The data below shows the sugar content in grams of several brands of children\'s
ID: 3365909 • Letter: T
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 ACA. Be sure to check the necessary assumptions and conditions. (Note: Do not assume that the variances of the two data sets are equal.)
Childrens_cereal :
59
46.2
42.6
54.7
49.3
51.3
41.2
43.9
44.1
46.7
44.4
38.3
56.9
48.9
51.8
39.3
58.1
42.5
Adult Cereal:
21.5
28.6
2.1
7.9
3.7
22.6
19.5
10.2
24.2
5.8
5.9
11.1
18 comma18,
11.1
0.6
17.7
0.4
3.7
2.1
5.6
12.1
1
2.3
4.5
7.7
3.9
15.6
9.4
16.2
11
The confidence interval is?
59
46.2
42.6
54.7
49.3
51.3
41.2
43.9
44.1
46.7
44.4
38.3
56.9
48.9
51.8
39.3
58.1
42.5
32Adult Cereal:
21.5
28.6
2.1
7.9
3.7
22.6
19.5
10.2
24.2
5.8
5.9
11.1
18 comma18,
11.1
0.6
17.7
0.4
3.7
2.1
5.6
12.1
1
2.3
4.5
7.7
3.9
15.6
9.4
16.2
11
Explanation / Answer
The formula for estimation is:
1 - 2 = (M1 - M2) ± ts(M1 - M2)
where:
M1 & M2 = sample means
t = t statistic determined by confidence level
s(M1 - M2) = standard error = ((s2p/n1) + (s2p/n2))
Calculation
Pooled Variance
s2p = (SS1 + SS2) / (df1 + df2) = 113.41 / 47 = 2.41
Standard Error
s(M1 - M2) = ((s2p/n1) + (s2p/n2)) = ((2.41/19) + (2.41/30)) = 0.46
Confidence Interval
1 - 2 = (M1 - M2) ± ts(M1 - M2) = 36.7053 ± (2.01 * 0.46) = 36.7053 ± 0.9162481
Result
1 - 2 = (M1 - M2) = 36.70526, 95% CI [35.7890119, 37.6215081].
You can be 95% confident that the difference between your two population means (1 - 2) lies between 35.7890119 and 37.6215081.
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