Question

The data below shows the sugar content in grams of several brands of​ children's and​ adults' cereals. Create and interpret a​ 95% confidence interval for the difference in the mean sugar​ content, μC−μA. Be sure to check the necessary assumptions and conditions.​ (Note: Do not assume that the variances of the two data sets are​ equal.)

Children's cereal:

40.2, 59.4, 47.3, 43.1, 51.5, 48.4, 54.8, 44.3, 41.6, 42, 45.5, 42.7, 37.8, 59.9, 48, 54.1, 38.9, 55.5, 42.8, 34.9

​Adults' cereal: 23.7, 25.3, 2.5, 8.7, 2.4, 21.4, 16.2, 14.4, 23.1, 7.4, 5.9, 12.8, 16.3, 10.8, 1.3, 16.4, 2.2, 4.5, 2.6, 9.7, 12.2, 4.5, 4, 1.4, 6.9, 0.1, 18.8, 6.9, 19.1, 13

A) The confidence interval is (___,___) round to two decimal places

B) Based on these samples, with 95% confidence, children's cereals average between the lower boundary of ___ and upper boundary of ___ more grams of sugar content than adults cereals. (round to two decimal places).

Answer 1

Let us find out mean and standard deviation for both the samples

Children's cereal sample mean is

Create the following table.

data	data-mean	(data - mean)2
40.2	-6.435	41.409225
59.4	12.765	162.945225
47.3	0.665	0.442225
43.1	-3.535	12.496225
51.5	4.865	23.668225
48.4	1.765	3.115225
54.8	8.165	66.667225
44.3	-2.335	5.452225
41.6	-5.035	25.351225
42	-4.635	21.483225
45.5	-1.135	1.288225
42.7	-3.935	15.484225
37.8	-8.835	78.057225
59.9	13.265	175.960225
48	1.365	1.863225
54.1	7.465	55.726225
38.9	-7.735	59.830225
55.5	8.865	78.588225
42.8	-3.835	14.707225
34.9	-11.735	137.710225

Find the sum of numbers in the last column to get.

So standard deviation is

For ​Adults' cereal:

Mean is

Create the following table.

data	data-mean	(data - mean)2
23.7	13.2167	174.68115889
25.3	14.8167	219.53459889
2.5	-7.9833	63.73307889
8.7	-1.7833	3.18015889
2.4	-8.0833	65.33973889
21.4	10.9167	119.17433889
16.2	5.7167	32.68065889
14.4	3.9167	15.34053889
23.1	12.6167	159.18111889
7.4	-3.0833	9.50673889
5.9	-4.5833	21.00663889
12.8	2.3167	5.36709889
16.3	5.8167	33.83399889
10.8	0.3167	0.10029889
1.3	-9.1833	84.33299889
16.4	5.9167	35.00733889
2.2	-8.2833	68.61305889
4.5	-5.9833	35.79987889
2.6	-7.8833	62.14641889
9.7	-0.7833	0.61355889
12.2	1.7167	2.94705889
4.5	-5.9833	35.79987889
4	-6.4833	42.03317889
1.4	-9.0833	82.50633889
6.9	-3.5833	12.84003889
0.1	-10.3833	107.81291889
18.8	8.3167	69.16749889
6.9	-3.5833	12.84003889
19.1	8.6167	74.24751889
13	2.5167	6.33377889

Find the sum of numbers in the last column to get.

So standard deviation is

μ₁ - μ₂ = (M₁ - M₂) = 36.16, 95% CI [31.86, 40.46].

A) The confidence interval is (31.86,40.46) round to two decimal places

B) Based on these samples, with 95% confidence, children's cereals average between the lower boundary of 31.86 and upper boundary of 40.46 more grams of sugar content than adults cereals. (round to two decimal places).