One Sample Hypothesis Testing

One Sample Hypothesis Testing The significance of earnings is a growing facade in today’s economy. Daily operation, individuals, and families alike rely heavily on each sale or paycheck to provide financial stability throughout. Depending on the nature of labor, wages are typically compensated in accords to one’s experience and education or specialization. Moreover, calculating the specified industry, occupation title, education, experience on-the-job, gender, race, age, and membership to a union will additionally influence wages.To help analyze operation pay scales and remain within budget a business should obtain data pertaining to current variations in wage. Today statistics allow a business or businesses to do so in a timely and proficient manner. The purpose of the succeeding report is to communicate a hypothesis statement regarding the wages of Hispanics and Caucasian workers. Team B would like to determine whether race has an influence on the wage of these specif ic workers. Team B will convey this data of wages in both a numerical and verbal manner.Moreover, it is to describe and perform the five-step hypothesis test on the wages and wage earner data set, including data tables and results of the computations of a z-test or t-test by way of graphical and tabular methods. Also the paper will depict the results of all testing and convey how the results given Team B’s hypothesis testing may be used to answer the research question. Hypotheses Learning Team B’s verbal hypothesis question asks â€Å"Does the mean salary of a Hispanic worker exceed thirty thousand dollars and that of the mean salary of a Caucasian worker? † The numerical question used for our hypothesis test is  µ > $30,000.Another numerical question is  µ1> µ2.  µ1 is defined as the sample mean of Hispanic workers salaries and  µ2 defined as the sample mean of Caucasian workers salaries. The Hispanic sample population is six workers from the â €Å"Wages and Wage Earners Data Set. † Learning Team B needs to consider whether or not the population is normal as the population size is less than 30. This also prohibits use of the Central Limit Theorem until the data set is proven normal. The wage of one worker being much higher than the others means our data will be skewed right and this data may not be a â€Å"good† sample.The existence of this outlier means our results will be skewed meaning we should find a better sample to base our results on. More importantly, the existence of an outlier reminds us that the mean is not always a good measure of the â€Å"typical† value of X. † (Doane & Seward, 2007). Five-step Hypothesis Test Team B would like to find if average Hispanic workers make more than $30,000 per year. The team’s null hypotheses or (HO) is that Hispanic pay is greater than or equal to $30,000. The team’s alternative hypothesis or (H1) is that Hispanic pay is less than $30,00 0.The significance level has been set at . 05 or 95%. The z score of . 05 is -1. 645. If the z-value is less than -1. 645 then the team can reject the null hypothesis and accept the alternative hypothesis. If the z-value is greater than -1. 645 then the team fails to reject the null hypothesis, meaning Hispanic workers do, in fact, make more than $30,000 a year. Hypotheses: HO Hispanic pay ? 30,000 H1 Hispanic pay > 30,000 Data Set: (University of Phoenix, 2007) 83,601 29,736 15,234 24,509 33,461 13,481 Formula 1: Mean = (83,601+29,736+15,234+24,509+33,461+13,481)/6M = 33,337 Formula 2: Standard Deviation = SQRT(((X1-M)Squared+(X2-M)Squared†¦)/(N-1)) SD = SQRT(((83,601-33,337)Squared+(29,736-33,337)Squared†¦)/(6-1)) SD = SQRT(((50,24)Squared =(3,601)Squared+(18,094)Squared†¦)/(5) SD = 25,841. 97 Hispanic pay mean = 33,337 Hispanic pay Standard deviation = 25,842 Sample size = 6 Formula 3: Z-Test = (Mean-X)/(Standard Deviation/SQRT(N)) Z = (33,337 – 30,000)/( 25842/SQRT(6)) Z = 3,337/10,549. 94 Z = . 3163 As a result, we find that Z > -1. 645 Next team B wanted to see what the wage difference was between Caucasians and Hispanics.The team’s null hypothesis or (HO) is that white pay wages are ? Hispanic pay wages. The teams alternative hypothesis or (H1) is White pay wages are < Hispanic pay wages. White wages mean = 31,387. 39 Hispanic Wage mean = 33,337. 00 White wages STDEV = 16,810. 03 Hispanic wage STDEV = 25,843. 24 Finally the team wanted to see if age played a part in the difference in pay wages. Our null hypothesis or (HO) is that White age is = to Hispanic ages. The alternative or (H1) is that White age is ? to Hispanic ages. White Wage age mean = 39. 71429 Hispanic wage age mean = 35. 5 White wage age STDEV = 12. 3484 Hispanic wage age STDEV = 14. 25132 Test Results This test is significant because it shows that, based on the sample population; the average Hispanic worker makes more than $30,000 per year. This is be cause the team performed a one tailed Z-Test to determine with 95% confidence that Hispanic wages were greater than $30,000 per year.This is a one tailed test because the alternate hypothesis is only proven when the Z Value is less than the critical value of $30,000 in this case. With a Z Value of . 3163, we find that our Z-Test has yielded a result significantly higher than -1. 45, which proves H0, or that Hispanic pay is greater than $30,000 per year. The test also concluded that Hispanic workers make more than Caucasian workers on average. We also gathered data showing the average age of Caucasian workers is higher than that of Hispanic workers. In conclusion, this paper has discussed and researched the various influence of one’s race and wages. Our results provided immense data relating to our hypotheses and both verbal and numerical hypothesis were proven to conclude that Hispanic workers on average make more than $30,000 a year and also more than the average Caucasian w orker.By using a smaller sample Team B was able to distinguish any correlations between both races and determine a sound result. In today’s economy wages are a momentous factor and whether ones Hispanic or not wages have a sizeable impact on one’s life. We believe our research shows that Hispanic’s have an advantage in the workplace over Caucasian workers. References: Doane, D. P. & Seward, L. E. , (2007). Applied Statistics in Business and Economics. Boston, MA: McGraw-Hill/Irwin.