OVERVIEW

In Modules 1 and 2, you began to define, collect, organize, visualize, and analyze a single set of data using the concepts and skills learned in this course. (This will be an application of the DCOVA framework.)

In this third module, you create a confidence interval with your data. Remember that a contribution to the project portfolio will be required for each module.

An example project demonstrating the requirements for these contributions for each module is provided in each module.

INSTRUCTIONS

In Modules 1 and 2, you accomplished the following tasks.

• You came up with a question or problem that you were interested in.
• You collected 30 data points needed for this project.
• You calculated key descriptive statistics using the Project Rubric as your guide.
• Clearly defined the purpose of your project and details of your collection of data.
• Organized your data into a frequency distribution and visualized your data with a histogram and relative percentage polygon.
• Made corrections and improvements from Module 1.
• Completed an initial analysis of your work after Modules 1 and 2.

For Module 3, you will:

1. include contributions from Modules 1 & 2 with corrections,
2. evaluate the type of sampling used and make recommendations for improvement for future sampling,
3. create a confidence interval that can be used to estimate the true population parameter for your data and
4. validate the proper sample size needed to carry on further study.

Project example contribution

Modules 1 & 2 Contribution 1. Purpose of project The purpose of this project is to determine the mean number of hoodies a resident of Colorado owns. By collecting data from a sample of thirty people in different parts of Colorado, information can be gained that might be useful to clothing manufacturers and retail sales outlets. 2. Data Collection The data was collected by personally asking friends, family, and co-workers, by text, the number of hoodies each currently owns. This convenience sample began with each person being messaged on September 10, 2020, and all responses were received by September 13. 3. Raw Data The 30 data points, in numbers of hoodies, in ascending order: 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 9, 10, 11, 12, 14, 15, 18, 20, 26, 30, 32, 38, 51 4. Frequency Distribution Number of Hoodies Frequency Relative Frequency (%) Cumulative Frequency (%) 0 - 9 18 60.00% 60.00% 10 - 19 6 20.00% 80.00% 20 - 29 2 6.67% 86.67% 30 - 39 3 10.00% 96.67% 40 - 49 0 0.00% 96.67% 50 - 59 1 3.33% 100.00% 5. Histogram 0 2 4 6 8 10 12 14 16 18 20 0 - 9 10 - 19 20 - 29 30 - 39 40 - 49 50 - 59 Hoodies Frequency 6. Relative Percentage Polygon 7. Sample Mean 12.57 hoodies 8. Sample Median 8.5 hoodies 9. Sample Mode 3 and 9 hoodies (two modes) 10. Sample Range 49 hoodies 11. Sample Variance 140.53 hoodies2 12. Sample Standard Deviation 11.85 hoodies 13. Coefficient of Variation 94.33% 0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 0 - 9 10 - 19 20 - 29 30 - 39 40 - 49 50 - 59 Hoodies (%) Relative Frequency (%) 14. Z Scores Number of Hoodies' Z Scores 2 -0.891 3 -0.807 4 -0.723 5 -0.638 6 -0.554 7 -0.470 8 -0.385 9 -0.301 10 -0.217 11 -0.132 12 -0.048 14 0.121 15 0.205 18 0.458 20 0.627 26 1.133 30 1.471 32 1.639 38 2.145 51 3.242 15. Initial Analysis of Data This set of data is positively skewed (since sample mean is greater than sample median). Data with positive skew is not symmetrical. There is one outlier of 51 hoodies. The person stating this level of ownership works for a sports clothing supplier. Module 3 Contribution 1. Sampling The sampling frame used for this study was my friends, family, and co-workers. I just chose the first thirty that came to mind and texted them. This is an example of convenience sampling. If I were to complete this research again, I would expand my sampling frame to include classmates that I know live in other parts of the state of Colorado. I would seek to have at least fifty people in a list that I could choose from using systematic random sampling. 2. Confidence Interval of Population Mean Using the sample standard deviation of 11.85 hoodies and the Students t distribution, the sampling error for this study is 4.43 hoodies. This error combined with the sample mean leads to a 95% confidence interval of 8.14 to 16.99 hoodies. I am 95% confident that the true population mean for the number of hoodies owned by an individual in Colorado is in that interval. 3. Revised Sample Size The sample error resulting from this study is 4.43 hoodies. I would like to have a margin of error of only 2 hoodies (my chosen margin of error e) so that I can be more sure of the state-wide result. Using the sample standard deviation at 95% confidence and a margin of error e = 2 hoodies results in a revised sample size of 135 people (for a 2nd round of study). * This project is based on work completed by Katie Pope during fall semester 2020.