Question

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

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 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.

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

Answer 1

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