Question

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:

7

2

6

3

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

9

8

6

2

5

8

Use a calculator with sample mean and sample standard deviation keys to calculate x₁, s₁, x₂, and s₂. (Round your answers to two decimal places.)

x1	= 1
s1	= 2
x2	= 3
s2	= 4

(a) Assuming 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 the population distributions of time lost due to intimidators and time lost due to stressors are each mound-shaped and symmetric.)(i) What is the level of significance?
5

State the null and alternate hypotheses.

H₀: μ₁ = μ₂; H₁: μ₁ ≠ μ₂H₀: μ₁ = μ₂; H₁: μ₁ < μ₂     H₀: μ₁ = μ₂; H₁: μ₁ > μ₂H₀: μ₁ < μ₂; H₁: μ₁ = μ₂

(ii) What sampling distribution will you use? What assumptions are you making?

The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. The Student's t. We assume that both population distributions are approximately normal with known standard deviations.     The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. The standard normal. We assume that both population distributions are approximately normal with known standard deviations.

What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate. (Test the difference μ₁ − μ₂. Do not use rounded values. Round your final answer to three decimal places.)
8

(iii) Find (or estimate) the P-value.

P-value > 0.250 0.125 < P-value < 0.250     0.050 < P-value < 0.125 0.025 < P-value < 0.050 0.005 < P-value < 0.025 P-value < 0.005

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?

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.     At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

(v) Interpret your conclusion in the context of the application.

Fail to reject the null hypothesis, there is sufficient evidence that the mean time lost due to stressors is greater than the mean time lost due to intimidators. Reject the null hypothesis, there is insufficient evidence that the mean time lost due to stressors is greater than the mean time lost due to intimidators.     Reject the null hypothesis, there is sufficient evidence that the mean time lost due to stressors is greater than the mean time lost due to intimidators. Fail to reject the null hypothesis, there is insufficient evidence that the mean time lost due to stressors is greater than the mean time lost due to intimidators.

(b) Find a 90% confidence interval for

μ₁ − μ₂.

(Round your answers to two decimal places.)

lower limit	13
upper limit	14

Explain the meaning of the confidence interval in the context of the problem.

Because the interval contains only positive numbers, this indicates that at the 90% confidence level, the population mean time lost due to "stressors" is less than the population mean time lost due to "intimidators." Because the interval contains both positive and negative numbers, this indicates that at the 90% confidence level, we cannot say that there is any difference in time lost due to "intimidators" and "stressors."     Because the interval contains both positive and negative numbers, this indicates that at the 90% confidence level, there is a difference in time lost due to "intimidators" and "stressors." Because the interval contains only negative numbers, this indicates that at the 90% confidence level, the population mean time lost due to "stressors" is greater than the population mean time lost due to "intimidators."

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