Question

Upon request, the Mars Company (the maker of M&M's) will provide the color distribution for their candies. As of August 2009, they noted that "Our color blends were selected by conducting consumer preference tests, which indicate the assortment of colors that pleased the greatest number of people and created the most attractive overall effect. On average, our mix of colors for M&M'S CHOCOLATE CANDIES is: M&M'S MILK CHOCOLATE: 24% cyan blue, 20% orange, 16% green, 14% bright yellow, 13% red, 13% brown." Data collected from a bag of Milk Chocolate M&M's are provided. Blue Brown Green Orange Red Yellow 110 47 52 103 58 50 We want to determine if this sample provides evidence that the color distribution has changed since August 2009. Report the p-value for your test. What conclusion can be made about the color distribution of Milk Chocolate M&M's. Use a 5% significance level.

          Upon request, the Mars Company (the maker of M&M's) will provide the color distribution for their candies. As of August 2009, they noted that
"Our color blends were selected by conducting consumer preference tests, which indicate the assortment of colors that pleased the greatest number of people and created the most attractive overall effect.
On average, our mix of colors for M&M'S CHOCOLATE CANDIES is:
M&M'S MILK CHOCOLATE: 24% cyan blue, 20% orange, 16% green, 14% bright yellow, 13% red, 13% brown."
Data collected from a bag of Milk Chocolate M&M's are provided.
Blue Brown Green Orange Red Yellow
110 47 52 103 58 50
We want to determine if this sample provides evidence that the color distribution has changed since August 2009.
Report the p-value for your test. What conclusion can be made about the color distribution of Milk Chocolate M&M's. Use a 5% significance level.

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Upon request, the Mars Company (the maker of M M's) will provide the color distribution for their candies. As of August 2009, they noted that
"Our color blends were selected by conducting consumer preference tests, which indicate the assortment of colors that pleased the greatest number of people and created the most attractive overall effect.
On average, our mix of colors for M M'S CHOCOLATE CANDIES is:
M M'S MILK CHOCOLATE: 24% cyan blue, 20% orange, 16% green, 14% bright yellow, 13% red, 13% brown."
Data collected from a bag of Milk Chocolate M M's are provided.
Blue Brown Green Orange Red Yellow
110 47 52 103 58 50
We want to determine if this sample provides evidence that the color distribution has changed since August 2009.
Report the p-value for your test. What conclusion can be made about the color distribution of Milk Chocolate M M's. Use a 5% significance level.

Added by Madison L.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Supreeta N

05/02/2023

Step 1

First, we need to set up our null hypothesis (H0) and alternative hypothesis (H1). H0: The color distribution has not changed since August 2009. H1: The color distribution has changed since August 2009. Show more…

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Upon request, the Mars Company (the maker of M&M's) will provide the color distribution for their candies. As of August 2009, they noted that "Our color blends were selected by conducting consumer preference tests, which indicate the assortment of colors that pleased the greatest number of people and created the most attractive overall effect. On average, our mix of colors for M&M'S CHOCOLATE CANDIES is: M&M'S MILK CHOCOLATE: 24% cyan blue, 20% orange, 16% green, 14% bright yellow, 13% red, 13% brown." Data collected from a bag of Milk Chocolate M&M's are provided. Blue Brown Green Orange Red Yellow 110 47 52 103 58 50 We want to determine if this sample provides evidence that the color distribution has changed since August 2009. Report the p-value for your test. What conclusion can be made about the color distribution of Milk Chocolate M&M's. Use a 5% significance level.

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Transcript

00:01 Hello students, by using the data given in the question, here we have to determine if this sample provides the evidence that the color distribution has changed since august 2009.

00:14 So, therefore, we can write the null hypothesis h0 as the color distribution is same as before.

00:32 That means the proportions are 24 % blue, then 13 % brown, then 16 % green, 20 % orange and 13 % red and 14 % yellow.

01:06 So that means the percentages are same as before and the alternative hypothesis that is h0 is the color distribution has changed.

01:23 Now, here to test this hypothesis, we are going to use the chi -square test and for that we need to first find the expected frequencies.

01:35 As observed frequencies we have already given to us.

01:39 So the formula for the expected frequency is expected frequency, frequency that is denoted by ei and that is equal to n into p.

01:55 Now here n is nothing but the sum of the observed frequency that is sum of the data we have given to us that is 110 plus 47 plus 52 plus 103 plus 58 plus 50 and that is equal to 420.

02:11 So n is 420 into the proportion of the respective colors.

02:17 So by using this we will get the expected frequency for the colors.

02:21 Now we have these observed frequencies that are given to us.

02:26 So to calculate the expected frequency for the first observed frequency that is for 110, this is equal to 420 into p that is proportion for the blue color that is 0 .24.

02:40 So this we will get as 100 .8.

02:45 Then similarly for the brown color it is 420 into the proportion of brown color is 0 .13...

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