10 3/30 = 0.10 4/30 = 0.13 7/30 = 0.23 5/30 = 0.17 5/30 = 0.17 1/30 = 0.03 6/30 = 0.20 8/30 = 0.27 1/30 = 0.03 5/30 = 0.17 Sample # 12345678 9 10 11 12 13 14 15 16 17 Sample Proportions for n = 60 18 19 20 Proportion of green M&M's 12/60 = 0.20 15/60 = 0.25 14/60 = 0.23 7/60 = 0.12 10/60 = 0.17 10/60 = 0.17 11/60 = 0.28 7/60 = 0.12 8/60 = 0.13 10/60 = 0.17 8/60 = 0.13 11/60 = 0.18 6/60 = 0.10 11/60 = 0.18 12/60 = 0.20 10/60 = 0.17 12/60 = 0.20 11/60 = 0.18 13/60 = 0.22 8/60 = 0.13
Dot Plots for Sample Proportions of Green M&M's for Sample Sizes n = 30 and n = 60
0
0.05
0.05
0.1
0.15
0.1
Proportion of Green M&M's
Sample Size n = 30
0.2
0.15
0.2
Proportion of Green M&M's
Sample Size n = 60
0.25
0.25
0.3
0.3
Transcribed Image Text:Dot Plots for Sample Proportions of Green M&M's for Sample Sizes n = 30 and n = 60 0 0.05 0.05 0.1 0.15 0.1 Proportion of Green M&M's Sample Size n = 30 0.2 0.15 0.2 Proportion of Green M&M's Sample Size n = 60 0.25 0.25 0.3 0.3
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