The data below shows the sugar content in grams of several brands of children\'s

Question

The data below shows the sugar content in grams of several brands of children's and adult's cereals. Create and interpret a 95% confidence interval for the difference in the mean sugar content, mu_ C - mu _x. Be sure to check the necessary assumptions and conditions. Children's cereal: 44, 58.3 47, 40.4, 53.7, 46.9, 51.5, 43.3, 41.4, 43.4, 45.9, 42.5, 99.4, 56.3, 47.8, 52.5, 35.8, 59.9, 40.5, 30.4 Adult's cereal: 20.1, 27. 2.5, 8.3, 0.2, 22.2, 18.5, 11.1, 22.1, 8.2, 8.3, 12.1, 17, 13.6, 2, 18.8, 2.1, 1.8, 3.2, 9.3, 11, 4.8, 0.5, 3, 5.5, 0.5, 17.6, 5.1, 18.6, 11.2 The confidence interval is (), (Interpret the confidence interval. Select the correct choice below and fill in the answer boxes to complete your choice. (Round in two decimal places as needed.) 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. Based on these samples, with 95% confidence, adult's cereals average between the lower boundary of and upper boundary of more grams of sugar content than adults' cereals.

Explanation / Answer

here

for above degree of freedom v=((s12/n1+s22/n2)2/((s12/n1)/(n1-1)+(s22/n2)/(n2-1))=42

for above degree of freedom ; at 95% Ci, t=2.018

and std error =(s12/n1+s22/n2)1/2 =2.1786

hence confidence interval =(x1-x2)+/- t*std error =31.305 ; 40.098

option A ) lower bound 31.305 ; upper bound 40.098

44 20.1 56.3 27 47 2.5 40.4 9.3 53.7 0.2 46.9 22.2 12 51.5 18.5 13 43.3 11.1 14 41.4 22.1 1 43.4 8.2 2 45.9 8.3 3 42.5 12.1 4 39.4 17 5 56.3 13.6 6 47.8 2 7 52.5 18.8 8 35.8 2.1 9 59.9 1.8 10 40.5 3.2 11 30.4 9.3 12 11 13 4.8 14 0.5 15 3 16 5.5 17 0.6 15 17.6 16 5.1 17 18.6 18 11.2 total 918.900 307.300 mean 45.945 10.243 std deviation(S) 7.420 7.733

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