MA135 Statistical Applications Final Project Rubric Project Rubric - Part 1 Organization & Writing: Maximum of 10 points Part 1 project report form is well organized, filled out completely. Overall writing is thorough with correct grammar, punctuation, spelling, and capitalization. (points are deducted for quality, missing information, and mechanics) ____________ Proposal: Maximum of 90 points (10 pts for each deliverable.) Research question is provided ____________ The research question allows the collection of quantitative data ____________ The data is bivariate. (There is a dependent and an independent variable.) ____________ Website links are provided from which the data can be obtained ____________ Data is provided in an Excel file ____________ The Excel file has three columns that are labeled with units ____________ Each variable has a minimum of n=30 data values ____________ A description is provided for the independent variable in a complete sentence with units noted ____________ A description is provided for the dependent variable in a complete sentence with units noted ____________ Total: ____________

Project Rubric - Part 2 Organization & Writing: Maximum of 10 points Part 2 project report form is well organized, filled out completely. Overall writing is thorough with correct grammar, punctuation, spelling, units given, and capitalization. (points are deducted for quality, missing information, and mechanics) ____________ Statistics: Maximum of 40 points Measures of Center for independent and dependent variable are correct (8 points) ____________ Measures of Variation for independent and dependent variables are correct (8 points) ____________ Measures of Relative Standing for independent and dependent variables are correct (8 points) ____________ Analysis is provided for each group (8 points) ____________ SS for each group is correct (8 points) ____________ Hypothesis Test: Maximum of 30 points Null and Alternate Hypothesis are stated correctly (5 points) ____________ Critical t value is correct (5 points) ____________ Pooled variance and standard error of the mean values are correct (5 points) ____________ Computation of the t statistic is correct (5 points) ____________ Decision regarding the hypothesis is correct (5 points) ____________ Conclusion regarding the hypothesis is correct (5 points) ____________ Writing: Maximum of 20 Points Complete statement of conclusion and student reflections are included. Overall writing is thorough with correct grammar, punctuation, spelling, and capitalization. (points are deducted for quality and mechanics) ____________ Extra Credit: Maximum of 5 points Graphics, graphs, Wow me! ____________ Total: ____________

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Example

MA135 Statistical Applications Final Project Part 1 Name: Part 1: Developing a Research Question & Selecting Bivariate Data For the final project you will determine whether there is sufficient evidence of difference between two variables. For part 1, you will develop a research question and select bivariate data for analysis. Your research question and data selection must be approved by the instructor. 1. Research question: To develop your research question, consider things that you are interested in or wondering about that may be answered with bivariate (two sets of) data. Some possible student research questions are: Do movies with a higher production budget result in a higher worldwide gross revenue? Do NFL athletes with higher QB performance have higher salaries? Do states with a higher college degree rate have a lower poverty rate? Do Coca-Cola beverages with higher sugar content have more calories? Do countries that consume more coffee per capita have longer working hours? Does a doctor with more residential training have higher salaries in New York? Do cars with more engine horsepower have higher average miles per gallon? Do counties, states, or regions with higher college degree rates have higher median income? Do countries with higher women's education levels have lower infant mortality rates? Do heavier baseball players have higher hitting averages? Do soccer players with a higher FIFA rating earn more money? Do YouTube Channels with a higher number of subscribers have a higher view count? Do Major League Baseball pitchers with a lower Earned Run Average have a higher number of credited wins? (The number of wins credited to the pitcher within one year's regular season.) Do states with a higher median household income have a higher percentage of homeless people? Do brands of cars in the United States with more horsepower cost more? Do states with a higher number of registered nurses (per 100,000 residents) have a higher median salary? Do states with higher percentages of immigration population have a higher crime rate? Do countries with high education levels have a lower fertility rate? Example Student Do states with higher Flu Vaccine Rates have lower Influenza/Pneumonia death rates? Do states with higher median household income have lower violent crime rates? Type your research question here: 2. Data selection and source Below is a list of websites students may use to obtain data. There are tons of resources where you can obtain real data. You may use other sites, but make sure that it is a legitimate website. Finding good data to analyze will take a good amount of time so plan ahead! https://www.data.gov/ https://www.census.gov/data.html https://www.cia.gov/library/publications/resources/the-world-factbook/appendix/appendix-e.html https://www.healthdata.gov/ https://www.cdc.gov/datastatistics/index.html http://www.gapminder.org/data/ http://www.pewinternet.org/datasets/ https://stats.nba.com/ http://mlb.mlb.com/stats/ http://hdr.undp.org/en/data http://www.espn.com/ https://www.glassdoor.com/Salries/index.htm https://www.aamc.org/ https://ourworldindata.org/ Do countries with higher female education levels have lower infant mortality rates?

Your sample size should be comprehensive. For example, you should have a minimum of n=30 for your data to be comprehensive. Remember that each data point needs two variables (dependent and independent variables). The data must be quantitative. Once you decide on a data set, ask for approval. Download, copy and paste the data it into Excel. You need three columns in Excel clearly labeled with units: Ex: (State names, median income ($), Homeless percentage of state population) a. Enter the website or source you obtained your data from: b. Explain how you selected the data: Determining the Independent and Dependent Variables: To determine the dependent and independent variables, take a look at how you have phrased the research question. For example, here is a research question: Do countries with higher levels of Determining the Independent and Dependent Variables: Decide how you will ask your research question. For example, a researcher may question whether countries with higher education for women have lower child mortality rates. The researcher may have asked this because s/he wanted to test the claim that that women's education may have an effect on child mortality rates. Therefore, women's education is the independent variable and child mortality rates is the dependent variable. 3. Independent (predictor) Variable () a. Identify the Independent Variable (): Write the name that you will use to label the independent variable in Excel www.childmortality.org www.healthmetricsandevaluation.org Mean years of schooling (females aged 25 years and above) in 2009 The data is from two separate sources. The dependent variable (y), under-five mortality rate (per 1000 births) for each country in 2009 is from www.childmortality.org. The independent variable (x), is mean years in school for women 25 years and above for each country in 2009 is from www.healthmetricsandevaluation.org. I deleted countries with missing data values and included only 33 countries that had both the dependent and independent variable data values. The sample size of paired data is n= 33.

b. Describe and explain the independent variable in a complete sentence with units and years, if applicable. Use the wording from the data source. 4. Dependent (response) Variable (y) a. Identify the dependent variable (y): Write the name that you will use to label the dependent variable in Excel. b. Describe and explain the dependent variable in a complete sentence with units and years, if applicable. Use the wording from the data source. Submit this document and Excel file of your data (with three columns clearly labeled with name of the data point, independent variable with units, dependent variable with units) Under age five mortality (per 1000 births) in 2009 The dependent variable is the number of deaths of children between birth and age five expressed per 1000 births in each country in 2009. --------------------------------------------------------------------------------------------------------------------------------

PART TWO ( Example)

a. You may paste the summary statics table from Excel below for the independent variable. Adjust the font size if necessary. ~optional~ b. Describe and determine the mean, median, and midrange of the independent variable. Include units. Carry one more decimal place than is present in the original set of values. {Chapter 3} Mean: Median: Midrange: 4. Measures of Variation of the Independent Variable () a. Determine the range, standard deviation, and variance of the independent variable. Include units. Carry one more decimal place than is present in the original set of values. {Chapter 4} Range: Standard Deviation: Variance: The independent variable is the mean years of education women (25 years of age or older) received in each country in 2009. Total of all values divided by n 7.66 years The middle value when the list is arranged in order. 8.4 years Add the highest value plus the lowest value and divide that total by 2. 6.8 years 12.40 years 3.40 years 11.53 years squared5. Measures of Relative Standing of the Independent Variable () a. Identify the measures of the independent variable. Include units. Minimum: Median: Maximum: b. Determine the data point that has the minimum and maximum values in your independent variables column. With Minimum Value: With Maximum Value: 6. Analysis Describe the independent variable in a short paragraph based on your analysis of the data. Bonus: Include graphs. The range shows a substantial difference of 12.4 years for mean years of schooling for women age 25 and older between the countries with minimum and maximum values. 50% of the countries have mean years of schooling for women that is less than 8.4 years which implies that half of the countries have mean years of schooling for women below 9 th grade high school. Countries that have mean years of schooling for women age 25 and older that is less than 0.86 years are considered unusual as they are more than two standard deviations below the mean. These nations have mean years of schooling below first grade in elementary school. The highest frequency for mean years of schooling for women age 25 and above in each country is between 9 and 10 years. 0.6 years 8.4 years 13.0 years The country, Chad, has the minimum (0.6) mean years of schooling for women 25 years and above in 2009. The United States has the maximum (13.0) mean years of schooling for women 25 years and above in 2009.Summary Statistics of the Dependent Variable (y) 1. Dependent (response) Variable (y) a. Identify the dependent variable (y): Write the name that you used to label the dependent variable. b. Describe and explain the dependent variable in a complete sentence with units and years if applicable. Use the wording from the data source (website). 2. Measures of Center of the Dependent Variable () a. You may paste the summary statics table below for the dependent variable. Adjust the font size if necessary. ~optional~ b. Determine the mean, median, and midrange of the dependent variable. Include units. Carry one more decimal place than is present in the original set of values. {Chapter 3} Mean: Median: Midrange: Under age five mortality (per 1000 births) in 2009 The dependent variable is the number of deaths of children between birth and age five expressed per 1000 births in each country in 2009. 41.98 deaths per 1000 children under 5 23.7 deaths per 1000 children under 5 95.0 deaths per 1000 children under 53. Measures of Variation of the Dependent Variable (&) a. Determine the range, standard deviation, and variance of the dependent variable. Include units. Carry one more decimal place than is present in the original set of values. {Chapter 4} Range: Standard Deviation: Variance: 4. Measures of Relative Standing of the Dependent Variable (y) a. Identify each value below. Include units. Minimum Median: Maximum: b. Determine the data point that has the minimum and maximum values in your dependent variables column. With Minimum Value: With Maximum Value: c. Separate the data for your dependent variable into two groups based on a designation of your independent variable - You may arrange the groups by location, age, alternating data, etc...per your choice. For example, Group one can be for any 15 values that correspond to the lower levels of the independent variable and Group two can be for the other 15 values that correspond to the higher levels of the independent variable. {Chapter 4} Group One Group Two N = 12 N = 8 M = Mean " = = = 15.75 M = Mean: " = = =12.5 Highest value - Lowest value = 187.38 - 2.6 = 184.8 deaths per 1000 children under 5 42.39 deaths per 1000 children under 5 1797.09 deaths per 1000 children under 5 squared The country, Luxembourg, in Europe, has the lowest number of deaths per 1000 children under age 5. In 2009, Angola, a country in Africa, has the highest number of deaths per 1000 children under age 5. 2.6 deaths per 1000 children under 5 23.7 deaths per 1000 children under 5 187.3 deaths per 1000 children under 5 SS = = ( " ) = 70.22 SS = = ( " ) = 78 Note: This work is from a different data set with fewer data items than 30. This is an example as if 12 countries were chosen from Europe and 8 from Asia, for example. This is only an example of what to do with your data computationally.5. Analysis a. Describe the dependent variable in a short paragraph (at least three sentences) based on your analysis of the data. Bonus: Include graphs The range of 184.8 indicates that there is a substantial gap in child mortality rates between the country with the lowest and highest child mortality rates per 1000 children. For the countries selected, the mean number of deaths per 1000 children under age 5 was 41.98 deaths. 50% of countries have child mortality rates greater than 23.7 (deaths per 1000 children under age 5). Countries that have a child mortality rate that is above 126.76 are considered unusual as they are more than two standard deviations above the mean. These nations have an unusually high number of deaths of children under age 5. The highest frequency for deaths of children under age 5 (per 1000 children) is between 0 and 10 deaths. This indicates that while it is evident that there is great disparity of health levels based on the wide range of the child mortality rate in the world, most countries have between 0 and 10 deaths per 100 children under age 5.Hypothesis Testing 1. Hypothesis Test Test the claim that there is a significant difference for your independent () variable between the two groups of the dependent () variable. a. State the null and alternative hypothesis. {Chapter 8} b. Find the pooled variance for the two groups. {Chapter 10} c. Compute the standard error of the difference between the means of the two groups. {Chapter 10} d. Hypothesis Test Based on the t-Test using a = 0.01 significance level. The null hypothesis ( ! ) : " = # The alternative hypothesis ( # ) : # " = + + = .+ + = . = 8.23 (2 32 ) = ( + = ( . + . = . + . = . = 1.31 t = 6666 3 6666 (&'&) = .3. . = . . = 2.48 My decision about the null hypothesis ( ! ): Reject the null hypothesis. Because the test statistic is in the critical area.e. Write a statement stating whether there is significant difference between the two groups as related to the independent and the dependent variables. f. Write 2 or more paragraphs stating your conclusions, observations, analysis, and evaluation. Reflect on your work too. Conclusion about the claim: There is a difference between the two groups. The evidence supports the claim that the mean number of deaths for children under age 5 is significantly different in countries in Europe as compared to countries in Asia. For this project I was able to...... The observations show that.... It is noticeable that...... One analysis may surmise that women with more education probably have better knowledge of how to take care of an infant or child care. A woman with access to more education may decide to get married and have children later in their lives and that access to education and age maturity may in turn decrease the number of early childhood deaths. Furthermore, educated women would make better informed reproductive and healthcare decision. An evaluation can indicate that the result of better infant care can reflect lower infant mortality rates. This project was... I was surprised that... If I had to do this project again, I would probably.....

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Statistical Applications Final Project Part 1

Name:

Part 1: Developing a Research Question & Selecting Bivariate Data

For the final project you will determine whether there is sufficient evidence of linear correlation between two variables. For part 1, you will develop a research question and select bivariate data for analysis. Your research question and data selection must be approved.

1. Research question:

To develop your research question, consider things that you are interested in or wondering about that may be answered with bivariate (two sets of) data.

Some past student research questions were:

• Do movies with a higher production budget result in a higher worldwide gross revenue?
• Do NFL athletes with higher QB performance have higher salaries?
• Do states with a higher college degree rate have a lower poverty rate?
• Do Coca-Cola beverages with higher sugar content have more calories?
• Do countries that consume more coffee per capita have longer working hours?
• Does a doctor with more residential training have higher salaries in Georgia?
• Do cars with more engine horsepower have higher average miles per gallon?
• Do counties or regions with higher college degree rates have higher median income?
• Do countries with higher women's education levels have lower infant mortality rates?
• Do heavier baseball players have higher hitting averages?
• Do soccer players with a higher FIFA rating earn more money?
• Do YouTube Channels with a higher number of subscribers have a higher view count?
• Do Major League Baseball pitchers with a lower Earned Run Average have a higher number of credited wins? (The number of wins credited to the pitcher within the 2017 regular season.)
• Do states with a higher median household income have a higher percentage of homeless people?
• Do brands of cars in the United States with more horsepower cost more?
• Do states with a higher number of registered nurses (per 100,000 residents) have a higher median salary?
• Do states with higher percentages of immigration population have a higher crime rate?
• Do countries with high education levels have a lower fertility rate?
• Do states with higher Flu Vaccine Rates have lower Influenza/Pneumonia death rates?
• Do states with higher median household income have lower violent crime rates?

Type your research question here:

2. Data selection and source

Below is a list of websites students have used in the past. There are tons of resources where you can obtain real data. You may use other sites, but make sure that it is a legitimate website. Finding good data to analyze will take a good amount of time so plan ahead!

https://www.data.gov/

https://www.census.gov/data.html

https://www.cia.gov/library/publications/resources/the-world-factbook/appendix/appendix-e.html

https://www.healthdata.gov/

https://www.cdc.gov/datastatistics/index.html

http://www.gapminder.org/data/

http://www.pewinternet.org/datasets/

https://stats.nba.com/

http://mlb.mlb.com/stats/

http://hdr.undp.org/en/data

http://www.espn.com/

https://www.glassdoor.com/Salries/index.htm

https://www.aamc.org/

https://ourworldindata.org/

Your sample size should be comprehensive. For example, you should have a minimum of n=30 for your data to be comprehensive.

Remember that each data point needs two variables (dependent and independent variables). The data must be quantitative. Once you decide on a data set, ask for approval.

Download, copy and paste the data it into Excel.

You need three columns in Excel clearly labeled with units:

Ex: (State names, median income ($), Homeless percentage of state population)

a. Enter the website or source you obtained your data from:

b. Explain how you selected the data:

Determining the Independent and Dependent Variables:

To determine the dependent and independent variables, take a look at how you have phrased the research question. For example, here is a research question: Do countries with higher levels of

Determining the Independent and Dependent Variables:

Decide how you will ask your research question.

For example, if a researcher questions whether countries with higher education for women have lower child mortality rates? The researcher may have asked this because s/he wanted to test the claim that that women's education may have an effect on child mortality rates. Therefore, women's education is the independent variable and child mortality rates is the dependent variable.

3. Independent (predictor) Variable ()

a. Identify the Independent Variable ():

Write the name that you will use to label the independent variable in Excel.

:

b. Describe and explain the independent variable in a complete sentence with units and years, if applicable. Use the wording from the data source.

4. Dependent (response) Variable (y)

a. Identify the dependent variable (y):

Write the name that you will use to label the dependent variable in Excel.

b. Describe and explain the dependent variable in a complete sentence with units and years, if applicable. Use the wording from the data source.

Submit this document and Excel file of your data (with three columns clearly labeled with name of the data point, independent variable with units, dependent variable with units)

MA135 Statistics Final Project

Part 2: Summary Statistics of the Independent Variable()

Your part 1 must be approved before you begin part 2.

Names:

Make sure to take a look at the student sample project for part 2 to get an idea of what is expected of your write-up.

1. Data selection methodology

In statistics, how the sample is obtained for data analysis is important. Explain how you obtained or selected your data. Did you choose all the data because it is comprehensive of your data sets (example: all 50 states)? Did you to delete some values because it was missing? Was your data selected because it meets the criteria? What is your sample size?

2. Independent Variable (

a. Identify the Independent Variable ():

Write the name that you used to label the independent variable in Excel

:

b. Describe and explain the independent variable in a complete sentence with units and years if applicable. Use the wording from the data source.

3. Measures of Center of the Independent Variable (

3. Measures of Center of the Independent Variable ()

a. You may paste the summary statics table from Excel below for the independent variable. Adjust the font size if necessary. ~optional~

b. Determine the mean, median, and midrange of the independent variable. Include units. Carry one more decimal place than is present in the original set of values. {Chapter 3}

Mean:	Median:	Midrange:

4. Measures of Variation of the Independent Variable (

a. Determine the range, standard deviation, and variance of the independent variable. Include units. Carry one more decimal place than is present in the original set of values. {Chapter 4}

Range:	Standard Deviation:	Variance:

5. Measures of Relative Standing of the Independent Variable ()

a. Identify the measures of the independent variable. Include units.

Min:	Median:	Maximum:

b. Determine the data point that has the minimum and maximum values in your independent variables column.

With Minimum Value:	With Maximum Value:

6. Analysis

Describe the independent variable in a short paragraph based on your analysis of the data.

Part 3: Summary Statistics of the Dependent Variable(y)

1. Dependent (response) Variable (y)

a. Identify the dependent variable (y):

Write the name that you used to label the dependent variable. Include units.

b. Describe and explain the dependent variable in a complete sentence with units and years if applicable. Use the wording from the data source (website).

2. Measures of Center of the Dependent Variable (

a. You may paste the summary statics table below for the dependent variable.Adjust the font size if necessary. ~optional~

b. Determine the mean, median, and midrange of the dependent variable. Include units. Carry one more decimal place than is present in the original set of values. {Chapter 3}

Mean:	Median:	Midrange:

3. Measures of Variation of the Dependent Variable (

a. Determine the range, standard deviation, and variance of the dependent variable. Include units. Carry one more decimal place than is present in the original set of values. {Chapter 4}

Range:	Standard Deviation:	Variance:

4. Measures of Relative Standing of the Dependent Variable (y)

a. Identify each value below. Include units.

Minimum	Median:	Maximum:

b. Determine the data point that has the minimum and maximum values in your dependent variables column.

With Minimum Value:	With Maximum Value:

c. Separate the data for your dependent variable into two groups - Group one is for values above the median and Group two is for values below the median. {Chapter 4}

Group One	Group Two
N =	N =
M =	M =

5. Analysis

a. Describe the dependent variable in a short paragraph (at least three sentences) based on your analysis of the data.

Part 4: Hypothesis Test

1. Hypothesis Test

Test the claim that there is a significant difference for your independent () variable between the two groups of the dependent () variable.

a. State the null and alternative hypothesis. {Chapter 8}

b. Find the pooled variance for the two groups. {Chapter 10}

c. Compute the standard error of the difference between the means of the two groups. {Chapter 10}

d. Hypothesis Test Based on the t-Test using a significance level.

e. Write a statement stating whether there is significant difference between the two groups as related to the independent and the dependent variables.

f. Write 2 or more paragraphs stating your conclusions, observations, analysis, and evaluation.