10. Focus Problem: Changing Population and Crime Rate Let x be a random variable representing percentage change in neighborhood population in the past few years, and let y be a random variable representing crime rate (crimes per 1000 population). A random sample of six Denver neighborhoods gave the following information (Source: Neighborhood Facts, The Piton Foundation).

x 29 2 11 17 7 6 y 173 35 132 127 69 53

©x 5 72; ©y 5 589; ©x2 5 1340; ©y2 5 72,277; ©xy 5 9499

(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 not zero at the 1% level of significance.

(e) For a neighborhood with x 5 12% change in population in the past few years, predict the change in the crime rate (per 1000 residents).

(f) Verify that Se < 22.5908.

(g) Find an 80% confidence interval for the change in crime rate when the percentage change in population is x 5 12%.

(h) Test the claim that the slope b of the population least-squares line is not zero at the 1% level of significance.

(i) Find an 80% confidence interval for b and interpret its meaning.