A manufacturer of colored candies states that 13% of the candies in a bag should be brown, 14% yellow, 13% red, 24% blue, 20% orange, and 16% green. A student randomly selected a bag of colored candies. He counted the number of candies of each color and obtained the results shown in the table. Test whether the bag of colored candies follows the distribution stated above at the α=0.05 level of significance.
A manufacturer of colored candies states that 13% of the candies in a bag should be brown, 14% yellow, 13% red, 24% blue, 20% orange, and 16% green. A student randomly selected a bag of colored candies. He counted the number of candies of each color and obtained the results shown in the table. Test whether the bag of colored candies follows the distribution stated above at the α=0.05 level of significance.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
A manufacturer of colored candies states that 13% of the candies in a bag should be brown, 14% yellow, 13% red, 24% blue, 20% orange, and 16% green. A student randomly selected a bag of colored candies. He counted the number of candies of each color and obtained the results shown in the table. Test whether the bag of colored candies follows the distribution stated above at the α=0.05 level of significance.
Determine the correct null and alternative hypothesis.
Compute the expected counts for each color:
| Color | Frequency | Expected Count |
| Brown | 59 | |
| Yellow | 63 | |
| Red | 55 | |
| Blue | 60 | |
| Orange | 85 | |
| Green | 65 |
Group of answer choices
50.31, 54.18, 50.31, 92.88, 77.40, 61.92 (respectively)
49.33, 53.84, 54.31, 88.78, 72.40, 66.12 (respectively)
30.31, 51.19, 50.31, 89.81, 61.20, 57.29 (respectively)
59, 63, 55, 60, 85, 65 (respectively)
What is the test statistic?
Group of answer choices
12.746
20.186
15.913
9.025
What is the P-value?
Group of answer choices
0.007
0.019
0.986
0.220
Based on the results, do the colors follow the same distribution as stated in the problem?
A. Do not reject \(H_0. \\)There is sufficient evidence that the distribution of colors is not the same as stated by the manufacturer.
B. Reject \(H_0. \\)There is sufficient evidence that the distribution of colors is not the same as stated by the manufacturer.
C. Do not reject \(H_0. \\)There is not sufficient evidence that the distribution of colors is not the same as stated by the manufacturer.
D. Reject \(H_0. \\)There is not sufficient evidence that the distribution of colors is not the same as stated by the manufacturer.
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