This problem is based on information regarding productivity in leading Silicon Valley companies. In large corporations, an “intimidator” is an employee who tries to stop communication, sometimes sabotages others, and, above all, likes to listen to him- or herself talk. Let x1 be a random variable representing productive hours per week lost by peer employees of an intimidator.
x1: 8 3 6 2 2 5 2
A “stressor” is an employee with a hot temper that leads to unproductive tantrums in corporate society. Let x2 be a random variable representing productive hours per week lost by peer employees of a stressor.
x2: 3 3 10 7 6 2 5 8
Use a calculator with mean and standard deviation keys to verify that 1 = 4.00, s1 ≈ 2.38, 2 = 5.5, and s2 ≈ 2.78.
(a) Assuming that the variables x1 and x2 are independent, do the data indicate that the population mean time lost due to stressors is greater than the population mean time lost due to intimidators? Use a 5% level of significance. (Assume that the population distributions of time lost due to intimidators and time lost due to stressors are each mound-shaped and symmetrical.)
(b) Find a 90% confidence interval for μ1 - μ2. Explain the meaning of the confidence interval in the context of the problem.
Please provide the following information for problem part (a):
(i) What is the level of significance? State the null and alternate hypotheses.
(ii) What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?
(iii) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(iv) Based on your answers in parts (i) – (iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
(v) Interpret your conclusion in the context of the application.