MATH153 Spring 2020

Inferences from Data on the "Working Poor" in the U.S.

MATH 153: Introductory Statisticsis a general education course designed to assist students in the development of critical life skills.One of the goals of this assignment is to assess student competence for each of these objectives:

I.Written and Oral Communicationeffectively communicate the results of a statistical analysis (CCO19),

II.Critical Analysis and Reasoningperform hypothesis testing to draw inferences regarding parameters (CCO13),

III.Technological Competenceselect appropriate technology to manage data, explore data, perform inference, and check conditions (CCO2),

V.Scientific and Quantitative or Logical Reasoninganalyze bivariate data using linear regression (CCO5),generate and interpret statisticalgraphs (CCO4),

VII.Personal and Professional Ethics construct a solution to real world problems using problem methods individually and in teams (CCO16).

ASSIGNMENT: There is a population of workers in this country who are employed butwho do not earn enough in wages to securely cover the cost of their family's basic needs. Although the numbers vary by state or district, these individuals and their families are similar in that they cross racial, cultural, and local boundaries. They are considered the nation's "Working Poor." This common graded assignment was designed to allow you, the Introductory Statistics student, to explore some data that may be related to this population. Through the use of multiple statistical concepts covered in your MATH 153 course you will complete the provided assignment below to demonstrate your understanding of the manipulation of data, the use of technology in statistical analysis, the relationships between related variables, estimating population parameters, and hypothesis testing.

Purpose:To assess your understanding of selected key statistical concepts through the use of real-world data related to the working poor in the U.S.

Audience:Present responses as if addressing individuals with a basic but thorough mastery of the appropriate statistical concepts and procedures required for the completion of this assignment.

Directions: Please complete this assignment by responding specifically to each of the items 1-15, provided. According to the instructions you will be expected to use technology to make calculations, to create and include graphical displays, and to support your responses with complete, well-organized, and clear statements and interpretations.

ASSIGNMENT SPECIFICATIONS:

All assignments must be completed using word processing software like Word.

All responses must be typed in Times New Roman 12-pt font.

Page margins should be set to 1" all around.

Approximately 5 pages typed, and double-spaced.

Include requested graphical displays using cut and paste from statistical software.

You will use the included data file on the Working Poor to complete the project. It is provided in hard-copy and, upon request, will be made available in electronic format for your convenience.

GRADING:

• This assignment will account for10%of the total course grade.
• See attached rubric for details about how your assignment will be graded.

SUBMISSION GUIDELINES:

DUE DATE: For full semester, the due date is May 4^th. For the 2nd 7-week sections, the due date is May 4^th.

Submit your completed assignment in hard copy, or electronic format by the selected due date.

Submit TWO copies. One copy should include your student ID, course name, and section; it should omit student and faculty names.

Electronic submissions should be made with the student's ID number (900# or 901#) as the file name through Blackboard. Student and instructor names should not appear on electronic submissions.

MATH 153 - Spring 2020Student ID__________________________ Section__________________Date_______________________________

GREAT PROJECT

Part 1: 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 nation's labor force.

1.Use technology to create and provide a scatterplot of the association between the "percent of low-income working families" and the "percent of 18-64 yr-olds with no high school diploma" data for each jurisdiction. Write at least two sentences explaining how/why it is appropriate to create such a scatterplot, and describe the characteristics of the association seen in the scatterplot. Be sure to use the actual names of the variables in their appropriate places in your response(s). (Print or copy-and-paste the scatterplot and be sure to clearly identify the predictor and response variables based on the possible believed association.)

2.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." (Round final values to two decimal places.)Provide this equation and write a brief interpretation of the slope using the variable names. (Print or copy-and-paste the printout that identified the equation of the linear regression line, or any other form of evidence that technology was used.)

3.A student states that a decrease in the "percent of 18-64 yr-olds with no high school diploma" will lead to a decrease in the "percent of low-income working families."Write at least two concise sentences addressing the key uses of linear correlation and comment on its limitations in a response to the student's statement.

4.Calculate and provide the R-squared value for the regression equation. Provide a statement about its meaning, in general, and, its specific interpretation in the context of this assignment.

5.After examining these data for all the jurisdictions, someone notes that certain areas have an unusually high "percent of 18-64 yr-olds with no high school diploma." Based on this finding, this individual concludes that the high percentages are due to the rising population of immigrants in those areas.Further, the individual argues that any estimates of the associated "percent of low-income working families" in those areas should be recalculated after removing this sub-population from the data set, as they are causing the area to "look bad".In addition to thinking critically, use the key rules about linear regression and extrapolation to write a statistically appropriate and socially responsible response to the individual's conclusion and argument.

Part 2: Confidence Intervals

During the recovery from the Great Recession of 2007-2009, the economic situation for many families 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 national average of the percent of low-income working families, a representative simple random sample of the percent of low-income working families from each of the country's reporting jurisdictions could be used to calculate a point estimate and create a related confidence interval.With this confidence interval a better picture of the nation's recovery can be had and legislative decisions can be made.

6.Describe in two or three sentences how a simple random sample of size n=20 could be obtained from the full list of jurisdictions provided for use with this assignment.

7.A researcher reported that a sample of size n=30 produced a sample mean of 32.56% and a sample standard deviation of 6.56%.Use this information to calculate a 90% confidence interval for the national average for the "percent of low-income working families".Provide the upper and lower limits of the confidence interval and the margin of error.(Round the limits to two decimal places.)

8.Provide an explanation as to why it would be very unlikely that a different sample of size n=30 would produce the same confidence interval.

9.Provide an appropriate statistical interpretation of the 90% confidence interval found in number 7.

10.If a limited amount of federal funds have been allocated to assist jurisdictions whose "percent of low-income working families" exceeds a threshold based on the upper limit of a confidence interval, what would be the effect of using a confidence level that is higher than 90%?

11.If a public official requests funds based on a confidence interval provided by constituents in his/her district, would this raise any ethical concerns, or constitute a misuse of statistics, or both? Provide at least two sentences to respond to the situation presented.

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 =0.10 significance level, test the claim that the national average percent of low-income working families had improved by 2014.

12.Clearly restate the claim associated with this test, and state the null and alternate hypotheses.

13.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.

14.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.)

15.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 fromhttp://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