Two Sample Hypothesis Testing Paper
According to the United States Department of Labor (2009), “women represent 47% of the nation’s labor force” (Women in the labor force: A databook, para. 8). Despite the increased participation of women in the labor force, women’s earnings still are 80% of male earnings (United States Department of Labor, 2009). In an effort to understand the disparity in wages between males and females, the following paper uses wages and wage earners data from 2005 to illustrate: (a) a verbal and numerical hypothesis statement, (b) the use of the five-step hypothesis test, (c) a summary of the test results, and (d) an explanation of how the findings of using the .01 significance level answers the research question that the annual mean wage of males is greater than the annual mean wage of females.
Numerical and Verbal Hypothesis
Recent research indicates the annual mean wage of males is greater than the annual mean wage females. A random sample from a 2005 wage and wage earners data set included a group of 53 males with an annual mean wage of $36,492.92 and 47 females with an annual mean wage of $24,451.51 (University of Phoenix, 2005).
The standard deviation of the wages of the 53 males was $18,447.57 and the standard deviation of the wages of the 47 females was $12,445.61. The .01 significance level will be used to test the hypothesis that the mean annual wage for men is greater than the mean annual wage for the females.
Five-Step Hypothesis Test
The five-step process can be used to validate if the hypothesis is reasonable, performing the following steps: (a) define the null hypothesis and the alternate hypothesis, (b) select the significance level, (c) identify the test statistics, (d) create a decision rule, and (e) draw from the results of the sample to develop an outcome (Lind, Marchal, & Wathen, 2004).
Step One: The Null and Alternate Hypothesis
A null hypothesis is a value that can be tested and is based on a theory of a...