Reflection Paper
Question One
Describe how you could use hypothesis testing to decide for your current job, a past job, or a life situation. Include a description of the resolution, what would be the null and alternative hypotheses, and how data could ideally be collected to test the hypotheses.
I previously worked in a plastics manufacturing company. The monthly salary was not enough for my personal needs. Therefore, I had to decide on shifting from my employment to a different source of income. In my decision, I sought a job that would give better pay compared to working in the industry. Therefore, my research question was, “can finding another job give more income than my current job?”
With the research question, my null hypothesis became, “earnings from the factory job is as good as any other job.” Therefore, my alternative hypothesis became “finding another well-paying job away from working in the industry.” In this case, my alternative hypothesis was setting up my own wholesale business and venture into self-employment.
I tested my hypothesis by comparing the mean monthly salary I gained in three months from working in the manufacturing company, which was $300, and the mean monthly profits I earned from the business in three months. The mean monthly earnings from the store were $600. From these figures, it is evident that self-employment was more profitable than working for the company. Therefore, I rejected the null hypothesis and adopted an alternative since it was giving more than double the earnings I got from the company.
Question Two
Describe how you could use confidence intervals to decide for your current job, a past job, or a life situation. Include a description of the resolution, how the range would impact the decision, and how data could ideally be collected to determine the interval.
Since confidence interval entails values within the span where the probability of a given value falling between is high, I calculated confidence interval for both hypotheses and compared the most viable theory before making a decision. The decision was whether to quit working for the company and starting my own business or keep working as an employee of the company. The following is the calculation for the confidence interval for the new business.
Let;
N represents the number of days present in a month
Z* represents the Z value for different confidence levels
Ϭ represent the estimated standard deviation, and
re represents the sample mean of money obtained in a day
Therefore is Z*
$20 =
Lower end = $17.87
Upper end = $22.13
While comparing these values with the mean daily earnings from working with the company, the company’s lower-end = $7.87 and upper end = $12.13.
Hence, using these confidence interval data above, I found out that self-employment earns me an average of $17.87 – $22.13 in a single day compared to working for the company, which will make me an average of $7.87 – $12.13 in a day.
Question Three
Describe how you could use regression analysis to decide for your current job, a past job, or a life situation. Include a description of the resolution, what would be the independent and dependent variables, and how data could ideally be collected to calculate the regression equation.
Regression study refers to a group of data in statistics used to approximate the cohesion existing between independent variables together with the dependent ones. It uses a linear equation to fit data. When this data is fed into a graph, a straight line is drawn connecting the various data points. In my case, I will use regression analysis to determine the relationship between the daily incomes from my business for thirty days, to determine the average monthly income from the store. It will help me predict the trends in profits from the store by studying the graph’s behavior.
While plotting my graph, I will let the Y-axis be the dependent variable, in this case, the business’s daily profits in dollars. The X-axis will contain the independent variable, which is the number of days in a month; in this case, I use thirty days as my average. Since the profits obtained in a day may vary, I will plot the different points on the graph as I advance to the end of the thirty days. I will, therefore, have several locations on the graph, which I will then draw a straight line passing through the majority of the points with a balance of points above and below the line. With this straight line, the slope of the graph can be found then incorporate it as a line equation given as y = mx+c. Using this graph, I can quickly tell the trend in my monthly profits and decide whether to continue with the business or quit it. If the graph is not giving a straight line, then there is a problem with the business, and an alternative decision is to be made. However, if the straight line is consistent in the graph, it is good to continue.