x1= 3.8571 s1= 7.3417 x2= 5.625 s2= 2.8754 (i)Level of significance: .05 H0: ?1 = ?2; H1: ?1 < ?2 (ii) The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. value of the sample test statistic: -0.598 (iii) P-value > 0.250 (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 ?? At the ? = 0.05 level, we 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 statistically significant. 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 not statistically significant. (v) Interpret your conclusion in the context of the application. 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. 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. (b) Find a 90% confidence interval for ?1 − ?2. (Round your answers to two decimal places.) lower limit ________ upper limit ________ 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."

x1= 3.8571 s1= 7.3417 x2= 5.625 s2= 2.8754 (i)Level of significance: .05 H0: ?1 = ?2; H1: ?1 < ?2 (ii) The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. value of the sample test statistic: -0.598 (iii) P-value > 0.250 (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 ?? At the ? = 0.05 level, we 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 statistically significant. 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 not statistically significant. (v) Interpret your conclusion in the context of the application. 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. 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. (b) Find a 90% confidence interval for ?1 − ?2. (Round your answers to two decimal places.) lower limit upper limit 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."

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

x₁= 3.8571

s₁= 7.3417

x₂= 5.625

s₂= 2.8754

(i)Level of significance: .05

H₀: ?₁ = ?₂; H₁: ?₁ < ?₂

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

value of the sample test statistic: -0.598

(iii) P-value > 0.250

(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 ??

_{At the ? = 0.05 level, we 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 statistically significant.}
_{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 not statistically significant.}

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

_{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.}
_{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.}

(b) Find a 90% confidence interval for

?₁ − ?₂.

(Round your answers to two decimal places.)

lower limit	________
upper limit	________

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."}

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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ISBN:

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Publisher:

John Wiley & Sons Inc