For my final project and presentation in my STAT 466 class (Survey Sampling), I had to work in a team to collaborate and sample different sampling methods on the topic of: Early Career Salary Potential For All 935 Ranked United States Colleges and Universities. Throughout this observational study we tested three different sampling methods to decide which sampling method was most useful, as well as compare each of the findings that was supposed to all target the same mean within their respective confidence intervals. The data collected was not modified. The mean early career pay salary potential calculated from the raw data was μ = $51,359.68. 

Stratified Random Sampling was used first to look at the statistical ranking of the schools in comparison to the average pay by creating boxplots within R-Studio. The same was done for each individual state and the early career pay. By using the cumulative square root of frequencies, this method provided my group and I the best homogeneous strata which allowed the strata to be an appropriate size. To estimate the bound of the target pay, we performed an analysis in minitab (N, Mean, Variance) and then used appropriate solvable equations ; our bound for this sampling method was Bound = 477.722. We achieved a confidence interval of ($50,808.35 , $51,763.78) from the bound, which captured the raw career salary pay. We are approximately 95% confident that the true mean value of the early career pay for all colleges is within the upper and lower bound. 

Simple Random Sampling was then used to create a histogram to compare 76 different early career pay options without replacement. The data found was suggested a right tail skewed, yet the histogram showed reasonable symmetry with no extreme outliers - making the assumptions for SRS met. The bound we estimated using population mean and sample size was bound = $1,970.41. Our mean estimate then became ($49,162.17 , $53,103.60) which again captured the average mean salary of $51,359.68. Although this is true, the bound of $1,970.41 is nearly four times as large as our desired bound - which is not a cause for a lot of concern. 

Systematic Sampling was used by creating another histogram and scatter plot, which showed the sample appearing to take on a random pattern. The data appeared to be slightly right skewed yet the shape of the sample size was large and mostly normal without any extreme outliers. The bound estimated from Systematic Sampling was equal to $1,718.22 which again was nearly four times the amount of our desired bound. The mean estimate/confidence interval found from this bound was ($50,202.28 , $53,638.73) which once again captured the true population mean of $51,359.68. 

All of our estimates were able to capture the true mean of the population ($51,359.68) which meant that all three sampling methods used computed accurate results. One is able to conclude that the average early career salary potential for a recent graduate will be between $49,162.47 and $53,638.73. 

Note: This study could be broken down to look into the different university rankings, different majors, degree type, percentage that have graduated, and specific locations of each college or university. All of these factors were not taken into account with this study.