Question

The company that makes M&Ms claims that the 6 colors are evenly distributed in each bag. Conduct a goodness of fit test to determine whether this claim is true or not. Choose two alpha values (level of significance.)

Colors of M&Ms: Blue, Green, Yellow, Brown, Red, Orange . Total=6

Observed Frequency: Blue=7, Green=7, Yellow=3, Brown=2, Red=4, Orange=2 Total=25

A) State the null hypothesis

B) what is expected frequency

what is (O-E)^2/E

C)Using the x^2 distribution table, find the critical value of x^2a

D)Reject or fail to reject the null

E) Explain your conclusion using real world language- no statistical terms or symbols

Answer 1

a)

Ho:6 colors are evenly distributed in each bag

H1: 6 colors are not evenly distributed in each bag

Chi square test for Goodness of fit  
  
b)

expected frequncy,E = expected proportions*total frequency =1/6*25=4.17
total frequency=   25

category	observed frequencey, O	expected proportion	expected frequency,E			(O-E)²/E
blue	7	0.167	4.17			1.927
green	7	0.167	4.17			1.927
yellow	3	0.167	4.17			0.327
brown	2	0.167	4.17			1.127
red	4	0.167	4.17			0.007
orange	2	0.167	4.17			1.127

chi square test statistic,X² = Σ(O-E)²/E =   6.440

c)

level of significance, α=   0.05              
Degree of freedom=k-1=   6   -   1   =   5
Critical value =    11.0705

d)

chi square test stat=6.440 < critical value, so,

Fail to reject Ho

e)

there is not enough evidence to reject the claim that  the 6 colors are evenly distributed in each bag