The Analysis of Variance. A research study compared beer consumed daily between 3 groups with 3 observations each. Group1 was UCB, Group 2 UCSD, and Group 3 UCI. Determine if there is a significant difference among the groups 5% level. Group1: UCB Group 2: UCSD Group 3: UCI The Results of this study are in the following table: Group1 Group2 Group3 Sample 3, 4, 5 3.2, 4, 4.2 3, 4, 3.3 Mean 4.0 3.7 3.4 S^2 4.4 5.2 6.1 null and alternative hypotheses are Null hypothesis Ho : There is a significant difference among the treatment group means Alternative Hypothesis Ha : At least one group mean is different from other group means the average mean due to treatments are Thus, the average mean due to treatments is 3.67 the Treatment Sum Square SSTR is Thus, the Treatment Sum Square (SSTR) is 0.550 The Mean Square Treatments MSTR Mean Square Treatments (MSTR) is 0.275 Based on MSTR and Mean Squared Error MSE = 4.5 should we reject Ho? Please use F table with 2 numerator df, 6 denominator df, alpha =0.05

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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The Analysis of Variance. A research study compared beer consumed daily between 3 groups with 3 observations each. Group1 was UCB, Group 2 UCSD, and Group 3 UCI. Determine if there is a significant difference among the groups 5% level.

Group1: UCB

Group 2: UCSD

Group 3: UCI

The Results of this study are in the following table:

Group1 Group2 Group3

Sample 3, 4, 5 3.2, 4, 4.2 3, 4, 3.3

Mean 4.0 3.7 3.4

S^2 4.4 5.2 6.1

null and alternative hypotheses are

Null hypothesis H_o : There is a significant difference among the treatment group means

Alternative Hypothesis H_a : At least one group mean is different from other group means

the average mean due to treatments are

Thus, the average mean due to treatments is 3.67

the Treatment Sum Square SSTR is

Thus, the Treatment Sum Square (SSTR) is 0.550

The Mean Square Treatments MSTR

Mean Square Treatments (MSTR) is 0.275

Based on MSTR and Mean Squared Error MSE = 4.5 should we reject Ho? Please use F table with 2 numerator df, 6 denominator df, alpha =0.05

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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