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 first variable x1 measures manager's hours per week lost due to hot tempers, flaming e-mails, and general unproductive tensions. x1: 1 3 6 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 3 2 5 9 4 10 3 (i) Use a calculator with sample mean and sample standard deviation keys to calculate x1, s1, x2, and s2. (Round your answers to four decimal places.) x1 = s1 = x2 = s2 = (ii) Does the information indicate that the population mean time lost due to hot tempers is different (either way) from population mean time lost due to disputes arising from technical workers' superior attitudes? Use ? = 0.05. Assume that the two lost-time population distributions are mound-shaped and symmetric. (a) What is the level of significance? State the null and alternate hypotheses. H0: ?1 = ?2; H1: ?1 < ?2H0: ?1 ≠ ?2; H1: ?1 = ?2 H0: ?1 = ?2; H1: ?1 ≠ ?2H0: ?1 = ?2; H1: ?1 > ?2 (b) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that both population distributions are approximately normal with known 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 Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. What is the value of the sample test statistic? (Test the difference ?1 − ?2. Do not use rounded values. Round your final answer to three decimal places.) (c) Find (or estimate) the P-value. P-value > 0.5000.250 < P-value < 0.500 0.100 < P-value < 0.2500.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010 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 ?? At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. (e) Interpret your conclusion in the context of the application. Reject the null hypothesis, there is sufficient evidence that there is a difference in mean time lost due to hot tempers and technical workers' attitudes.Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean time lost due to hot tempers and technical workers' attitudes. Reject the null hypothesis, there is insufficient evidence that there is a difference in mean time lost due to hot tempers and technical workers' attitudes.Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean time lost due to hot tempers and technical workers' attitudes.

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 first variable x1 measures manager's hours per week lost due to hot tempers, flaming e-mails, and general unproductive tensions. x1: 1 3 6 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 3 2 5 9 4 10 3 (i) Use a calculator with sample mean and sample standard deviation keys to calculate x1, s1, x2, and s2. (Round your answers to four decimal places.) x1 = s1 = x2 = s2 = (ii) Does the information indicate that the population mean time lost due to hot tempers is different (either way) from population mean time lost due to disputes arising from technical workers' superior attitudes? Use ? = 0.05. Assume that the two lost-time population distributions are mound-shaped and symmetric. (a) What is the level of significance? State the null and alternate hypotheses. H0: ?1 = ?2; H1: ?1 < ?2H0: ?1 ≠ ?2; H1: ?1 = ?2 H0: ?1 = ?2; H1: ?1 ≠ ?2H0: ?1 = ?2; H1: ?1 > ?2 (b) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that both population distributions are approximately normal with known 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 Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. What is the value of the sample test statistic? (Test the difference ?1 − ?2. Do not use rounded values. Round your final answer to three decimal places.) (c) Find (or estimate) the P-value. P-value > 0.5000.250 < P-value < 0.500 0.100 < P-value < 0.2500.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010 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 ?? At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. (e) Interpret your conclusion in the context of the application. Reject the null hypothesis, there is sufficient evidence that there is a difference in mean time lost due to hot tempers and technical workers' attitudes.Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean time lost due to hot tempers and technical workers' attitudes. Reject the null hypothesis, there is insufficient evidence that there is a difference in mean time lost due to hot tempers and technical workers' attitudes.Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean time lost due to hot tempers and technical workers' attitudes.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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 first variable x₁ measures manager's hours per week lost due to hot tempers, flaming e-mails, and general unproductive tensions.

x₁:

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:

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

x₁	=
s₁	=
x₂	=
s₂	=

(ii) Does the information indicate that the population mean time lost due to hot tempers is different (either way) from population mean time lost due to disputes arising from technical workers' superior attitudes? Use ? = 0.05. Assume that the two lost-time population distributions are mound-shaped and symmetric.
(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: ?₁ = ?₂; H₁: ?₁ < ?₂H₀: ?₁ ≠ ?₂; H₁: ?₁ = ?₂ H₀: ?₁ = ?₂; H₁: ?₁ ≠ ?₂H₀: ?₁ = ?₂; H₁: ?₁ > ?₂

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

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

What is the value of the sample test statistic? (Test the difference ?₁ − ?₂. Do not use rounded values. Round your final answer to three decimal places.)

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

P-value > 0.5000.250 < P-value < 0.500 0.100 < P-value < 0.2500.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010

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 ??

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

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

Reject the null hypothesis, there is sufficient evidence that there is a difference in mean time lost due to hot tempers and technical workers' attitudes.Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean time lost due to hot tempers and technical workers' attitudes. Reject the null hypothesis, there is insufficient evidence that there is a difference in mean time lost due to hot tempers and technical workers' attitudes.Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean time lost due to hot tempers and technical workers' attitudes.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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