Self-Employment According to the Bureau of Labor Statistics, 10.1 % of Americans are self-employed. A researcher wants to determine if the self-employment rate in a certain area is different. She takes a random sample of 500 working residents from the area and finds that 62 are self-employed. a. Test the hypothesis that the proportion of self-employed workers in this area is different from 10.1 % . Use a 0.05 significance level. b. After conducting the hypothesis test, a further question one might ask, “What proportion of workers in this area are self-employed?” Use the sample data to find a 95 % confidence interval for the proportion of workers who are self-employed in the area from which the sample was drawn. How does this confidence interval support the hypothesis test conclusion?
Self-Employment According to the Bureau of Labor Statistics, 10.1 % of Americans are self-employed. A researcher wants to determine if the self-employment rate in a certain area is different. She takes a random sample of 500 working residents from the area and finds that 62 are self-employed. a. Test the hypothesis that the proportion of self-employed workers in this area is different from 10.1 % . Use a 0.05 significance level. b. After conducting the hypothesis test, a further question one might ask, “What proportion of workers in this area are self-employed?” Use the sample data to find a 95 % confidence interval for the proportion of workers who are self-employed in the area from which the sample was drawn. How does this confidence interval support the hypothesis test conclusion?
Solution Summary: The author explains how to perform a z-test to determine whether the population proportion is different from 10.1 or not.
Self-Employment According to the Bureau of Labor Statistics,
10.1
%
of Americans are self-employed. A researcher wants to determine if the self-employment rate in a certain area is different. She takes a random sample of 500 working residents from the area and finds that 62 are self-employed.
a. Test the hypothesis that the proportion of self-employed workers in this area is different from
10.1
%
.
Use a
0.05
significance level.
b. After conducting the hypothesis test, a further question one might ask, “What proportion of workers in this area are self-employed?” Use the sample data to find a
95
%
confidence interval for the proportion of workers who are self-employed in the area from which the sample was drawn. How does this confidence interval support the hypothesis test conclusion?
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Part (b)
Draw a scatter plot of the ordered pairs.
N
Life
Expectancy
Life
Expectancy
80
70
600
50
40
30
20
10
Year of
1950
1970 1990
2010 Birth
O
Life
Expectancy
Part (c)
800
70
60
50
40
30
20
10
1950
1970 1990
W
ALT
林
$
#
4
R
J7
Year of
2010 Birth
F6
4+
80
70
60
50
40
30
20
10
Year of
1950 1970 1990
2010 Birth
Life
Expectancy
Ox
800
70
60
50
40
30
20
10
Year of
1950 1970 1990 2010 Birth
hp
P.B.
KA
&
7
80
% 5
H
A
B
F10
711
N
M
K
744
PRT SC
ALT
CTRL
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