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

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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

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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