Question

Question 9

The following data concerning income and educational attainment for several counties in Alabama were taken from the U.S. Census Website.

County	% High School Grads	Per Capita Income
Autauga	78.7	18,518
Chilton	66.2	15,303
Coosa	65.7	14,875
Dallas	70.3	13,638
Elmore	77.6	17,650
Jefferson	80.9	20,892
Lee	81.4	17,158
Lowndes	64.3	12,457
Macon	70.0	13,714
Montgomery	80.3	19,358
Pike	69.1	14,904
Shelby	86.8	27,176
Sum	891.3	205,643
Sum of Squares	66,818.87	3,705,400,931

?xy = 15,567,083.8

Find the least squares regression equation for predicting per capita income using the percentage of high school graduates.

a.

y = 46.587 + 0.001616x

b.

y = -9,577.8 + 518.662x

c.

y = 4,634.9 + 358.472x

d.

y = -18,096.5 + 474.365x

e.

y = 12,781.2 + 753.291x

Question 10

Find the sample correlation coefficient between per capita income and percentage of high school graduates.

a.

-0.8049

b.

0.7664

c.

-0.9116

d.

0.8755

e.

0.5922

Question 11

Find the value of the t statistic for testing H₀: ?₁ = 0 vs. H_A: ?₁ ? 0.

a.

5.728

b.

-2.929

c.

9.400

d.

-4.188

e.

32.866

Question 12

Which of the following correctly describes the p-value for the test statistic in #11?

a.

p-value < .01

b.

.01 < p-value < .05

c.

.05 < p-value < .10

d.

.10 < p-value < .20

e.

p-value > .20

Question 13

Considering #11-12 above, do the data provide significant evidence at the .05 level of a linear relationship between per capita income and the percentage of high school graduates?

a.

yes

b.

no

c.

maybe

d.

cannot be determined

e.

six

Question 14

What is the expected change in per capita income associated with a 1% increase in the proportion of high school graduates?

	a.	about $474.36
	b.	about $1,273.41
	c.	about $226.19
	d.	about $1.62
	e.	about $358.47