Question

Masterfoods USA states that their color blends were selected by conducting consumer preference tests, which indicated the assortment of colors that pleased the greatest number of people and created the most attractive overall effect. On average, they claim the following percentages of colors for M&Ms® milk chocolate candies: 24% blue, 20% orange, 16% green, 14% yellow, 13% red and 13% brown.

Question: On average, they claim that a 1.69 oz bag will contain more than 54 candies. Test this claim (µ > 54) at the 0.01 significance (σ unknown).

Blue	Orange	Green	Yellow	Red	Brown	Total Number of Candies in Bag
6	17	10	8	10	7	58
8	8	11	12	9	10	58
8	13	14	4	12	7	58
7	13	10	7	14	7	58
12	13	4	13	5	10	57
13	8	12	13	1	10	57
8	8	14	7	9	11	57
16	10	10	5	11	4	56
11	11	8	13	6	7	56
10	9	14	10	9	4	56
6	12	13	8	9	8	56
14	10	2	13	7	10	56
11	10	11	12	5	7	56
14	11	8	6	7	10	56
14	8	9	5	5	15	56
11	12	10	12	7	3	55
12	9	12	8	5	9	55
7	12	10	7	10	9	55
8	9	13	11	10	4	55
10	11	9	10	6	9	55
10	10	9	10	7	9	55
9	3	9	13	8	13	55
10	8	13	10	9	5	55
11	6	11	7	8	12	55
12	13	10	11	5	3	54
12	8	5	15	8	6	54
12	8	5	15	8	6	54
14	14	9	4	6	7	54
13	7	12	9	4	9	54
13	10	11	8	5	6	53
7	11	10	9	7	9	53
9	14	8	6	6	10	53
12	10	8	7	9	6	52
10	7	11	7	8	8	51
11	3	12	8	7	10	51
8	10	12	6	7	6	49

Answer 1

let X denotes the total number of candies in a bag.

: Mean total number of candies in a bag.

We have to test the hypothesis that

The bag will contain more than 54 candies or not.

i.e. Null Hypothesis -

against

Alternative Hypothesis- ( Right-tailed test).

Since population standard deviation (sigma) is unknown.

We used one sample t-test for testing population mean.

The value of test statistic is

X	( X-Xbar)^2
58	9.3364
58	9.3364
58	9.3364
58	9.3364
57	4.2253
57	4.2253
57	4.2253
56	1.1142
56	1.1142
56	1.1142
56	1.1142
56	1.1142
56	1.1142
56	1.1142
56	1.1142
55	0.0031
55	0.0031
55	0.0031
55	0.0031
55	0.0031
55	0.0031
55	0.0031
55	0.0031
55	0.0031
54	0.8920
54	0.8920
54	0.8920
54	0.8920
54	0.8920
53	3.7809
53	3.7809
53	3.7809
52	8.6698
51	15.5586
51	15.5586
49	35.3364
1978	149.8889

The value of test statistic t = 2.7383.

Alpha : Level of significance = 0.01

Since the test is right-tailed and value of test statistic is 2.7383, p-value is obtained by

p-value = P ( t _n-1 > 2.7383) = P ( t ₃₅ > 2.7383) = 0.0048

p-value = 0.0048

Decision : Since p-value is less than level of significance alpha, we reject Ho at 1% level of significance.

Conclusion: There is sufficient evidence support to claim that The bag will contain more than 54 candies.