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,

mu Subscript Upper C Baseline minus mu Subscript Upper AμC−μA.

Be sure to check the necessary assumptions and conditions.​ (Note: Do not assume that the variances of the two data sets are​ equal.)

Full data set

​Children's cereal: 40.6 comma40.6, 58.3 comma58.3, 47 comma47, 42.6 comma42.6, 52.2 comma52.2, 47 comma47, 53.3 comma53.3, 41.7 comma41.7, 44.9 comma44.9, 43 comma43, 47.9 comma47.9, 40.2 comma40.2, 35.6 comma35.6, 56.4 comma56.4, 48.5 comma48.5, 54.3 comma54.3, 36.9 comma36.9, 56.4 comma56.4, 44.7 comma44.7, 34.834.8

​Adults' cereal: 21.8 comma21.8, 26.1 comma26.1, 1.8 comma1.8, 7.4 comma7.4, 3.1 comma3.1, 24.3 comma24.3, 16.6 comma16.6, 12.3 comma12.3, 24.8 comma24.8, 9.3 comma9.3, 6.9 comma6.9, 10.6 comma10.6, 15.9 comma15.9, 11.5 comma11.5, 1.8 comma1.8, 18.8 comma18.8, 1.6 comma1.6, 2.3 comma2.3, 2.6 comma2.6, 9.3 comma9.3, 11.1 comma11.1, 1.7 comma1.7, 2.9 comma2.9, 3.6 comma3.6, 6.8 comma6.8, 2.7 comma2.7, 17.1 comma17.1, 7.9 comma7.9, 17.5 comma17.5, 13.9

Answer 1

The 95% confidence interval for the difference in the mean sugar​ content,μC−μA, is between 32.0585 and 40.6292.

We are 95% confident that the true mean difference in the mean sugar​ content,μC−μA, is between 32.0585 and 40.6292.

​Children's cereal	Adults' cereal
40.6	21.8
58.3	26.1
47	1.8
42.6	7.4
52.2	3.1
47	24.3
53.3	16.6
41.7	12.3
44.9	24.8
43	9.3
47.9	6.9
40.2	10.6
35.6	15.9
56.4	11.5
48.5	1.8
54.3	18.8
56.4	1.6
44.7	2.3
34.8	2.6
	9.3
	11.1
	1.7
	2.9
	3.6
	6.8
	2.7
	17.1
	7.9
	17.5
	13.9
​Children's cereal	Adults' cereal
46.811	10.467	mean
6.936	7.689	std. dev.
19	30	n
	41	df
	36.3439	difference (​Children's cereal - Adults' cereal)
	2.1220	standard error of difference
	32.0585	confidence interval 95.% lower
	40.6292	confidence interval 95.% upper
	4.2854	margin of error

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