F IL E The h o m eo w n ersh ip ra te in th e U.S. w as 67.4% in 2009. In o rd er to d e te rm in e if h o m eo w n ersh ip is linked w ith incom

e, 2009 sta te level d a ta on th e h o m eo w n ersh ip rate (O w nership) an d m edian h o u seh o ld incom e (Incom e)

w ere co llected . A p o rtio n o f th e d a ta is show n below ; th e co m p lete d a ta can be fo u n d on th e te x t w eb site, lab eled H om e O w nership.

State Income Ownership Alabama $39,980 74.1%

Alaska $61,604 66.8%

Wyoming $52,470 73.8%

Source: w w w .c e n s u s .g o v .

a. Estim ate: O w nership = β 0 + β1Incom e + ε .

b. At th e 5% significance level, is Incom e linearly related to O w nership? Show th e step s of a hypothesis te s t using th e critical value approach.

c. C onstruct a 95% confidence interval for th e expected value of O w nership if Incom e is $50,000.

d. Compare the above confidence interval w ith a 95%
prediction interval for Ownership.