Project Approval. Decide upon a project consisting of 2 sets of data, or samples, that are dependent upon each other. You may find data on the Internet or you may want to perform a survey, but you will need at least 30 items in each of the two sets of data. Before beginning the project you will want to check with me regarding your project so that you do not spend too much time on something that may not work.
Project Definition. Once you receive the go ahead from me you will want to define your project and explain how you will obtain your data. In addition, you will want to make a conjecture as to what you believe the population mean will be for each group. These conjectures may be used to perform hypotheses tests on each of the samples or on both of them compared in some fashion. Email this section to me as soon as you complete it and I will give you a final go ahead for your project.
Summarize Data. Summarize your data into a frequency table or tables. This data can then be further summarized into a histogram or line graph. What do these summaries tell you about the data?
Analysis of Data. For each of the two sets, calculate a summary of the various statistics we studied, such as mean, variance, standard deviation, etc. What do these statistics tell you about the data? Use the 5 number summary to create a box plot for each of the two samples. Did you have any outliers? Did you consider them for real and continue to use them? Does your data appear to be normal based upon the box plot? Create a normal probability plot to see if the data is approximately normal.
Testing of Data. Create a confidence interval about the population for some level of confidence. Does this interval seem reasonable to you? Does your hypothesized mean fall within your confidence interval? What amount of error are you willing to live with? Use this amount of error to determine the sample size you would need in order to have 99% confidence interval consistent with the error size you chose. Would the hypothesized mean still be within this new confidence interval?
Comparison of the Samples. Compute a confidence interval and perform a hypothesis test regarding the difference between the two means. What can you say about the means of the two samples? Are they significantly different? Compute a correlation coefficient in order to show how much these samples depend upon each other. Create a scatter plot with a line of best fit included. Does your data appear to be linear? If not, what sort of equation might best fit your data.
Conclusions. Summarize all of your findings from this project. What statements can you make from these findings?
