Constructing confidence intervals for the proportion

Question

Discuss the below:

We will be constructing confidence intervals for the proportion of each color as well as the mean number of candies per bag.

Construct a 95% Confidence Interval for the proportion of blue M&Ms® candies.

Construct a 95% Confidence Interval for the proportion of orange M&Ms® candies.

Construct a 95% Confidence Interval for the proportion of green M&Ms® candies.

Construct a 95% Confidence Interval for the proportion of yellow M&Ms® candies.

Construct a 95% Confidence Interval for the proportion of red M&Ms® candies.

Construct a 95% Confidence Interval for the proportion of brown M&Ms® candies.

Construct a 95% Confidence Interval for the mean total number of candies (large samples).

Q: How many candies should be sampled to obtain a 95% CI of the proportion of blue candies with a 4% margin of error if the known proportion of blue candies is 0.24?

Blue	Orange	Green	Yellow	Red	Brown	Total		bin
10	10	14	8	7	9	58		51
7	11	14	10	7	5	54		52
9	8	7	13	12	10	59		53
10	14	7	8	9	7	55		54
16	12	9	10	4	5	56		55
17	6	6	11	6	8	54		56
14	11	11	5	8	8	57		57
15	16	11	12	1	2	57		58
9	10	8	15	7	6	55		59
22	16	4	8	3	4	57		60
9	13	17	7	8	5	59
15	19	7	6	3	9	59
10	6	9	10	11	9	55
8	9	8	6	12	13	56
11	12	10	11	5	7	56
15	10	15	10	3	2	55
7	15	16	6	6	9	59
11	14	8	14	8	3	58
8	7	16	7	9	13	60
13	14	5	6	7	12	57
18	6	7	11	8	8	58
14	9	10	8	10	6	57
11	19	10	5	9	7	61
11	12	15	4	7	4	53
11	8	10	5	16	7	57
16	8	9	5	11	10	59
8	4	18	6	10	12	58
14	14	8	8	6	6	56
11	12	10	12	7	3	55
12	9	12	8	5	9	55
4	7	17	4	14	6	52
6	10	12	12	9	8	57
13	12	16	5	6	5	57
16	7	13	8	5	6	55
12	11	8	7	7	12	57
16	9	14	4	4	9	56
23	9	8	7	8	5	60
5	6	27	2	1	2	43
13	13	11	11	6	4	58
5	12	12	7	9	7	52
10	11	17	4	9	6	57
19	10	9	5	4	7	54
14	11	6	8	7	9	55
10	15	7	9	5	10	56
10	7	9	13	8	8	55
14	11	10	13	7	3	58
10	14	12	7	4	5	52
13	10	4	8	14	5	54
14	11	10	13	7	3	58
10	14	12	7	4	5	52
13	10	4	8	14	5	54
9	6	16	7	8	11	57
14	10	11	9	11	5	60
15	10	13	8	8	5	59
13	15	9	7	8	3	55
6	12	10	7	7	10	52
5	8	11	4	15	10	53
12	10	12	6	5	9	54
9	13	14	1	10	12	59
10	7	15	7	9	8	56
7	14	10	2	3	7	43
9	3	10	5	6	6	39
10	6	15	16	11	5	63
12	13	8	16	5	0	54
13	10	5	13	5	10	56
15	6	9	9	11	6	56
7	4	10	7	6	12	46
9	8	6	12	8	9	52
14	6	8	5	10	5	48
801	715	741	558	523	481	3819	<-- Total Number of candies sampled
0.2097	0.1872	0.194	0.1461	0.1369	0.1259		phats, sample proportions for each color