One_Sample

One Sample Hypothesis Testing Paper The current economic downturn has resulted in drastic changes among wage earners in the United States over the past ten years. College graduates are finding it difficult to find work and those already employed are facing challenges to stay competitive in their line of work. Retirees have had to come out of retirement and return to the workforce on a part-time or full-time basis. The market for skilled employees from all nationalities has increased, in spite of the closing of businesses and downsizing due to poor economic conditions. According to the Wage and Wage Earners data set compiled as of 2005, the average age of workers is 39.11. This paper will present a one sample hypothesis testing using data from the Wage and Wage Earners data set with respect to the average age of non-white wage earners in the workforce. The null hypothesis test will show the average age of non-white workers that are greater than or equal to 35. The alternate hypothesis test will show the average age of non-white workers that are less than 35. Null Hypothesis = the average age among non-white wage earners is greater than or equal to 35 X ≥ 35 Alternate Hypothesis = the average age among non-white wage earners is less than 35 X < 35 Five Step Hypothesis Testing Step 1: Formulate the null and alternate hypothesis Ho: μ ≥ 35 Ha: μ < 35 Step 2: Develop decision rules We decide that we want to be 99% confident in our answer; therefore ά is .001 or 1% => z = 2.32 (using the z table under the normal curve). Step 3: Test statistic Because the sample size is greater than 30 (100 workers were sampled), we can assume normality and use a Z statistic in our hypothesis. A one tail-right test will be conducted to determine the alternate hypothesis and state the direction for the average age among non-white wage earners of 35. Zcal = (X – Xbar)/(s/SQRT(n)) whereas X = 39.11, Xbar = 35, s (standard deviation) = 12.57 and n = 100 => Zcal = (39.11-35)/(12.57/SQRT(100) = 3.27 Step 4: Compare our critical value with our calculated value Since Zcal = 3.27 > z = 2.32 as mentioned in step 2, we shall reject Ho Step 5 Conclusion In deed, the average age among non-white wage earners is less than 35. Reference Lind, Marchal and Wathen (2008), Statistical Techniques in Business & Economics, 13th ed., New York, NY, McGraw-Hill