Question

based on this assignment: For this assignment, you will undertake an analysis based on a self-designed fictitious study that utilizes statistical methodologies. You will first develop a fictitious problem to examine - it can be anything. For example, maybe you want to look at whether scores on a standardized college placement test (like the SAT) are related to the level of income a person makes 10 years after college; Or, whether those who participate in a Leadership Training program rated as better managers compared to those who do not; Or, whether ones political affiliation is related to gender. These are just a few examples; be creative and think about what piques your interest. You might also address a problem that you may want to look at in future research for a dissertation. Your analysis report should include the following components: 1. Describe your research study. 2. State a hypothesis. 3. List and explain the variables you would collect in this study. There must be a minimum of three variables and two must meet the assumptions for a correlational analysis. 4. Create a fictitious data set that you will analyze. The data should have a minimum of 30 cases, but not more than 50 cases. 5. Conduct a descriptive data analysis that includes the following: a. a measure of central tendency b. a measure of dispersion c. at least one graph 6. Briefly interpret the descriptive data analysis. 7. Conduct the appropriate statistical test that will answer your hypothesis. It must be a statistical test covered in this course such as regression analysis, single t-test, independent t-test, cross-tabulations, Chi-square, or One-Way ANOVA. Explain your justification for using the test based on the type of data and the level of measurement that the data lends to for the statistical analysis. 8. Report and interpret your findings. Use APA style and include a statement about whether you reject or fail to reject the null hypothesis. 9. Copy and paste your data output and place it in an appendix. I want to use this data of improper payment rates they agency 1 and agency 2 have projected a rate of Agency 1, 14.8% and Agency 2. 17.2% for year 32. data:

Agency 1 Agency 2
year 1 11.0% 8.0%
year 2 11.3% 8.2%
year 3 10.3% 7.4%
year 4 11.0% 8.0%
year 5 10.1% 7.8%
year 6 10.9% 7.8%
year 7 10.9% 7.8%
year 8 10.1% 10.0%
year 9 10.3% 10.1%
year 10 10.1% 10.2%
year 11 10.0% 10.7%
year 12 10.5% 11.1%
year 13 10.3% 12.1%
year 14 10.6% 12.0%
year 15 11.2% 10.0%
year 16 11.7% 9.9%
year 17 12.0% 9.1%
year 18 11.3% 9.0%
year 19 11.42% 9.17%
year 20 10.00% 9.20%
year 21 9.32% 8.12%
year 22 9.90% 8.90%
year 23 11.58% 9.23%
year 24 11.00% 9.60%
year 25 10.73% 8.44%
year 26 11.00% 8.70%
year 27 11.6% 7.4%
year 28 11.8% 7.6%
year 29 12.5% 8.8%
year 30 12.4% 8.7%
year 31 13.0% 8.4%

Answer 1

Descriptive Statistics

We will be using ANOVA.

Null and Alternative Hypothesis:

H₀: µ_{Agency 1} = µ_{Agency 2}

H₁: Not all Means are equal

Alpha = 0.05

N = 62

n = 31

Degress of Freedom:

df_Between = a – 1 = 2-1 =1

df_Within = N-a = 62-2 = 60

df_Total = N-1 = 62-1 = 61

Critical Values:

Time (df_Between, df_Within): (1,60) = 4.001

Decision Rule:

If F is greater than 4.001, reject the null hypothesis

Test Statistics:

SS_Betwen = ∑(∑a_i)²/n - T²/N = 54.99

SS_Within = ∑(Y)² - ∑(∑a_i)²/n = 69.21

SS_Total = SS_{Betwen ­­}+ SS_Within = 124.2

MS = SS/df     

F = MS_effect / MS_error

Hence,

F = 54.99/1.15 = 47.67

Result:

Our F = 47.67, we reject the null hypothesis

Conclusion:

Not all means are equal.