In her book Red Ink Behaviors, Jean Hollands reports on the assessment of leading Silicon Valley companies regarding a manager’s lost time due to inappropriate behavior of employees. Consider the following independent random variables. The variable x1 measures manager’s hours per week lost due to hot tempers, flaming e-mails, and general unproductive tensions:
x1: 1 5 8 4 2 4 10
The variable x2 measures manager’s hours per week lost due to disputes regarding technical workers’ superior attitudes that their colleagues are “dumb and dispensable”:
x2: 10 5 4 7 9 4 10 3
Use a calculator with sample mean and standard deviation keys to verify that 1 ≈ 4.86, s1 ≈ 3.18, 2 = 6.5, and s2 ≈ 2.88.
(a) Does the information indicate that the population mean time lost due to hot tempers is different (either way) from the population mean time lost due to disputes arising from technical workers’ superior attitudes? Use α = 0.05. Assume that the two lost-time population distributions are mound-shaped and symmetrical.
(b) Find a 95% 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.