GREAT PROJECT

Correlation and Linear Regression

It is widely believed that the more education one receives the higher the income earned at the time of first employment and over the course of a career. However, due to varying reasons, many people never complete high school and, thus, never receive their high-school diploma. Although individuals without a high-school diploma are often able to find employment, they experience economic outcomes quite different from those who finish high school before entering the workforce to earn a living. Across the nation, there are millions of individuals with families who are now working but do not possess the credentials of a high-school diploma. Many of these individuals and their families are considered to be a part of the working poor that make up a considerable portion of this nations labor force.

1. Use technology to create a scatterplot of the percent of low-income working families and the percent of 18-64 yr-olds with no high school diploma information (The Working Poor Families Project, 2011) in each jurisdiction.Print or copy and paste the scatterplot and be sure to clearly identify the predictor and response variables based on the believed association between education and income.

2. Write one or two sentences to describe the association between the predictor and response variables in your scatterplot. Be sure to use the actual names of the variables in their appropriate places in your response.

3. Use technology to find the regression equation for the linear association between the percent of low-income working families and the percent of 18-64 yr-olds with no high school diploma. Provide this equation and write a brief interpretation of its slope (Be sure to use the same predictor and response variable assignments that you chose for the scatterplot).

4. Identify the R-squared value for this regression equation. Provide this value and write a sentence to interpret its meaning.

5. A student states that a decrease in the percent of 18-64 yr-olds with no high school diploma will no doubt lead to a decrease in the percent of low-income working families. Based on what you know about correlation, write a brief response to this statement.

6. The student in number 5 also believes that the majority of those with no high-school diploma are similar in terms of their nationality, native language, and disability status.The student, therefore, believes that it is the responsibility of these sub-groups of the population and their advocates to address the working poor issue themselves.Use the key rules about samples and extrapolation when making inferences from correlations to write a socially responsible and statistically appropriate response regarding the validity of the students beliefs.

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Confidence Intervals

During the recent recovery from the Great Recession of 2007-2009, the economic situation for many families has improved. However, in 2011 the recovery was slow and it was uncertain as to how much had really changed on the national level. To estimate the population parameter of the percent of lowincome working families, a representative simple random sample could be used to calculate a point estimate and a confidence interval.

7. Write an appropriate sampling procedure that will enable a researcher to collect a simple random sample of size n=20 from the full list of jurisdictions.

8. Carry out a sampling of the jurisdictions by using a random number generator, random number table, or the sampling capabilities of technology to select a simple random sample of size n=20 from the full list of the jurisdictions. Provide the selected sample of 20 in the table included below, making sure to include the corresponding percent of low-income working families (%LIWF) information for each jurisdiction selected.

Jurisdiction %LIWF Jurisdiction %LIWF Jurisdiction %LIWF Jurisdiction %LIWF

9. Use technology to calculate the sample mean and sample standard deviation of the percent of low-income working families for the selected 20 jurisdictions in your sample. Provide your mean and standard deviation and express in detail why it is unlikely that any two samples would produce the same results.

10. A different sample of size n=20 produced a sample mean of 31.08% and a sample standard deviation of 5.48%. Use these values to calculate a 90% confidence interval (without the use of statistical technology) for the national mean percent of low-income working families. Please show all calculations and provide the upper and lower limits that make up the confidence interval. (Round the limits to two decimal places.)

11. Express an appropriate statistical interpretation of the 90% confidence interval included in the answer to number 10.

12. In any of the 20-value samples selected, some jurisdictions may have a percent of low-income working families that is not included in the 90% confidence interval calculated above. If federal funds are available only for jurisdictions whose percent of low-income working families falls within the reported confidence interval, explain whether an interval with a higher or lower confidence level would be more advantageous to the jurisdictions.

13. If a lawmaker reports only research results that ensure that the jurisdiction he or she represents gets federal aid, explain whether such an action would constitute a misuse of statistics. If the

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action is not a misuse, state why it is appropriate. If the action is a misuse, state an alternate reporting practice that would be more appropriate. Hypothesis Testing

In 2011, the national percent of low-income working families had an approximately normal distribution with a mean of 31.3% (The Working Poor Families Project, 2011). Although it has remained slow, some politicians now claim that the recovery from the Great Recession has been steady and noticeable. As a result, it is believed that the national percent of low-income working families is significantly lower now in 2014 than it was in 2011. To support this belief, a recent 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 a 0.10 significance level, test the claim that the national average percent of low-income working families has improved since 2011.

14. Write a few brief sentences to state the type of test that should be performed and state the assumptions and conditions that justify its appropriateness.

15. Clearly identify and state the null and alternate hypothesis for this test.

16. Use technology to identify the test statistic and the P-value associated with the hypothesis test. Provide these values.

17. State the decision of the hypothesis test based on a 0.10 significance level.

18. Provide the appropriate conclusion about the claim that the national average percent of low income working families has improved since 2011.

Reference(s)

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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

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West Virginia 36.1 12.9 Wisconsin 28.7 8.5 Wyoming 28.1 8