Question

A study that looked at beverage consumption used sample sizes that were much smaller than previous national surveys. One part of this study compared 20 children who were 7 to 10 years old with 5 who were 11 to 13. The younger children consumed an average of 8.2 oz of sweetened drinks per day while the older ones averaged 14.1 oz. The standard deviations were 10.8 oz and 8.2 oz respectively.

Required:
Do you think that it is reasonable to assume that these data are Normally distributed? Explain why or why not?

Answer 1

Explanation:

In statistics, about 68 percent of values come in one standard deviation of the mean by using a standard normal model. Approximately 95% of the data were all within two standard deviations from the mean. Almost all of the data are in the range of three standard deviations of the mean (roughly 99.7%).

The 68-95-99.7 law, also known as the Empirical Rule, is based on this evidence. 68 percent of the data values of a naturally distributed data collection of small children with a mean of 8.2 and a standard deviation of 10.8 would be between -2.2 and 19.0.

Within a mean of 14.1 as well as a standard deviation of 8.2, 68 percent of the data values in a usually distributed data collection of older children would be between 5.9 and 22.3.

However, we cannot conclude that the data is naturally distributed since the real actual data vary from the usual normal curve computed above.

Hence, various measures like either goodness of fit or theory testing, would be used for this.