7.83 ● The authors of the paper “Development of Nutritionally At-Risk Young Children is Predicted by Malaria, Anemia, and Stunting in Pemba, Zanzibar” (The Journal of Nutrition [2009]:763–772) studied factors that might be related to dietary deficiencies in children. Children were observed for a length of time and the time spent in various activities was recorded. One variable of interest was the length of time (in minutes) a child spent fussing.

The authors comment that the distribution of fussing times was skewed and that they used a square root transformation to create a distribution that was more approximately normal. Data consistent with summary quantities in the paper for 15 children are given in the accompanying table. Normal scores for a samples size of 15 are also given.

Fussing Time Normal Score 0.05 21.739 0.10 21.245 0.15 20.946 0.40 20.714 Fussing Time Normal Score 0.70 20.515 1.05 20.333 1.95 20.165 2.15 0.000 3.70 0.165 3.90 0.335 4.50 0.515 6.00 0.714 8.00 0.946 11.00 1.245 14.00 1.739

a. Construct a normal probability plot for the fussing time data. (Hint: See Example 7.31.)

b. Does the plot from Part

(a) look linear? Do you agree with the authors of the paper that the fussing time distribution is not normal?

c. Transform the data by taking the square root of each data value. Construct a normal probability plot for the square root transformed data.

d. How do the normal probability plots from Parts

(a) and

(c) compare?