The expected proportions of colors of M&Ms according to the Mars candy company can be found in the table below. In addition, the table contains the number of M&M's of each color that were found in a case of candy. At the 5% level, do the observed frequencies support the claim of M&M? M&M Observed Counts and Expected Proportions   blue brown green orange red yellow Total Observed Frequencies 481 361 480 551 372 361 2606 Expected Proportion 0.24 0.13 0.16 0.2 0.13 0.14   H: Hypotheses     H0:H0:The distribution of        for            the stated distribution.        HA:HA:The distribution of        for            the stated distribution. A: Assumptions In this problem     data were collected for       variable(s) from      sample(s). Which of the following assumptions must be checked? Check all that apply. All observed counts are at least 5 Population standard deviations are known All sample sizes are at least 30 N >= 20n All expected counts are less than 5 All observed counts are less than 5 N < 20n Population standard deviations are unknown All expected counts are at least 5 Check the assumptions:      1. Enter the list of expected values (round values to 2 decimal places):                      Are all of the expected values greater than or equal to 5?          2. No N is given, we will assume N          N: Name the test      The conditions are met to use a          . T: Test Statistic      The formula set up of the first and last term of the test statistic are as follows:      Round initial values to 2 decimal places: χ2=Σ(O−E)2Eχ2=Σ(O-E)2E = ( -  )^2^2/ + ... + ( -  )^2^2/      Final answer from technology rounded to 2 decimal places:      χ2χ2 =  O: Obtain the P-value      Report the final answer to 4 decimal places.      It is possible when rounded that a p-value is 0.0000      P-value =  M: Make a decision      Since the p-value          , we        . S: State a conclustion There     significant evidence to conclude that the distribution of        for            the stated distribution.

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The expected proportions of colors of M&Ms according to the Mars candy company can be found in the table below. In addition, the table contains the number of M&M's of each color that were found in a case of candy. At the 5% level, do the observed frequencies support the claim of M&M?

M&M Observed Counts and Expected Proportions

  blue brown green orange red yellow Total
Observed Frequencies 481 361 480 551 372 361 2606
Expected Proportion 0.24 0.13 0.16 0.2 0.13 0.14  



H: Hypotheses
    H0:H0:The distribution of        for            the stated distribution.    

   HA:HA:The distribution of        for            the stated distribution.

A: Assumptions

  • In this problem     data were collected for       variable(s) from      sample(s).
  • Which of the following assumptions must be checked?
  • Check all that apply.
    • All observed counts are at least 5
    • Population standard deviations are known
    • All sample sizes are at least 30
    • N >= 20n
    • All expected counts are less than 5
    • All observed counts are less than 5
    • N < 20n
    • Population standard deviations are unknown
    • All expected counts are at least 5


Check the assumptions:

     1. Enter the list of expected values (round values to 2 decimal places):      

 
 
 
 
 
 
    •    Are all of the expected values greater than or equal to 5?    


     2. No N is given, we will assume N         

N: Name the test

     The conditions are met to use a          .

T: Test Statistic

     The formula set up of the first and last term of the test statistic are as follows:

     Round initial values to 2 decimal places:

χ2=Σ(O−E)2Eχ2=Σ(O-E)2E = ( -  )^2^2/ + ... + ( -  )^2^2/

     Final answer from technology rounded to 2 decimal places:

     χ2χ2 = 

O: Obtain the P-value

     Report the final answer to 4 decimal places.

     It is possible when rounded that a p-value is 0.0000

     P-value = 

M: Make a decision

     Since the p-value          , we        .

S: State a conclustion

There     significant evidence to conclude that the distribution of        for            the stated distribution.

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