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

Here we have six colors, we have to use chi square distribution to test that the colors are evenly distributed

A) null hypothesis is

H₀: All colors are evenly distributed in the bag.

Ha: All colors are not evenly distributed in the bag.

B) expected frequency is given as-

since N=25 and we have 6 colors, then under H₀ probability of selecting any color is 1/6

then expected frequency for each color=25*(1/6)=4.16

obs	exp	(o-e)^2	(o-e)^2/e
7	4.15	8.1225	1.957229
7	4.15	8.1225	1.957229
3	4.15	1.3225	0.318675
2	4.15	4.6225	1.113855
4	4.15	0.0225	0.005422
2	4.15	4.6225	1.113855
		sum	6.466265

Here, observed value of chi square=6.466( from the above table)

c) critical value of chi square=11.7(this is found from chi square of table with probability 0.05)

D) Here, observed value is less than the critical value,so we fail to reject the null hypothesis.

E) as a non statistical point of view,almost number of different color are same.