Science Institute Statistical Analysis
Mrs. Speirs
Name __________________________________________ Period ____
Directions: Using the sample data and a 0.05 significance level, test the claim that the color distribution is as claimed by Mars, Inc.
Problem
Mars, Inc. claims that its M&M plain candies are distributed with the color percentages of 30% brown, 20% yellow, 20% red, 10% orange, 10% green, and 10% blue. The colors of the M&Ms listed are summarized in Table 10-4.
|
Frequencies of M&M Plain Candies |
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|
Brown |
Yellow |
Red |
Orange |
Green |
Blue |
|
|
Observed Frequency |
33 |
26 |
21 |
8 |
7 |
5 |
|
Expected Frequency |
30 |
20 |
20 |
10 |
10 |
10 |
H0: pbr = 0.3 and py = 0.2 and pr = 0.2 and po = 0.1 and pg = 0.1 and pbl = 0.1
H1: At least one of the above proportions is different from the claimed value.
|
Calculating the X2 Test Statistic for M&M Data |
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|
Color category |
Observed frequency |
Expected frequency |
O - E |
(O-E)2 |
(O-E)2 E |
|
Brown |
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|
Yellow |
|||||
|
Red |
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|
Orange |
|||||
|
Green |
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|
Blue |
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|
100 |
100 |
X2 = E (O-E)2 E |
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What are the degrees of freedom?
What is the critical value for X2?
What is the test statistic for X2?
Is the null hypothesis rejected or accepted? Why?