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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 the a=0.05 level of significance. Click the icon to view the table. Compute the expected counts for each color. Color Brown Yellow Red Blue Orange Green Frequency 61 64 54 59 97 67 Expected Co (Round to two d Observed Distribution of Colors Color Frequency Claimed Proportion Colored Candies in a bag Brown Yellow Red Blue 61 64 59 0.13 0.14 0.24 Print 0.13 Done Orange Green 97 67 0.20 0.16

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 a=0.05 level of significance. Click the icon to view the table. Compute the expected counts for each color. Color Brown Yellow Red Blue Orange Green Frequency 61 64 54 59 97 67 Expected Co (Round to two d Observed Distribution of Colors Color Frequency Claimed Proportion Colored Candies in a bag Brown Yellow Red Blue 61 64 59 0.13 0.14 0.24 Print 0.13 Done Orange Green 97 67 0.20 0.16

MATLAB: An Introduction with Applications
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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### Observed Distribution of Colored Candies In this experiment, a student tests whether a bag of colored candies follows the manufacturer's stated distribution at a 0.05 level of significance. The manufacturer claims the distribution is as follows: 13% brown, 14% yellow, 13% red, 24% blue, 20% orange, and 16% green. #### Table 1: Observed and Claimed Distribution **Observed Frequencies:** - **Brown:** 61 - **Yellow:** 64 - **Red:** 54 - **Blue:** 59 - **Orange:** 97 - **Green:** 67 **Claimed Proportions:** - **Brown:** 0.13 - **Yellow:** 0.14 - **Red:** 0.13 - **Blue:** 0.24 - **Orange:** 0.20 - **Green:** 0.16 #### Experimental Analysis The table on the left displays the observed frequency of each candy color, which is used to compute the expected counts based on the claimed proportions. The objective is to perform a statistical test, such as a chi-square goodness-of-fit test, to determine whether the observed frequencies align with the claimed distribution. **Steps to Carry Out the Analysis:** 1. **Calculate Expected Counts:** Multiply the total number of candies by each claimed proportion. 2. **Perform the Statistical Test:** Compare observed and expected counts to see if the differences are statistically significant. 3. **Decision Making:** Based on the test results, determine if the bag follows the claimed distribution. This experiment is key in understanding applied statistics and hypothesis testing in real-world scenarios.
Transcribed Image Text:### Observed Distribution of Colored Candies In this experiment, a student tests whether a bag of colored candies follows the manufacturer's stated distribution at a 0.05 level of significance. The manufacturer claims the distribution is as follows: 13% brown, 14% yellow, 13% red, 24% blue, 20% orange, and 16% green. #### Table 1: Observed and Claimed Distribution **Observed Frequencies:** - **Brown:** 61 - **Yellow:** 64 - **Red:** 54 - **Blue:** 59 - **Orange:** 97 - **Green:** 67 **Claimed Proportions:** - **Brown:** 0.13 - **Yellow:** 0.14 - **Red:** 0.13 - **Blue:** 0.24 - **Orange:** 0.20 - **Green:** 0.16 #### Experimental Analysis The table on the left displays the observed frequency of each candy color, which is used to compute the expected counts based on the claimed proportions. The objective is to perform a statistical test, such as a chi-square goodness-of-fit test, to determine whether the observed frequencies align with the claimed distribution. **Steps to Carry Out the Analysis:** 1. **Calculate Expected Counts:** Multiply the total number of candies by each claimed proportion. 2. **Perform the Statistical Test:** Compare observed and expected counts to see if the differences are statistically significant. 3. **Decision Making:** Based on the test results, determine if the bag follows the claimed distribution. This experiment is key in understanding applied statistics and hypothesis testing in real-world scenarios.
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