A company manufactures printers and fax machines at plants located in Atlanta, Dallas, and Seattle. To measure how much employees at these plants know about quality management, a random sample of 6 employees was selected from each plant and the employees selected were given a quality awareness examination. The examination scores for these 18 employees are shown in the following table. The sample means, sample variances, and sample standard deviations for each group are also provided. Managers want to use these data to test the hypothesis that the mean examination score is the same for all three plants. Plant 1AtlantaPlant 2DallasPlant 3 Seattle 857159 757564 827362 767469 716975 858267 Samplemean797466 Samplevariance34.020.032.0 Samplestandarddeviation5.834.475.66 Set up the ANOVA table for these data. (Round your values for MSE and F to two decimal places, and your p-value to four decimal places.)Sourceof VariationSumof SquaresDegreesof FreedomMeanSquareFp-valueTreatments5162258??Error?15? Total?17 Test for any significant difference in the mean examination score for the three plants. Use ? = 0.05.State the null and alternative hypotheses.-H0: ?1 = ?2 = ?3Ha: ?1 ≠ ?2 ≠ ?3-H0: ?1 = ?2 = ?3Ha: Not all the population means are equal. - H0: ?1 ≠ ?2 ≠ ?3Ha: ?1 = ?2 = ?3-H0: At least two of the population means are equal.Ha: At least two of the population means are different.-H0: Not all the population means are equal.Ha: ?1 = ?2 = ?3 Find the value of the test statistic. (Round your answer to two decimal places.)Test statistic=??Find the p-value. (Round your answer to four decimal places.)p-value = ??State your conclusion.-Do not reject H0. There is not sufficient evidence to conclude that the means for the three plants are not equal.-Reject H0. There is sufficient evidence to conclude that the means for the three plants are not equal. -Reject H0. There is not sufficient evidence to conclude that the means for the three plants are not equal.-Do not reject H0. There is sufficient evidence to conclude that the means for the three plants are not equal.

Answered: A company manufactures printers and fax…

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

A company manufactures printers and fax machines at plants located in Atlanta, Dallas, and Seattle. To measure how much employees at these plants know about quality management, a random sample of 6 employees was selected from each plant and the employees selected were given a quality awareness examination. The examination scores for these 18 employees are shown in the following table. The sample means, sample variances, and sample standard deviations for each group are also provided. Managers want to use these data to test the hypothesis that the mean examination score is the same for all three plants.

	Plant 1 Atlanta	Plant 2 Dallas	Plant 3 Seattle
	85	71	59
	75	75	64
	82	73	62
	76	74	69
	71	69	75
	85	82	67
Sample mean	79	74	66
Sample variance	34.0	20.0	32.0
Sample standard deviation	5.83	4.47	5.66

Set up the ANOVA table for these data. (Round your values for MSE and F to two decimal places, and your p-value to four decimal places.)

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
Treatments	516	2	258	?	?
Error	?	15	?
Total	?	17

Test for any significant difference in the mean examination score for the three plants. Use

? = 0.05.

State the null and alternative hypotheses.

-H₀: ?₁ = ?₂ = ?₃
H_a: ?₁ ≠ ?₂ ≠ ?₃

-H₀: ?₁ = ?₂ = ?₃
H_a: Not all the population means are equal.

- H₀: ?₁ ≠ ?₂ ≠ ?₃
H_a: ?₁ = ?₂ = ?₃

-H₀: At least two of the population means are equal.
H_a: At least two of the population means are different.

-H₀: Not all the population means are equal.
H_a: ?₁ = ?₂ = ?₃

Find the value of the test statistic. (Round your answer to two decimal places.)

Test statistic=??

Find the p-value. (Round your answer to four decimal places.)

p-value = ??

State your conclusion.

-Do not reject H₀. There is not sufficient evidence to conclude that the means for the three plants are not equal.

-Reject H₀. There is sufficient evidence to conclude that the means for the three plants are not equal.

-Reject H₀. There is not sufficient evidence to conclude that the means for the three plants are not equal.

-Do not reject H₀. There is sufficient evidence to conclude that the means for the three plants are not equal.

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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