Medical: Fat Babies Modern medical practice tells us not to encourage babies to become too fat. Is there a positive correlation between the weight x of a 1-year-old baby and the weight y of the mature adult

(30 years old)? A random sample of medical files produced the following information for 14 females:

x (lb) 21 25 23 24 20 15 25 y (lb) 125 125 120 125 130 120 145 x (lb) 21 17 24 26 22 18 19 y (lb) 130 130 130 130 140 110 115 Sx 5 300; Sy 51775; Sx2 5 6572;

Sy2 5 226,125; Sxy 5 38,220.

(a) Draw a scatter diagram for the data.

(b) Find x , y ,

b, and the equation of the leastsquares line. Plot the line on the scatter diagram of part (a).

(c) Find the sample correlation coefficient r and the coefficient of determination. What percentage of the variation in y is explained by the least-squares model?

(d) Test the claim that the population correlation coefficient r is positive at the 1% level of significance.

(e) If a female baby weighs 20 pounds at 1 year, what do you predict she will weigh at 30 years of age?

(f) Verify that Se < 8.38.
(g) Find a 95% confidence interval for weight at age 30 of a female who weighed 20 pounds at 1 year of age.
(h) Test the claim that the slope b of the population least-squares line is positive at the 1% level of significance.
(i) Find an 80% confidence interval for b and interpret its meaning.AppendixLO1