The Great Project Part 3: Hypothesis Testing In 2011, the national percent of low-income working families had an approximately normal distribution with a mean of 31.3% and a standard deviation of 6.2% (The Working Poor Families Project, 2011). Although it remained slow, some politicians claimed that the recovery from the Great Recession was steady and noticeable. As a result, it was believed that the national percent of low-income working families was significantly lower in 2014 than it was in 2011. To support this belief, a spring 2014 sample of n=16 jurisdictions produced a sample mean of 29.8% for the percent of low-income working families, with a sample standard deviation of 4.1%. Using α=0.10 significance level, test the claim that the national average percent of low-income working families had improved by 2014. Clearly restate the claim associated with this test, and state the null and alternate hypotheses. Provide two or three sentences to state the type of test that should be performed based on the hypotheses. Additionally, state the assumptions and conditions that justify the appropriateness of the test. Use technology to identify, and then provide the test statistic and the resulting P-value associated with the given sample results. Provide a statement that explains the interpretation of the P-value. (Print or copy-and-paste the output that identified these values, or any other form of evidence that technology was used.) State, separately, both the decision/result of the hypothesis test, and the appropriate conclusion/statement about the claim. Reference(s): The Working Poor Families Project. (2011). Indicators and Data. Retrieved from http://www.workingpoorfamilies.org/indicators/ 2011 Data Jurisdiction Percent of low income working families (<200% poverty level) Percent of 18-64 year olds with no HS diploma Alabama 37.3 15.3 Alaska 25.9 8.6 Arizona 38.9 14.8 Arkansas 41.8 14 California 34.3 17.6 Colorado 27.6 10.1 Connecticut 21.1 9.5 Delaware 27.8 11.9 District of Columbia 23.2 10.8 Florida 37.3 13.1 Georgia 36.6 14.9 Hawaii 25.8 7.2 Idaho 38.6 10.7 Illinois 30.4 11.5 Indiana 31.9 12.2 Iowa 28.8 8.1 Kansas 32 9.7 Kentucky 34.1 13.6 Louisiana 36.3 16.1 Maine 30.4 7.1 Maryland 19.5 9.7 Massachusetts 20.1 9.1 Michigan 31.6 10 Minnesota 24.2 7.3 Mississippi 43.6 17 Missouri 32.7 11.1 Montana 36 7 Nebraska 31.1 8.7 Nevada 37.4 16.6 New Hampshire 19.7 7.3 New Jersey 21.2 10.1 New Mexico 43 16.2 New York 30.2 13 North Carolina 36.2 13.6 North Dakota 27.2 5.9 Ohio 31.8 10.3 Oklahoma 37.4 13.2 Oregon 33.9 10.8 Pennsylvania 26 9.4 Rhode Island 26.9 12 South Carolina 38.3 14.2 South Dakota 31 8.7 Tennessee 36.6 12.7 Texas 38.3 17.8 Utah 32.3 9.9 Vermont 26.2 6.6 Virginia 23.3 10.2 Washington 26.4 10.2 West Virginia 36.1 12.9 Wisconsin 28.7 8.5 Wyoming 28.1
The Great Project
Part 3: Hypothesis Testing
In 2011, the national percent of low-income working families had an approximately normal distribution with a mean of 31.3% and a standard deviation of 6.2% (The Working Poor Families Project, 2011). Although it remained slow, some politicians claimed that the recovery from the Great Recession was steady and noticeable. As a result, it was believed that the national percent of low-income working families was significantly lower in 2014 than it was in 2011. To support this belief, a spring 2014 sample of n=16 jurisdictions produced a sample mean of 29.8% for the percent of low-income working families, with a sample standard deviation of 4.1%. Using α=0.10 significance level, test the claim that the national average percent of low-income working families had improved by 2014.
- Clearly restate the claim associated with this test, and state the null and alternate hypotheses.
- Provide two or three sentences to state the type of test that should be performed based on the hypotheses. Additionally, state the assumptions and conditions that justify the appropriateness of the test.
- Use technology to identify, and then provide the test statistic and the resulting P-value associated with the given sample results. Provide a statement that explains the interpretation of the P-value. (Print or copy-and-paste the output that identified these values, or any other form of evidence that technology was used.)
- State, separately, both the decision/result of the hypothesis test, and the appropriate conclusion/statement about the claim.
Reference(s): The Working Poor Families Project. (2011). Indicators and Data. Retrieved from http://www.workingpoorfamilies.org/indicators/
|
2011 Data |
|
|
|
Jurisdiction |
Percent of low income working families (<200% poverty level) |
Percent of 18-64 year olds with no HS diploma |
|
Alabama |
37.3 |
15.3 |
|
Alaska |
25.9 |
8.6 |
|
Arizona |
38.9 |
14.8 |
|
Arkansas |
41.8 |
14 |
|
California |
34.3 |
17.6 |
|
Colorado |
27.6 |
10.1 |
|
Connecticut |
21.1 |
9.5 |
|
Delaware |
27.8 |
11.9 |
|
District of Columbia |
23.2 |
10.8 |
|
Florida |
37.3 |
13.1 |
|
Georgia |
36.6 |
14.9 |
|
Hawaii |
25.8 |
7.2 |
|
Idaho |
38.6 |
10.7 |
|
Illinois |
30.4 |
11.5 |
|
Indiana |
31.9 |
12.2 |
|
Iowa |
28.8 |
8.1 |
|
Kansas |
32 |
9.7 |
|
Kentucky |
34.1 |
13.6 |
|
Louisiana |
36.3 |
16.1 |
|
Maine |
30.4 |
7.1 |
|
Maryland |
19.5 |
9.7 |
|
Massachusetts |
20.1 |
9.1 |
|
Michigan |
31.6 |
10 |
|
Minnesota |
24.2 |
7.3 |
|
Mississippi |
43.6 |
17 |
|
Missouri |
32.7 |
11.1 |
|
Montana |
36 |
7 |
|
Nebraska |
31.1 |
8.7 |
|
Nevada |
37.4 |
16.6 |
|
New Hampshire |
19.7 |
7.3 |
|
New Jersey |
21.2 |
10.1 |
|
New Mexico |
43 |
16.2 |
|
New York |
30.2 |
13 |
|
North Carolina |
36.2 |
13.6 |
|
North Dakota |
27.2 |
5.9 |
|
Ohio |
31.8 |
10.3 |
|
Oklahoma |
37.4 |
13.2 |
|
Oregon |
33.9 |
10.8 |
|
Pennsylvania |
26 |
9.4 |
|
Rhode Island |
26.9 |
12 |
|
South Carolina |
38.3 |
14.2 |
|
South Dakota |
31 |
8.7 |
|
Tennessee |
36.6 |
12.7 |
|
Texas |
38.3 |
17.8 |
|
Utah |
32.3 |
9.9 |
|
Vermont |
26.2 |
6.6 |
|
Virginia |
23.3 |
10.2 |
|
Washington |
26.4 |
10.2 |
|
West Virginia |
36.1 |
12.9 |
|
Wisconsin |
28.7 |
8.5 |
|
Wyoming |
28.1 |
8 |
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