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Understandable Statistics, Concepts and Methods

Please provide the following information for Problems.

(a) What is the level of significance? State the null and alternate hypotheses.

(b) Check Requirements What sampling distribution will you use? What assumptions are you making? Compute the sample test statistic and corresponding $z$ or $t$ value as appropriate.

(c) Find (or estimate) the $P$ -value. Sketch the sampling distribution and show the area corresponding to the $P$ -value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level $\alpha ?$

(e) Interpret your conclusion in the context of the application. Note: For degrees of freedom $d . f .$ not in the Student's $t$ table, use the closest $d . f .$ that is smaller. In some situations, this choice of $d . f .$ may increase the $P$ -value a small amount and therefore produce a slightly more "conservative" answer.

Management: Intimidators and Stressors This problem is based on information regarding productivity in leading Silicon Valley companies (see reference in Problem 25 ). 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 $x_{1}$ be a random variable representing productive hours per week lost by peer employees of an intimidator.

A "stressor" is an employee with a hot temper that leads to unproductive tantrums in corporate society. Let $x_{2}$ be a random variable representing productive hours per week lost by peer employees of a stressor.

i. Use a calculator with mean and standard deviation keys to verify that $\bar{x}_{1}=4.00, s_{1} \approx 2.38, \bar{x}_{2}=5.5,$ and $s_{2} \approx 2.78$

ii. Assuming the variables $x_{1}$ and $x_{2}$ 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 the population distributions of time lost due to intimidators and time lost due to stressors are each mound-shaped and symmetric.