Compute the expected counts for each color. Color Brown Yellow Red Blue Orange Green Frequency 59 65 57 59 99 64 What is the test statistic? x² = Expected Count 52.39 56.42 52.39 96.72 80.60 64.48 (Round to two decimal places as needed.) (Round to three decimal places as needed.)
Compute the expected counts for each color. Color Brown Yellow Red Blue Orange Green Frequency 59 65 57 59 99 64 What is the test statistic? x² = Expected Count 52.39 56.42 52.39 96.72 80.60 64.48 (Round to two decimal places as needed.) (Round to three decimal places as needed.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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What is the test statistic?
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![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 \( \alpha = 0.05 \) level of significance. Using the level of significance \( \alpha = 0.05 \), test whether the color distribution is the same.
**Click here to view the table. Click here to view the table of critical values of the chi-square distribution.**
### Table: Expected Counts for Each Color
| Color | Frequency | Expected Count |
|--------|-----------|----------------|
| Brown | 59 | 52.39 |
| Yellow | 65 | 56.42 |
| Red | 57 | 52.39 |
| Blue | 59 | 96.72 |
| Orange | 99 | 80.60 |
| Green | 64 | 64.48 |
*(Round to two decimal places as needed.)*
**What is the test statistic?**
\[ \chi^2_0 = \text{□} \]
*(Round to three decimal places as needed.)*
### Diagram Explanation
The table above presents the observed and expected frequencies for each color of candy. The expected counts are based on the manufacturer's specified percentage distribution applied to the total count of candies. The chi-square test will compare these observed and expected frequencies to determine if the actual color distribution significantly deviates from the expected distribution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb0ce43c-1343-4636-bcaf-407be51cc0c4%2Ffa9191e5-19a7-460d-9ca0-1fdc8e39e5fb%2Fjcky4yf_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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 \( \alpha = 0.05 \) level of significance. Using the level of significance \( \alpha = 0.05 \), test whether the color distribution is the same.
**Click here to view the table. Click here to view the table of critical values of the chi-square distribution.**
### Table: Expected Counts for Each Color
| Color | Frequency | Expected Count |
|--------|-----------|----------------|
| Brown | 59 | 52.39 |
| Yellow | 65 | 56.42 |
| Red | 57 | 52.39 |
| Blue | 59 | 96.72 |
| Orange | 99 | 80.60 |
| Green | 64 | 64.48 |
*(Round to two decimal places as needed.)*
**What is the test statistic?**
\[ \chi^2_0 = \text{□} \]
*(Round to three decimal places as needed.)*
### Diagram Explanation
The table above presents the observed and expected frequencies for each color of candy. The expected counts are based on the manufacturer's specified percentage distribution applied to the total count of candies. The chi-square test will compare these observed and expected frequencies to determine if the actual color distribution significantly deviates from the expected distribution.
Transcribed Image Text:**Observed Distribution of Colors**
This data represents the distribution of colored candies in a bag, presented in tabular form. The table is divided into two rows for each color, listing the observed frequency and claimed proportion.
| Color | Frequency | Claimed Proportion |
|--------|-----------|--------------------|
| Brown | 59 | 0.13 |
| Yellow | 65 | 0.14 |
| Red | 57 | 0.13 |
| Blue | 59 | 0.24 |
| Orange | 99 | 0.20 |
| Green | 64 | 0.16 |
**Explanation:**
- **Frequency**: This column lists the number of times each color appears in the sample bag of candies.
- **Claimed Proportion**: This column shows the expected or claimed proportion of each color in the overall distribution.
Each color has a corresponding frequency and a claimed proportion, helping in the analysis of whether the observed distribution aligns with the claimed distribution proportions.
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