Question 9 The following data concerning income and educational attainment for s
ID: 1100663 • Letter: Q
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.
y = 46.587 + 0.001616x
y = -9,577.8 + 518.662x
y = 4,634.9 + 358.472x
y = -18,096.5 + 474.365x
y = 12,781.2 + 753.291x
Question 10
Find the sample correlation coefficient between per capita income and percentage of high school graduates.
-0.8049
0.7664
-0.9116
0.8755
0.5922
Question 11
Find the value of the t statistic for testing H0: ?1 = 0 vs. HA: ?1 ? 0.
5.728
-2.929
9.400
-4.188
32.866
Question 12
Which of the following correctly describes the p-value for the test statistic in #11?
p-value < .01
.01 < p-value < .05
.05 < p-value < .10
.10 < p-value < .20
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?
yes
no
maybe
cannot be determined
six
Question 14
What is the expected change in per capita income associated with a 1% increase in the proportion of high school graduates?
about $474.36
about $1,273.41
about $226.19
about $1.62
about $358.47
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
Explanation / Answer
Find the least squares regression equation for predicting per capita income using the percentage of high school graduates
c.y = 4,634.9 + 358.472x
10.Find the sample correlation coefficient between per capita income and percentage of high school graduates.
b.0.7664
11.Find the value of the t statistic for testing H0: ?1 = 0 vs. HA: ?1 ? 0.
a.5.728
12.Which of the following correctly describes the p-value for the test statistic in #11?
d.10 < p-value < .20
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
14.What is the expected change in per capita income associated with a 1% increase in the proportion of high school graduates?
e.about $358.47