Question

5.         A spokesperson for the Mars Company stated that MM’s are produced in the following color proportions:

            15% Brown, 15% Yellow, 20% Blue, 15% Red, 20% Green, and 15% Orange. To test this claim a Math 15

            class at SRJC randomly selected 928 MM’s. The results appear below. (These are actually the results

            we saw from the Handout 4 assignment last semester). Test the claim at a = 0.5  (2,2,3,3)

MM color	Number	Expected Value
Brown	144
Yellow	140
Blue	180
Red	129
Green	209
Orange	126

a.         State the Null and Alternative hypotheses.  (2)

            b.         Assuming the Null Hypothesis is correct, find the expected values. (2)

c.         State and label the test statistic. Show at least two parts of summation. (3)

d.         What is the conclusion about the claim and how you made the decision? (3)

Answer 1

a.         State the Null and Alternative hypotheses.  (2)

Ans: Null Hypothesis: Mars Company produces the MM’s in the following color proportions: 15% Brown, 15% Yellow, 20% Blue, 15% Red, 20% Green, and 15% Orange.

Alternative Hypothesis: Mars Company does not produce the MM’s in the following color proportions: 15% Brown, 15% Yellow, 20% Blue, 15% Red, 20% Green, and 15% Orange.

b.         Assuming the Null Hypothesis is correct, find the expected values. (2).

Ans:

MM color	Number (O)	Proportion (P)	Expected Value=P*928
Brown	144	0.15	139.2
Yellow	140	0.15	139.2
Blue	180	0.2	185.6
Red	129	0.15	139.2
Green	209	0.2	185.6
Orange	126	0.15	139.2
	928

c.         State and label the test statistic. Show at least two parts of the summation. (3)

Ans:

MM color	Number (O)	Proportion (P)	Expected Value=P*928	(O-E)^2/E
Brown	144	0.15	139.2	0.165517241
Yellow	140	0.15	139.2	0.004597701
Blue	180	0.2	185.6	0.168965517
Red	129	0.15	139.2	0.747413793
Green	209	0.2	185.6	2.950215517
Orange	126	0.15	139.2	1.251724138
	928			5.288433908

The test statistic, Chi-square=5.29

The p-value for the Chi-square=5.29 at (6-1)=5 degree of freedom is 0.3817.

d.         What is the conclusion about the claim and how you made the decision? (3)

Ans: The p-value is 0.3817 and greater than 0.05 level of significance. Hence, fail to reject the null hypothesis and accept the claim of a spokesperson for the Mars Company stated that MM’s are produced in the following color proportions: 15% Brown, 15% Yellow, 20% Blue, 15% Red, 20% Green, and 15% Orange.