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?
Examine the Variables: Carefully review and note the names of all variables in the dataset. Examples of these variables include:
Mileage (mpg)
Number of Cylinders (cyl)
Displacement (disp)
Horsepower (hp)
Research: Google to understand these variables.
Statistical Analysis: Select mpg variable, and perform the following statistical tests. Once you are done with these tests using mpg variable, repeat the same with hp
Mean
Median
First Quartile (Q1)
Second Quartile (Q2)
Third Quartile (Q3)
Fourth Quartile (Q4)
10th Percentile
70th Percentile
Skewness
Kurtosis
Document Your Results:
In RStudio: Before running each statistical test, provide a heading in the format shown at the bottom. “# Mean of mileage – Your name’s command”
In Microsoft Word: Once you've completed all tests, take a screenshot of your results in RStudio and paste it into a Microsoft Word document. Make sure that snapshots are very clear. You will need multiple snapshots. Also transfer these results to the…
Examine the Variables: Carefully review and note the names of all variables in the dataset. Examples of these variables include:
Mileage (mpg)
Number of Cylinders (cyl)
Displacement (disp)
Horsepower (hp)
Research: Google to understand these variables.
Statistical Analysis: Select mpg variable, and perform the following statistical tests. Once you are done with these tests using mpg variable, repeat the same with hp
Mean
Median
First Quartile (Q1)
Second Quartile (Q2)
Third Quartile (Q3)
Fourth Quartile (Q4)
10th Percentile
70th Percentile
Skewness
Kurtosis
Document Your Results:
In RStudio: Before running each statistical test, provide a heading in the format shown at the bottom. “# Mean of mileage – Your name’s command”
In Microsoft Word: Once you've completed all tests, take a screenshot of your results in RStudio and paste it into a Microsoft Word document. Make sure that snapshots are very clear. You will need multiple snapshots. Also transfer these results to the…
2 (VaR and ES) Suppose X1
are independent. Prove that
~
Unif[-0.5, 0.5] and X2
VaRa (X1X2) < VaRa(X1) + VaRa (X2).
~
Unif[-0.5, 0.5]
Chapter 8 Solutions
The King's minion: Richelieu, Louis XIII, and the affair of Cinq-Mars
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