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, Hc -HA. Be sure to check the necessar assumptions and conditions. (Note: Do not assume that the variances of the two data sets are equal.) Full data setD Children's cereal: 44.8, 55.3, 48.4, 41.5, 50.7, 49.1, 50.2, 42.5, 42.2, 44.7, 48, 44.4, 37.1, 59.1, 45.9, 54.9, 35.6, 56.3, 42.3, 32.3 Adults' cereal: 20.2, 25.2, 4, 8.4, 2.8, 21.2, 19.9, 13.5, 22.9, 6.9, 7.2, 12, 17.3, 10.9, 0.5, 17,1. 4.5, 4.5, 3.5, 9.6, 14.6, 0.8, 3.2, 4.8, 8.7, 0.4, 19.6, 5.6, 16,5, 11.1 The confidence interval is ( D (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.) O A. 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 children's cereals. O B. 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 adult's cereals.

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Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.