Question

Several years ago, the Mars, Incorporated website reported the following percentages of the various colors of its M&M'S candies for the "milk chocolate" variety.†

A graphical display lists 6 colors. Beside each color is a picture of an M&M with the percentage listed below the picture. The colors and percentages are as follows.

• Brown: 13%
• Yellow: 14%
• Red: 13%
• Blue: 24%
• Orange: 20%
• Green: 16%

A 14-ounce bag of milk chocolate M&M'S is randomly selected and contains 72 brown, 74 yellow, 59 red, 116 blue, 109 orange, and 84 green candies. Do the data substantiate the percentages reported by Mars, Incorporated? Use the appropriate test and describe the nature of the differences, if there are any. (Use α = 0.10.)

Given:

H₀: p₁ = 0.13; p₂ = 0.14; p₃ = 0.13; p₄ = 0.24; p₅ = 0.20; p₆ = 0.16

H_a: At least one p_i is different from the specified value.

Find:

Find the test statistic. (Round your answer to two decimal places.)

Χ² = ??

Find the rejection region. (Round your answer to two decimal places.)

Χ² >??

Answer 1

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
1	0.13	72.00	66.82	0.63	0.402
2	0.14	74.00	71.96	0.24	0.058
3	0.13	59.00	66.82	-0.96	0.915
4	0.24	116.00	123.36	-0.66	0.439
5	0.20	109.00	102.80	0.61	0.374
6	0.16	84.00	82.24	0.19	0.038
total	1.000	514	514		2.2253
test statistic X2 =		2.23

degree of freedom =categories-1=

5

for 0.1 level and 5 df :rejection region X2 > 9.24