1.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
Clanton 78.7 18,518
Shelby 66.2 15,303
Alexander City 65.7 14,875
Baldwin 70.3 13,638
Mobile 77.6 17,650
Chilton 80.9 20,892
Hoover 81.4 17,158
Dothan 64.3 12,457
Chilton 70.0 13,714
Macon 80.3 19,358
Pike 69.1 14,904
Lee 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 = 4,634.9 + 358.472x
b. y = -18,096.5 + 474.365x
c. y = 46.587 + 0.001616x
d. y = -9,577.8 + 518.662x
e. y = 12,781.2 + 753.291x
2.Find the sample correlation coefficient between per capita income and percentage of high school graduates.
a.
-0.8049
b.
0.8755
c.
0.5922
d.
0.7664
e.
-0.9116
3.Find the value of the t statistic for testing H0: ?1 = 0 vs. HA: ?1 ? 0.
a.
5.728
b.
-2.929
c.
9.400
d.
-4.188
e.
32.866
4.Which of the following correctly describes the p-value for the test statistic in #3?
a.
p-value < .01
b.
.01 < p-value < .05
c.
.05 < p-value < .10
d.
.10 < p-value < .20
e.
p-value > .20
5.Considering #3-4 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
6 .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 $1.62
d.
about $226.19
e.
about $358.47
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