Question

1. Calculate the mean, median, and standard deviation for the total number of candies (per bag).

2. Construct a histogram of the total number of candies (per bag).

3. Use the z-score method to identify any potential outliers and outliers.

4. Assume the total number of candies is normally distributed, calculate the probability that a randomly sampled bag has at least 55 candies in a bag.

5. If a random sample of 50 bags is selected, find the probability that the mean number of candies in a bag is at least 56 candies.  Assume the total number of candies is normally distributed.

6. Assume the total number of candies is normally distributed, find a 95% confidence interval for the mean total number of candies.

7. Construct a probability distribution for the colors of the M&M^® candies sample:

Color                Probability

Blue

Orange

Green

Yellow

Red

Brown

8. Mars Inc. indicates that the M&M^® colors are distributed as follows:

Color                Proportion

Blue                        24%

Orange                     20%

Green                      16%

Yellow                    14%

Red                         13%

Brown                     13%

Conduct a hypothesis test (α=0.05) to see if the proportion of blue is the same as the company states.  Specify the hypothesis of the test, critical value, test statistic, p-value, decision (reject the null/ fail to reject the null), and the conclusion of what the decision means.

1. At the 0.01 level of significance, test if the true mean total number of candies (per bag) is greater than 54.  Specify the hypotheses of the test, critical value, test statistic, p-value, decision (reject the null/ fail to reject the null), and the conclusion of what the decision means.

Bag	Blue	Orange	Green	Yellow	Red	Brown	Total Number of Candies
1	7	23	9	11	4	6	60
2	16	16	4	7	9	4	56
3	14	14	3	10	5	11	57
4	13	14	7	8	8	6	56
5	18	12	7	10	5	7	59
6	12	9	11	9	8	8	57
7	15	16	6	6	6	8	57
8	15	17	8	4	6	7	57
9	12	14	10	5	10	7	58
10	16	16	7	5	6	2	52
11	18	10	6	9	9	3	55
12	21	12	7	6	6	4	56
13	18	12	9	5	7	2	53
14	18	10	7	5	8	5	53
15	18	16	7	4	7	4	56
16	19	6	7	4	8	11	55
17	15	15	7	6	9	3	55
18	21	10	7	9	6	4	57
19	20	8	5	4	13	6	56
20	15	15	7	2	8	10	57
21	13	11	11	3	15	5	58
22	14	12	7	11	8	3	55
23	11	15	6	10	7	6	55
24	12	16	7	8	7	7	57
25	15	16	6	5	8	6	56
26	15	10	8	6	12	7	58
27	20	14	5	4	5	8	56
28	18	13	11	6	6	5	59
29	12	13	11	4	9	8	57
30	8	16	10	8	7	8	57
31	15	10	9	9	6	5	54
32	22	8	5	8	4	10	57
33	14	12	5	11	9	5	56
34	11	16	10	3	7	9	56
35	13	17	5	3	12	4	54
36	10	20	6	2	8	7	53
37	10	12	10	6	11	6	55
38	15	11	4	4	8	11	53
39	14	16	3	7	8	7	55
40	14	10	8	6	12	5	55
41	16	17	10	5	5	3	56
42	19	15	5	5	5	7	56
43	13	14	6	5	7	10	55
44	17	16	4	7	7	10	61
45	13	12	11	4	10	6	56
46	19	13	4	5	9	4	54
47	17	15	6	8	7	4	57
48	11	12	6	6	7	9	51
49	19	12	5	2	7	12	57
50	11	15	7	3	10	1	47
51	15	13	5	8	8	9	58
52	15	17	4	3	10	10	59
53	15	16	4	3	5	11	54
54	16	12	7	6	8	9	58
55	13	17	8	4	9	6	57
56	18	20	4	3	5	5	55
57	14	18	5	7	8	6	58
58	12	16	7	5	5	9	54
59	10	13	7	10	7	8	55
60	16	14	6	10	7	4	57
61	8	21	3	5	10	9	56
62	17	17	7	4	9	3	57
63	7	16	8	7	10	8	56
64	15	20	2	3	6	10	56
65	14	19	5	5	5	9	57
66	15	11	8	6	10	5	55
67	14	13	9	9	4	2	51
68	15	15	5	7	8	5	55
69	16	15	5	8	4	8	56
70	16	7	7	10	10	6	56
71	13	16	10	8	2	6	55
72	11	11	5	10	8	9	54

Answer 1

Calculate the mean, median, and standard deviation for the total number of candies (per bag).

Mean	55.79167
Median	56
Standard Deviation	2.142379

Construct a histogram of the total number of candies (per bag).

Use the z-score method to identify any potential outliers and outliers.

2 outliers.

Assume the total number of candies is normally distributed, calculate the probability that a randomly sampled bag has at least 55 candies in a bag.

55.000	hypothesized value
55.792	mean Total Number of Candies
2.142	std. dev.
0.252	std. error
72	n
71	df
3.136	t
.0012	p-value (one-tailed, upper)

Probability = 0.0012.