Sales: Insurance Dorothy Kelly sells life insurance for the Prudence Insurance Company. She sells insurance by making visits to her clients’ homes.

Dorothy believes that the number of sales should depend, to some degree, on the number of visits made. For the past several years, she has kept careful records of the number of visits (x) she makes each week and the number of people (y) who buy insurance that week. For a random sample of 15 such weeks, the x and y values follow:

x 11 19 16 13 28 5 20 14 22 7 15 29 8 25 16 y 3 11 8 5 8 2 5 6 8 3 5 10 6 10 7 Sx 5 248; Sy 5 97; Sx2 5 4856; Sy2 5 731;

Sxy 51825

(a) Draw a scatter diagram for the data.

(b) Find x , y,

b, and the equation of the least-squares 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) In a week during which Dorothy makes 18 visits, how many people do you predict will buy insurance from her?

(f) Verify that Se < 1.731.

(g) Find a 95% confidence interval for the number of sales Dorothy would make in a week during which she made 18 visits.

(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