Question
In: Statistics and Probability
The distribution of M&M colors is 24% blue, 20% orange, 16% green, 14% yellow, 13% red,...
The distribution of M&M colors is 24% blue, 20% orange, 16% green, 14% yellow, 13% red, and 13% brown.
You have a small bag of M&M's and count the colors. Your bag has 9 blue, 9 orange, 4 green, 12 yellow, 3 red, and 6 brown M&M's.
Before you begin, how many M&M's do you need in your sample (minimum) to be able to do this test? Remember, your assumption for chi-square is that every expected frequency has at least 5 in the cell, that is, if the calculated E is less than 5, you cannot do the problem.
The assumption here is E >/= 5, where E = n(p).
Find the Test statistic
What is the critical value? CV(chi-square)
What was your decision regarding the null?
What does your data show? In words.
Solutions
Expert Solution
Assuming level of significance to be 5%.
| Chi-Square Goodness of Fit test |
| (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: H0: p1 =0.24, p2 =0.2, p3=0.16, p4=0.14, p5 =0.13, p6=0.13 Ha: Some of the population proportions differ from the values stated in the null hypothesis This corresponds to a Chi-Square test for Goodness of Fit. (2) Degrees of Freedom The number of degrees of freedom is df=n-1=6-1=5 
(3) Test Statistics The Chi-Squared statistic is computed as follows: 
(4)Critical Value and Rejection Region Based on the information provided, the significance level is α=0.05, the number of degrees of freedom is df=n-1=6-1=5, so the critical value becomes 11.0705. Then the rejection region for this test is R={χ2:χ2>11.0705}. (5)P-value The P-value is the probability that a chi-square statistic having 5 degrees of freedom is more extreme than 11.0705. The p-value is p=Pr(χ2>8.5634)=0.1278 (6) The decision about the null hypothesis Since it is observed that χ2=8.5634≤χc2=11.0705, it is then concluded that the null hypothesis is not rejected. (7) Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is NOT enough evidence to claim that some of the population proportions differ from those stated in the null hypothesis, at the α=0.05 significance level. |
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orchestra answered 2 years agoRelated Solutions
M&M'S MILK CHOCOLATE: 24% cyan blue, 20% orange, 16% green, 14% bright yellow, 13% red, 13%...
M&M'S MILK CHOCOLATE: 24% cyan blue, 20% orange, 16%
green, 14% bright yellow, 13% red, 13% brown.
Each large production batch is blended to those ratios and
mixed thoroughly. However, since the individual packages are filled
by weight on high-speed equipment, and not by count, it is possible
to have an unusual color distribution.
Part 1: Confidence Interval for Small n
Milk Chocolate M&M’s come in 6 colors; blue, orange, green,
yellow, red, and brown.
Choose the color of M&M’s...
M&M'S MILK CHOCOLATE: 24% cyan blue, 20% orange, 16% green, 14% bright yellow, 13% red, 13%...
M&M'S MILK CHOCOLATE: 24% cyan
blue, 20% orange, 16% green, 14% bright yellow, 13% red, 13%
brown.
Each large production batch is
blended to those ratios and mixed thoroughly. However, since the
individual packages are filled by weight on high-speed equipment,
and not by count, it is possible to have an unusual color
distribution.
1. Treat your bag of M&M's as a simple random sample
and:
a. Count the following --
Number of GREEN M&M's: 9
Total number of M&M's:...
M&M'S MILK CHOCOLATE: 24% cyan blue, 20% orange, 16% green, 14% bright yellow, 13% red, 13%...
M&M'S MILK CHOCOLATE: 24% cyan
blue, 20% orange, 16% green, 14% bright yellow, 13% red, 13%
brown.
Confidence Interval for Small n
Choose the color of M&M’s you will
be working with for this project
Color:
Using the collected data below from a single fun-sized bag,
provide the frequency and proportion of M&M’s in your color of
choice.
Red
Orange
Yellow
Green
Blue
Brown
2
1
2
3
5
1
Number of M&M's in your
color:
Total number of
M&M's:...
Milk Chocolate M&M’s come in 6 colors; blue, orange, green, yellow, red, and brown. 1. Choose...
Milk Chocolate M&M’s come in 6 colors; blue, orange,
green, yellow, red, and brown.
1. Choose your favorite color of M&M’s you will be working
with for this project. State the color and give the counts
below.
Color of choice:
Number of M&M's in your color:
Total number of M&M's:
Proportion of M&M's in your color:
2. Construct a 95% confidence interval for the proportion of
M&M’s one can expect to find in the color of your choice.
3. Give...
Bag Blue Orange Green Yellow Red Brown Total Number of Candies 1 9 13 14 10...
Bag
Blue
Orange
Green
Yellow
Red
Brown
Total Number of Candies
1
9
13
14
10
7
7
60
2
13
10
6
9
9
8
55
3
13
12
4
10
9
6
54
4
16
13
8
6
6
8
57
5
10
10
12
5
15
4
56
6
9
18
3
6
12
12
60
7
11
13
6
15
8
6
59
8
12
18
5
9
6
5
55
9
12
10
8
15...
Bag Blue Orange Green Yellow Red Brown Total Number of Candies 1 9 13 14 10...
Bag
Blue
Orange
Green
Yellow
Red
Brown
Total Number of Candies
1
9
13
14
10
7
7
60
2
13
10
6
9
9
8
55
3
13
12
4
10
9
6
54
4
16
13
8
6
6
8
57
5
10
10
12
5
15
4
56
6
9
18
3
6
12
12
60
7
11
13
6
15
8
6
59
8
12
18
5
9
6
5
55
9
12
10
8
15...
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Colored Candies in a bag
Color
Brown
Yellow
Red
Blue
Orange
Green
Frequency
61
67
57...
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