The Daily News reported that the color distribution for plai

The Daily News reported that the color distribution for plain M&M

Solution

a) Ho: Published color distribution is correct
Ha: Published color distribution is NOT correct

b) Color: Brown Yellow Orange Green Tan
O:---------- 42 ------ 21 ----- 15 ------- 9 ---- 13 Total: 100
E: --------- 40 ------ 20 ------ 20 ------ 10 --- 10 Total: 100
O denotes observed number
E denotes expected number
E of brown color = 40% of 100 = 40 so on ....
Test statistic = X^2 (Chi-square) = sigma [(O-E)^2/E]
= [(42-40)^2/40] + [(21-20)^2/20] + [(15-20)^2/20] + [(9-10)^2/10] + [(13-10)^2/10]
= 0.10 + 0.05 + 1.25 + 0.10 + 0.90
= 2.40

c) Degrees of freedom = n-1 = 5-1 = 4
n denotes number of colors
Alpha = 0.10
Critical value of X^2 for 4 df at alpha = 0.10 is 7.78

d) Since the test statistic of X^2 (2.40) < the critical value of X^2 (7.78), it can be said that the Ho can be accepted at 0.10 level of significance.
There is NO evidence to reject the Ho
In other words, there is sufficient evidence to support the claim that the published color distribution is correct.