math case

MATH 2100 Gender/Racial Income Inequality Project

At this point you have completed 5 separate parts of this project. You have run multiple different statistics on the same data set comparing the income made between White Females, Black Females and Males. You will now compile all 5 parts into one document. Please make sure you have made all necessary changes before copying the individual sections into one document.

This final report needs to be a paper in paragraph form. You should introduce all tests and figures before you add the images. This needs to flow like a paper and should not just be a copy and paste of the previous 5 parts. There needs to be linking paragraphs to flow from one case study into the next to make one fluid paper.

After you have compiled the 5 previous sections (Chapter 3, 7, 9, 10, and 11 Statcrunch) write an introduction and conclusion paragraph reiterating the overall and final results you have come to at the end of this project. Your final paragraph should include advice or thoughts on how we can reduce the racial income gap. What can we do as a community to make sure all people regardless of race receive equal pay?

1

The goal of the project is to make comparison of the income data from 51 different areas based on three groups which include White women, Black Women, and all men. The data came from Census 2013 American Consumer surveys.

The income distribution of white women data is rightly skewed. The average income of the white men was 39930 with a standard deviation of 7188.1. The 80th percentile of the income in White women is $45892.38.

The income distribution of black women data is approximately normal. The average income of the white men was 33620 with a standard deviation of 5506.8. The 80th percentile of the income in White women is $38256.73

The income distribution of the men data is rightly skewed. The average income of the men was 47339 with a standard deviation of 6342.3. The 80th percentile of the income in Men is $52679.22.

The data had income inequalities based on gender. According to the data, Men had earned a higher income than women.

2

The dataset came from the American Consumer Survey, which was part of the Census in 2013. The dataset mainly contained the income of three groups of individuals, which include white women, black women, and men. A one-sample t-confidence interval was performed to determine the range at which the mean income of each individual lies. 

The average income earned by white women, black women, and men is $39929.88, $33620.10, and $47339.22, respectively. The first sample t confidence interval was performed at a 90% confidence interval. From the table above, we are 90% confident that the mean income of white women is between 38243.03 and 41616.73, that of black women lies between $32133.43 and $35106.77, and that of men lies between $45850.85 and $48827.58.

Moreover, another one-sample t test was performed at a 98% confidence interval. From the table above, we are 98% confident that the mean income of white women is between $37510.92 and 42348.85, that of black women lies between $31478.60 and $35761.61, and that of men lies between $45204.88 and $49473.55.

Therefore, the width of the confidence interval increases as the confidence interval increases. This is because the error bound becomes large as the confidence interval increases. The results above clearly show that men earn a higher income as compared to both white and black women.

1

Paired T test

The Data was collected by the American Consumer Survey as a part of the Census in 2013. The data was composed of the income of white women, black women, and all males. The first test is the paired t test which involves mean comparison between White women and Black women. The tests investigates whether the mean difference between white women and Black women is significantly different.

The results shows that the mean of the difference between white women and black women is significant, t (38) =12.825, p<0.0001. Since the p value is less than 0.05, the null hypothesis is rejected. Therefore, it can be concluded that the mean of the difference between White women and Black Women is significant.

The second test is the construction of the paired mean confidence interval between White and black women.

We are 95% confident that the mean of difference between white women and black women lies between 5909.0375 and 8124.0395.

The third test is the construction of the paired mean confidence interval between White women and men.

We are 95% confident that the mean of difference between White women and Men lies between -8515.80 and -6302.87.

Math 2101: Elementary Statistics Laboratory Name:

Report Grading Rubric

	Excellent	Very Good	Satisfactory	Fair	Poor	Unacceptable
	5 or 10 points	4 or 8 points	3 or 6 points	2 or 4 points	1 or 2 points	0 points
Formatting & Style (5 pts)	Correctly follows the formatting requirements. The writing style is professional and academic. Free of grammatical and spelling errors.	Correctly follows the formatting requirements. The writing style is professional and academic. Very few grammatical or spelling errors.	Mostly correct formatting. Very few lapses in style that are unprofessional or too informal for academic writing. Few grammatical or spelling errors.	Mostly correct formatting. Some lapses in style that are unprofessional or too informal for academic writing. Some grammatical or spelling errors.	Incorrect formatting. The writing style is unprofessional or too informal for academic writing. Several grammatical or spelling errors.	Illegible or incoherent. Inappropriate or offensive language.
Mathematical Detail & Computation (10 pts)	Completely correct. Work is presented in a well organized format.	Very few errors. Work is presented in a well organized format.	Mostly correct, but with several errors or work is poorly presented.	Mostly correct, but with several errors and work is poorly presented.	Many significant errors. Limited detail presented.	No evidence of mathematical detail or computation.
Mathematical Analysis (10 pts)	Draws correct conclusions that are well supported by the analysis of the presented calculations.	Draws mostly correct conclusions that are supported by the analysis of the presented calculations.	Draws mostly correct conclusions that are not well supported by the analysis of the presented calculations.	Draws incorrect conclusions from the supporting analysis of the calculations; or lacks supporting analysis.	Conclusions are incorrect or do not follow from the calculations.	No evidence of analysis or conclusions presented.
Written Interpretation (10 pts)	Well organized and articulated; correct use of mathematical terms and notation.	Mostly well organized and articulated; some misuse of mathematical terms and notation.	Lacks organization or is difficult to follow in some places; some misuse of mathematical terms and notation.	Poorly organized, but readable. Several instances of incorrect use of mathematical terms and notation.	Difficult to follow. Frequent incorrect use of mathematical terms and notation.	Incoherent or impossible to follow.
Use of figures (graphs, charts, tables, etc.) (5 pts)	Includes all appropriate figures. Figures are neatly designed and easy to interpret. Excellent explanations given.	Includes most of the appropriate figures. Figures are neatly designed and easy to interpret. Good explanations given.	Missing one important figure; or figures are poorly designed and presented with limited explanation given.	Missing one or more important figure; and figures are poorly designed and presented with limited explanation given.	Missing several important figures; figures are difficult to interpret.	No figures included.