Answer the following multiple choice questions. You must show some relavent work and/or explanation for each statement.The test statistic of the single-factor ANOVA equals:sum of squares for treatments / sum of squares for error.sum of squares for error / sum of squares for treatments.mean square for treatments / mean square for error.mean square for error / mean square for treatments. In a single-factor analysis of variance, MST is the mean square for treatments and MSE is the mean square for error. The null hypothesis of equal population means is rejected if:MST is much larger than MSE.MST is much smaller than MSE.MST is equal to MSE.None of these choices. In a one-way ANOVA, error variability is computed as the sum of the squared errors, SSE, for all values of the response variable. This variability is the:the total variation.within-treatments variation.between-treatments variation.None of these choices. Which of the following is not a required condition for one-way ANOVA?The sample sizes must be equal.The populations must all be approximately normally distributed.The population variances must be equal.The samples for each treatment must be selected randomly and independently.

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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 13PPS

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Answer the following multiple choice questions. You must show some relavent work and/or explanation for each statement.

The test statistic of the single-factor ANOVA equals:

sum of squares for treatments / sum of squares for error.
sum of squares for error / sum of squares for treatments.
mean square for treatments / mean square for error.
mean square for error / mean square for treatments.

In a single-factor analysis of variance, MST is the mean square for treatments and MSE is the mean square for error. The null hypothesis of equal population means is rejected if:

MST is much larger than MSE.
MST is much smaller than MSE.
MST is equal to MSE.
None of these choices.

In a one-way ANOVA, error variability is computed as the sum of the squared errors, SSE, for all values of the response variable. This variability is the:

the total variation.
within-treatments variation.
between-treatments variation.
None of these choices.

Which of the following is not a required condition for one-way ANOVA?

The sample sizes must be equal.
The populations must all be approximately normally distributed.
The population variances must be equal.
The samples for each treatment must be selected randomly and independently.

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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