In: Statistics and Probability
Many people feel that cereal is healthier alternative for children over glazed donuts. Table #8.3.5 contains the amount of sugar in a sample of cereal that isgeared towards children ("Healthy breakfast story," 2013) Estimate the mean amount of sugar in children cereal using a 95% confidence level.
Table #8.3.5: Sugar Amounts(g) in Children’s Cereal
10
14
12
9
13
13
13
11
12
15
9
10
11
3
6
12
15
12
12
Confidence level estimate of the population mean :

n : sample size :19
x : amount of sugar in a sample of cereal
Sample mean :

Sample standard deviation :

| S.No. | x: Sugar Amounts(g) in Children’s Cereal | 
x-![]()  | 
(x- )2 | 
| 1 | 10 | -1.1579 | 1.3407 | 
| 2 | 14 | 2.8421 | 8.0776 | 
| 3 | 12 | 0.8421 | 0.7091 | 
| 4 | 9 | -2.1579 | 4.6565 | 
| 5 | 13 | 1.8421 | 3.3934 | 
| 6 | 13 | 1.8421 | 3.3934 | 
| 7 | 13 | 1.8421 | 3.3934 | 
| 8 | 11 | -0.1579 | 0.0249 | 
| 9 | 12 | 0.8421 | 0.7091 | 
| 10 | 15 | 3.8421 | 14.7618 | 
| 11 | 9 | -2.1579 | 4.6565 | 
| 12 | 10 | -1.1579 | 1.3407 | 
| 13 | 11 | -0.1579 | 0.0249 | 
| 14 | 3 | -8.1579 | 66.5512 | 
| 15 | 6 | -5.1579 | 26.6039 | 
| 16 | 12 | 0.8421 | 0.7091 | 
| 17 | 15 | 3.8421 | 14.7618 | 
| 18 | 12 | 0.8421 | 0.7091 | 
| 19 | 12 | 0.8421 | 0.7091 | 
| Total | 212 | 156.5263 | |
Mean:
 212/19= | 
11.1579 | 

| Sample Size : n | 19 | 
| Degrees of freedom : n-1 | 18 | 
| Confidence Level : | 95 | 
  =
(100-95)/100 | 
0.05 | 
 /2 | 
0.025 | 
![]()  | 
2.1009 | 
95% confidence level Estimate of the mean amount of sugar in children cereal


95% confidence level Estimate of the mean amount of sugar in children cereal = (9.7366, 12.5792)