The following data summarize the results from an independent measures study comparing three treatment conditions. I II III 5 3 6 3 3 8 1 7 5 1 4 2 5 3 4 T =15 T =20 T = 25 G = 60 SS =16 SS =12 SS =20 ΣX2 = 298 Use an ANOVA with α = .01 to determine whether there are any significant differences among the three treatment means The null hypothesis in symbols is: H0: μ1 ≠ μ2≠ μ3 H0: μ1 = μ2 = μ3 H0: M1 = M2 = M3 H0: M1 ≠ M2≠ M3 H0: μ1> μ2> μ3 H0: μ1 ≤ μ2≤ μ3 The alternative hypothesis is: There are no significant differences among the three treatment means All pairs of means are significantly different from each other There is at least one significant mean difference: At least two means significantly differ from each other H1: μ1 ≠ μ2≠ μ3 The Critical F-value is: The F-statistic is: Your decision is: Reject the null hypothesis and conclude that there are no significant mean differences among the treatments Reject the null hypothesis and conclude that there are significant mean differences among the treatments Fail to reject the null hypothesis and conclude that there are no significant mean differences among the treatments Fail to reject the null hypothesis and conclude that there are significant mean differences among the treatments

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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The following data summarize the results from an independent measures study comparing three treatment conditions.

I	II	III
5	3	6
3	3	8
1	7	5
1	4	2
5	3	4
*T =15*	*T =20*	*T = 25*	G = 60
*SS =16*	*SS =12*	*SS =20*	ΣX² = 298

Use an ANOVA with α = .01 to determine whether there are any significant differences among the three treatment means

The null hypothesis in symbols is:

H0: μ1 ≠ μ2≠ μ3

H0: μ1 = μ2 = μ3

H0: M1 = M2 = M3

H0: M1 ≠ M2≠ M3

H0: μ1> μ2> μ3

H0: μ1 ≤ μ2≤ μ3

The alternative hypothesis is:

There are no significant differences among the three treatment means

All pairs of means are significantly different from each other

There is at least one significant mean difference:

At least two means significantly differ from each other

H1: μ1 ≠ μ2≠ μ3

The Critical F-value is:

The F-statistic is:

Your decision is:

Reject the null hypothesis and conclude that there are no significant mean differences among the treatments

Reject the null hypothesis and conclude that there are significant mean differences among the treatments

Fail to reject the null hypothesis and conclude that there are no significant mean differences among the treatments

Fail to reject the null hypothesis and conclude that there are significant mean differences among the treatments

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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