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Math 1040 Term Project: Statistical Analysis Of College Graduates’ Starting CompensationsMajor FieldBusinessCommun-icationsComputer ScienceEducationEngi-neeringHumanities & Social SciencesMath & SciencesSample Mean54,53746,22759,54240,02160,66438,81741,923SampleStd. Dev.7,231.7237,214.3174,669.9692,364.8167,878.8567,146.1824,938.288In this project, we are examining the starting pay for seven different fields of work. This is all actual data that was taken from the US Department of Labor Statistics simple random sample. College students graduated and went into their respected fields. These numbers are a bit high since they also include compensations such as retirement and insurance. For the first part, we will be putting all the pay amounts into a frequency graph to see how the spread looks in a histogram. Then we will be making box plots for each of the seven job fields to see if there are any outliers for each job field. From there, we can continue with our project. All of the histograms are pictured below the paragraphs. The graphs reflected what I did expect to see. The most common amounts were within 1 or 2 standard deviations of the mean and the histograms did reflect that. Business, Education, Humanities and Social Sciences, and Mathematics and Science were the ones that were symmetric. Communications, Computer Science, and Engineering appeared to be slightly skewed either left or right. All the histograms appeared to be bell-shaped or skewed either right or left. None of them appeared to be random or following a different distribution. It was interesting that the Education and Mathematics and Science histograms seemed to be the most bell-shaped. They must be regulated through a very strict company or a government job of sorts. All the others seemed to be very dependent on other factors like college degrees, seniority, type of work, and more. My field that I intend to go into doesn’t appear to be under any of the options. I would like to be an Emergency room nurse and I don’t think any of the job fields above would recognize that job. lefttopNone of the boxplots have any outliers. The Engineering and Computer Science fields seemed to have higher values then the rest of the job fields. Education, Humanities and Social Sciences, and Mathematics and Sciences had lower values then the rest of the job fields. Business and Communications both had relatively average values. I think that some fields have higher values may be because they work for more profit and it may not be as regulated. Some jobs are regulated by the government and therefore, may have lower or more average values. We can use the T-distribution since the sample size is large and there are no outliers. Confidence Interval DiscussionConfidence Intervals are a method that involves showing a range of values that the true value will likely fall into. How likely the parameter will fall into a set of values is based on the confidence level we use. We use the higher confidence intervals to be more precise and the lower confidence intervals are not so precise. 90 or 95% (0.90 or 0.95) confidence intervals are the most common and usually the most precise we can get. The next portion of the project has me constructing a 95% and an 80% confidence interval. They are in the following pages. Based on a 95% Confidence Interval, the true mean of starting compensations for students graduating in the field of Humanities and Social Sciences is between $36,787 and $40,847. The sample mean that we took from that field, $38,817, was in those parameters. The sample mean was also the lowest mean starting compensation for any of the fields we looked at, so these parameters are most likely pretty accurate. For our second Confidence Interval test, an 80% CI doesn’t seem like a way to really inspire confidence in a person. I feel like people want assurance and confidence. Starting out with an 80% CI doesn’t seem very confident to tell you the truth. A 90 or 95% confidence rate would have been much more comforting to see. Although, this CI test is telling me a minority of college graduates (0.389, 0.457) are obtaining a starting compensation package starting at 50,000 or more. So even after college, Americans are still having to work their way up in a job or company to get the desired salary. Hypothesis Test DiscussionA hypothesis test is a method of testing a hypothesis of a population mathematically. In order to perform a hypothesis test, we need a Null hypothesis and an Alternative hypothesis. A Null hypothesis is a statement of equality regarding some aspect of a population. An Alternative hypothesis is a statement that contradicts the Null hypothesis. Along with our Null and Alternative hypotheses, we have to have a Level of Significance. The significance level is the complement of the confidence level or 1-alpha. Similar to confidence levels, we set up the significance level so we can specify how secure we are with our results. After we perform our calculations, we know whether to reject the null hypothesis or fail to reject the null hypothesis in favor of the alternative hypothesis. My calculations of the hypothesis tests are on a separate sheet of paper that you will see in the following pages. Hypothesis test 1 revealed that there was not sufficient evidence to reject the null hypothesis. This tells us that graduates from the field of Education have a starting compensation package of 35,000. My mother is a school teacher and thankfully my father works too because I don’t think our family could survive on a school teacher budget alone. But it is a good thing they make more as they work and gain more experience. Hypothesis test 2 revealed that there are plenty of graduates that are finding jobs out college with a starting compensation of $40,000. I think that is a good statistic that also shows how beneficial a college degree can be. People who question why going to college or back to college to further their education could look at this test result and say that maybe it would benefit them to go back or go to college. ReflectionFrom this project, I have learned two things. The first thing was that I really learned how to use and maneuver excel a lot better. My dad works for American Express in their compliance department and he is a “whiz” on excel. He is so fast when he uses it and I know it’s from years of practice, but he is still so fast and has been more than willing to help me if I got stuck on something in the project that we were doing on Excel. I know absolutely nothing about excel. I needed all the help on excel that I could get because I hadn’t ever really used it that much, so I didn’t have much of a knowledge of it. This course and project have given me a basic knowledge of excel. It has also shown me a small portion of all the mathematical features it can help do, which is amazing. The second thing I learned was being able to gain experience looking at the histograms and box plots and the confidence intervals and being able to understand what I was looking at. The statistics and results make sense when I read them. They aren’t just a jumble of words and numbers that I don’t know anymore. The skills I have applied in this project and the skills I have learned from this class alone will help me as I continue on in school and into my career. In school, if I take math further, a basic knowledge of Statistics will help me to think more critically when I look at data. In my career, I won’t be looking at charts and statistics very often. I would like to be an Emergency Room nurse and therefore, I will most likely be stabilizing sick people and not staring at stats. But it is a good skill to have for life because we can think critically and we can make sure the stats are accurate in elections and in data about buying a car and so many other things. I think the histograms were a big part in the project. When people present results, they sometimes do graphs to make the results more visual so people will understand them. But as we learned in class, graphs are not always accurate, so understanding how to read them and the data in them is highly important. I think that it is a good general idea to know how to read any graph and we will see those in almost every math class, if not all math classes. We will also see them in every-day life, so it is really important to know how to read the data being presented in the graphs correctly. The project helped me develop my problem solving skills through analyzing the confidence intervals and the hypothesis tests. Analyzing the data and having to decide if the hypothesis needs to be rejected or accepted and then writing up why we are doing so helps me to think about the problem. If I get to the end of the problem and the results don’t seem to add up, then I have to go back and see if I made any mistakes which I think is a great way to develop problem solving skills.This project showed me a small, but very real portion of what real math applications can help figure out in the “real world.” I didn’t realize before taking this class, what statistics really encompassed. After taking the class, I realize how much statistics is a part of daily life and I also realized how the basic knowledge we received in this class can be put to use in applications such as this project. We can use our skills to test starting compensations for graduating college students or to read the pie graph in our favorite fashion magazine or whatever it may be. But this project and class really opened my eyes to what statistics is all about. ................
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