Question

The amount of sugar in a Krispy Kream glazed donut is 10 grams. Many people feel that cereal is healthier alternative for children over glazed donuts. Assume the table below contains the amount of sugar (in grams) in a random sample of cereals that are geared towards children. Estimate the mean amount of sugar in all children's cereals using a 98% confidence level.

sugar amount in grams 16 11 10 17 19 20 12 10 12 10 17 14 15 11 16 12

Answer 1

With a 98% confidence level, the estimated mean amount of sugar in all children's cereals is between 12.35 grams and 17.78 grams. This calculation is based on a sample of sugar amounts ranging from 10 to 20 grams.

To estimate the mean amount of sugar in all children's cereals with a 98% confidence level, we use a t-distribution based calculation. Given the sample of sugar amounts (in grams): 10, 10, 10, 11, 11, 12, 12, 14, 15, 16, 16, 17, 17, 19, 20.

The sample mean (bar x) is approximately 15.07, and the sample standard deviation ( s ) is approximately 3.18. The t-value for a 98% confidence level with 14 degrees of freedom is approximately 2.65. The margin of error (ME) is approximately 2.72.

The confidence interval is (12.35, 17.78). Therefore, we estimate with 98% confidence that the mean amount of sugar in all children's cereals is between 12.35 grams and 17.78 grams.