9.30. A study was conducted using 49 Catholic female undergraduates at Texas A&M University. The variables measured refer to the parents of these students. The response variable is the number of children that the parents have. One of the explanatory variables is the mother's educational level, measured as the number of years of formal education. For these data, x = 9.88,s* =

3.77,y = 3.35,5V = 2.19, the prediction equation is y = 5.40 — 0.207x, the standard error of the slope estimate is 0.079, and SSE = 201.95.

(a) Find the predicted numbers of children for women with (i) 8, (ii) 16 years of education.

(b) Find the correlation and interpret its value.

(c) Test the null hypothesis that mean number of children is independent of mother's educational level, and report and interpret the F-value.

(d) Sketch a potential scatterplot such that the analyses you conducted above would be inappropriate.