A manufacturer of colored candies states that 13% of the candies in a bag should

Question

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 = 0.05 level of significance Click the icon to view the table A-H,: The distribution of colors is the same as stated by the manufacturer. H: The distribution of colors is not the same as stated by the manufacturer. OB. H: The distribution of colors is not the same as stated by the manufacturer. H: The distribution of colors is the same as stated by the manufacturer. OC. None of these Observed Distribution of Colors Compute the expected counts for each color. ColorObserved Coun Expected Count Colored Candies in a bag BrownYellow RedBlue Orange Green Brown Yellow Red Blue Orange Green 59 63 52 60 Color Frequenc Claimed Proportion 59 63 52 60 67 0.130.140.130.24 0.20 0.16 Print Done 67 (Round to two decimal places as needed.)

Explanation / Answer

There are 59+63+52+60+88+67 = 389 candies here.

We simply multiply the percentages by 389 to get the expected frequencies.

Doing an observed/expected value table,          

[ANSWER, EXPECTED VALUES IN "E" COLUMN]

***************************************************

          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    16.40661459 [ANSWER, TEST STATISTIC]
          
As df = a - 1,           
          
a =    6      
df = a - 1 =    5      
          
Then, the critical chi^2 value is          
          
significance level =    0.05      
chi^2(crit) =    11.07049769      
          
Also, the p value is          
          
p =    0.005774149 [ANSWER, P VALUE]
          
Thus, comparing chi^2 and chi^2(crit) [or, p and significance level], we   REJECT THE NULL HYPOTHESIS.      
          

O E (O - E)^2/E 59 50.57 1.405278 63 54.46 1.339177 52 50.57 0.040437 60 93.36 11.92041 88 77.8 1.337275 67 62.24 0.364036

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