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.) Full data set   ​Children's cereal: 42.3, 57.4, 49.3, 43.3, 51.7, 45.6, 54.5, 42.4, 41.8, 43.9, 48.8, 42.5, 37.6, 55.3, 49.2, 51.2, 38.5, 55.4, 42.1, 32.9   ​Adults' cereal: 23.8, 28.1, 1.6, 9.1, 3.5, 24.8, 17.7, 13.4, 23.9, 6.4, 6.1, 13.1, 18.2, 11.1, 4.5, 16.6, 0.8, 1.5, 2.9, 5.5, 12.8, 2.7, 0.6, 4.5, 9.8, 0.6, 17.1, 6.1, 15.1, 13 The confidence interval is ,. ​(Round to two decimal places as​ needed.) Interpret the confidence interval. Select the correct choice below and fill in the answer boxes to complete your choice. ​(Round to two decimal places as​ needed.)   A. Based on these​ samples, with​ 95% confidence,​ children's cereals average between the lower boundary of nothing and upper boundary of nothing more grams of sugar content than​ adult's cereals.   B. Based on these​ samples, with​ 95% confidence,​ adult's cereals average between the lower boundary of nothing and upper boundary of nothing more grams of sugar content than​ children's cereals.

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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.)
Full data set
 
​Children's cereal:
42.3,
57.4,
49.3,
43.3,
51.7,
45.6,
54.5,
42.4,
41.8,
43.9,
48.8,
42.5,
37.6,
55.3,
49.2,
51.2,
38.5,
55.4,
42.1,
32.9
 
​Adults' cereal:
23.8,
28.1,
1.6,
9.1,
3.5,
24.8,
17.7,
13.4,
23.9,
6.4,
6.1,
13.1,
18.2,
11.1,
4.5,
16.6,
0.8,
1.5,
2.9,
5.5,
12.8,
2.7,
0.6,
4.5,
9.8,
0.6,
17.1,
6.1,
15.1,
13
The confidence interval is ,.
​(Round to two decimal places as​ needed.)
Interpret the confidence interval. Select the correct choice below and fill in the answer boxes to complete your choice.
​(Round to two decimal places as​ needed.)
 
A.
Based on these​ samples, with​ 95% confidence,​ children's cereals average between the lower boundary of
nothing
and upper boundary of
nothing
more grams of sugar content than​ adult's cereals.
 
B.
Based on these​ samples, with​ 95% confidence,​ adult's cereals average between the lower boundary of
nothing
and upper boundary of
nothing
more grams of sugar content than​ children's cereals.
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