The following data are from a completely randomized design. Treatment A B C 161 141 125 143 156 123 166 124 139 144 143 139 148 135 149 168 159 129 Sample mean 155 143 134 Sample variance 128.0 170.8 100.4 (a) Compute the sum of squares between treatments. (b) Compute the mean square between treatments. (c) Compute the sum of squares due to error. (d) Compute the mean square due to error. (Round your answer to two decimal places.) (e) Set up the ANOVA table for this problem. (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 300 Error Total 440 (f) At the ? = 0.05 level of significance, test whether the means for the three treatments are equal. State the null and alternative hypotheses. H0: Not all the population means are equal. Ha: ?A = ?B = ?CH0: ?A = ?B = ?C Ha: ?A ≠ ?B ≠ ?C H0: At least two of the population means are equal. Ha: At least two of the population means are different.H0: ?A = ?B = ?C Ha: Not all the population means are equal.H0: ?A ≠ ?B ≠ ?C Ha: ?A = ?B = ?C Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Reject H0. There is sufficient evidence to conclude that the means for the three treatments are not equal.Reject H0. There is not sufficient evidence to conclude that the means for the three treatments are not equal. Do not reject H0. There is not sufficient evidence to conclude that the means for the three treatments are not equal.Do not reject H0. There is sufficient evidence to conclude that the means for the three treatments are not equal.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

The following data are from a completely randomized design.

	Treatment
A	B	C
	161	141	125
143	156	123
166	124	139
144	143	139
148	135	149
168	159	129
Sample mean	155	143	134
Sample variance	128.0	170.8	100.4

(a)

Compute the sum of squares between treatments.

(b)

Compute the mean square between treatments.

(c)

Compute the sum of squares due to error.

(d)

Compute the mean square due to error. (Round your answer to two decimal places.)

(e)

Set up the ANOVA table for this problem. (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	300
Error
Total	440

(f)

At the ? = 0.05 level of significance, test whether the means for the three treatments are equal.

State the null and alternative hypotheses.

H₀: Not all the population means are equal.
H_a: ?_A = ?_B = ?_CH₀: ?_A = ?_B = ?_C
H_a: ?_A ≠ ?_B ≠ ?_C H₀: At least two of the population means are equal.
H_a: At least two of the population means are different.H₀: ?_A = ?_B = ?_C
H_a: Not all the population means are equal.H₀: ?_A ≠ ?_B ≠ ?_C
H_a: ?_A = ?_B = ?_C

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

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

p-value =

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that the means for the three treatments are not equal.Reject H₀. There is not sufficient evidence to conclude that the means for the three treatments are not equal. Do not reject H₀. There is not sufficient evidence to conclude that the means for the three treatments are not equal.Do not reject H₀. There is sufficient evidence to conclude that the means for the three treatments 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 + ...

Expert Solution