The manufacturer of a certain candy states that 13% of the candies are brown, 24% yellow, 14% red, 23% blue, 15% orange, 11% green. A student randomly selected a giant bag of candy and counted the number of each color. The results are in the table below. Does the candy follow the stated distribution? (a) Complete the table. Report all answers accurate to 2 decimal places. Color Yellow Red Blue Frequency 31 18 50 Expected Frequency Brown 38 Orange 22 Green 22
The manufacturer of a certain candy states that 13% of the candies are brown, 24% yellow, 14% red, 23% blue, 15% orange, 11% green. A student randomly selected a giant bag of candy and counted the number of each color. The results are in the table below. Does the candy follow the stated distribution? (a) Complete the table. Report all answers accurate to 2 decimal places. Color Yellow Red Blue Frequency 31 18 50 Expected Frequency Brown 38 Orange 22 Green 22
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![**Candy Color Distribution Analysis**
The manufacturer of a certain candy states that their candies come in the following color distributions: 13% brown, 24% yellow, 14% red, 23% blue, 15% orange, and 11% green. A student randomly selected a giant bag of candy and counted the number of each color. The results are tabulated below. The question posed is whether the actual candy distribution aligns with the manufacturer's stated distribution.
**(a) Complete the table. Report all answers accurate to 2 decimal places.**
| Color | Brown | Yellow | Red | Blue | Orange | Green |
|--------|-------|--------|-----|------|--------|-------|
| Frequency | 38 | 31 | 18 | 50 | 22 | 22 |
| Expected Frequency | | | | | | |
**(b) Select the null and alternative hypotheses.**
1. \( H_0: P_{Br} = P_Y = P_R = P_{BL} = P_O = P_G = \frac{1}{6} \)
\( H_a: \) at least one proportion is different
2. \( H_0: \) The colors are independent
\( H_a: \) The colors are dependent
3. \( H_0: P_{Br}=0.13, P_Y=0.24, P_R=0.14, P_{BL}=0.23, P_O=0.15, P_G=0.11 \)
\( H_a: \) at least one proportion is different
**(c) What is the chi-square test statistic for this data? Round your answer to 3 decimals.**
\[ \chi^2 = \]
**(d) What is the P-Value? Round your answer to 4 decimals.**
P-Value = ______
This analysis involves comparing the observed frequencies of candy colors to the expected frequencies as stipulated by the manufacturer using a chi-square test to determine if the observed distribution fits the expected distribution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee710977-90c8-4f84-9cb1-1102aa3efb9b%2F3606db46-c372-468b-8ba5-8d303b5be20d%2Fo39os6h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Candy Color Distribution Analysis**
The manufacturer of a certain candy states that their candies come in the following color distributions: 13% brown, 24% yellow, 14% red, 23% blue, 15% orange, and 11% green. A student randomly selected a giant bag of candy and counted the number of each color. The results are tabulated below. The question posed is whether the actual candy distribution aligns with the manufacturer's stated distribution.
**(a) Complete the table. Report all answers accurate to 2 decimal places.**
| Color | Brown | Yellow | Red | Blue | Orange | Green |
|--------|-------|--------|-----|------|--------|-------|
| Frequency | 38 | 31 | 18 | 50 | 22 | 22 |
| Expected Frequency | | | | | | |
**(b) Select the null and alternative hypotheses.**
1. \( H_0: P_{Br} = P_Y = P_R = P_{BL} = P_O = P_G = \frac{1}{6} \)
\( H_a: \) at least one proportion is different
2. \( H_0: \) The colors are independent
\( H_a: \) The colors are dependent
3. \( H_0: P_{Br}=0.13, P_Y=0.24, P_R=0.14, P_{BL}=0.23, P_O=0.15, P_G=0.11 \)
\( H_a: \) at least one proportion is different
**(c) What is the chi-square test statistic for this data? Round your answer to 3 decimals.**
\[ \chi^2 = \]
**(d) What is the P-Value? Round your answer to 4 decimals.**
P-Value = ______
This analysis involves comparing the observed frequencies of candy colors to the expected frequencies as stipulated by the manufacturer using a chi-square test to determine if the observed distribution fits the expected distribution.
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