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 alpha equals 0.05 level of significance.

(A) Compute the expected counts for each color

(B) what is the test statistic

(C) What is the P value

Color
Brown	63
Yellow	63
Red	55
Blue Orange Green	59 87 65

Answer 1

Here expected value = P(Color) * Total value of that color/Total value

Here is the expected value table with chi-square table

=

Color	Observed value	Proportion	Expected value	Chi-square
Brown	63	0.13	50.96	2.845
Yellow	63	0.14	54.88	1.201
Red	55	0.13	50.96	0.320
Blue	59	0.24	94.08	13.080
Orange	87	0.2	78.4	0.943
Green	65	0.16	62.72	0.083
Total	392	1	392	18.473

Chi-square = = 18.473

dF = n -1 = 6 -1 = 5

p - value = CHIDIST(18.473,5) = 0.0024

that p - value is less than 0.05 so we reject the null hypothesis and conclude that the candies doesn't follow the pattern as provided.