Question 1

The mean square is the sum of squares divided by
A)the total number of observations
B)its corresponding degrees of freedom
C)its corresponding degrees of freedom minus one
D)None of these alternatives is correct.

Accepted Answer

The answer of The mean square is the sum of...

Question 2

A term that means the same as the term "variable" in an ANOVA procedure is
A)factor
B)treatment
C)replication
D)variance within

Accepted Answer

In an ANOVA procedure, a "factor" refers to the independent variable(s) being studied, which can be considered equivalent to a "variable." For example, in a study comparing the effects of three different teaching methods on student performance, the teaching methods would be considered the "factors" or "variables" being examined.

Question 3

In a completely randomized design involving three treatments, the following information is provided:  The overall mean for all the treatments is
A)7.00
B)6.67
C)7.25
D)4.89

Accepted Answer

The answer of In a completely randomized design involving three...

Question 4

In an analysis of variance, one estimate of $\sigma$² is based upon the differences between the treatment means and the A)means of each sample B)overall sample mean C)sum of observations D)populations have equal means

Accepted Answer

The estimate of F in analysis of variance is based on the differences between the treatment means and the overall sample mean.

Question 5

An ANOVA procedure is applied to data obtained from 6 samples where each sample contains 20 observations. The degrees of freedom for the critical value of F are
A)6 numerator and 20 denominator degrees of freedom.
B)5 numerator and 20 denominator degrees of freedom
C)5 numerator and 114 denominator degrees of freedom
D)6 numerator and 20 denominator degrees of freedom

Accepted Answer

The answer of An ANOVA procedure is applied to data...

Question 6

An ANOVA procedure is used for data obtained from four populations. Four samples, each comprised of 30 observations, were taken from the four populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are
A)3 and 30
B)4 and 30
C)3 and 119
D)3 and 116

Accepted Answer

The answer of An ANOVA procedure is used for data...

Question 7

The F ratio in a completely randomized ANOVA is the ratio of
A)MSTR/MSE
B)MST/MSE
C)MSE/MSTR
D)MSE/MST

Accepted Answer

The F ratio in a completely randomized ANOVA is the ratio of Mean Square Treatment (MSTR) to Mean Square Error (MSE). Therefore, the correct choice is A, MSTR/MSE.

Question 8

An ANOVA procedure is used for data that was obtained from four sample groups each comprised of five observations. The degrees of freedom for the critical value of F are
A)3 and 20
B)3 and 16
C)4 and 17
D)3 and 19

Accepted Answer

The answer of An ANOVA procedure is used for data...

Question 9

In ANOVA, which of the following is not affected by whether or not the population means are equal? A) $ \overline{\mathrm{x}} $ B)between-samples estimate of $\sigma$² C)within-samples estimate of $\sigma$² D)None of these alternatives is correct.

Accepted Answer

The answer of In ANOVA, which of the following is...

Question 10

If we are interested in testing whether the mean of items in population 1 is significantly smaller than the mean of items in population 2, the A)null hypothesis should state $\mu$₁- $\mu$₂ < 0 B)null hypothesis should state P₁ - P₂ $\ge$ 0 C)alternative hypothesis should state P₁ - P₂ > 0 D)alternative hypothesis should state $\mu$₁- $\mu$₂ < 0

Accepted Answer

The alternative hypothesis should state that the mean of population 1 is less than the mean of population 2, which is $\mu$₁ - $\mu$₂ < 0.

Question 11

Which of the following is not a required assumption for the analysis of variance?
A)The random variable of interest for each population has a normal probability distribution.
B)The variance associated with the random variable must be the same for each population.
C)At least 2 populations are under consideration.
D)Populations have equal means.

Accepted Answer

The assumption of equal means across populations is not required for the analysis of variance. In fact, the purpose of the analysis of variance is to test whether there is evidence of differences in means across populations. The other assumptions listed (normality of the random variable, equality of variances, and consideration of at least 2 populations) are all required for the validity of the analysis of variance.

Question 12

In order to determine whether or not the means of two populations are equal,
A)a t test must be performed
B)an analysis of variance must be performed
C)either a t test or an analysis of variance can be performed
D)a chi-square test must be performed

Accepted Answer

The answer of In order to determine whether or not...

Question 13

If we are interested in testing whether the mean of population 1 is significantly larger than the mean of population 2, the correct null hypothesis is A)H₀: $\mu$₁- $\mu$₂ $\ge$ 0 B)H₀: $\mu$₁- $\mu$₂ = 0 C)H₀: $\mu$₁- $\mu$₂ > 0 D)H₀: $\mu$₁- $\mu$₂ < 0

Accepted Answer

The answer of If we are interested in testing whether...

Question 14

An ANOVA procedure is used for data obtained from five populations. five samples, each comprised of 20 observations, were taken from the five populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are
A)5 and 20
B)4 and 20
C)4 and 99
D)4 and 95

Accepted Answer

The numerator degrees of freedom are equal to the number of populations minus one, which is 5-1=4. The denominator degrees of freedom are equal to the total number of observations minus the number of populations, which is (5*20)-5=95. So the correct choice is D, with numerator degrees of freedom as 4 and denominator degrees of freedom as 95.

Question 15

The required condition for using an ANOVA procedure on data from several populations is that the
A)the selected samples are dependent on each other
B)sampled populations are all uniform
C)sampled populations have equal variances
D)sampled populations have equal means

Accepted Answer

The required condition for using an ANOVA procedure is that the sampled populations have equal variances.

Question 16

The critical F value with 8 numerator and 29 denominator degrees of freedom at $\alpha$ = 0.01 is
A)2.28
B)3.20
C)3.33
D)3.64

Accepted Answer

The answer of The critical F value with 8 numerator...

Question 17

Which of the following is not a required assumption for the analysis of variance?
A)The random variable of interest for each population has a normal probability distribution.
B)The variance associated with the random variable must be the same for each population.
C)At least 2 populations are under consideration.
D)Populations have equal means.

Accepted Answer

The assumption of equal means is not required for the analysis of variance. However, the assumption of normality, equal variances, and more than 2 populations are required assumptions.

Question 18

The critical F value with 6 numerator and 60 denominator degrees of freedom at $\alpha$ = .05 is
A)3.74
B)2.25
C)2.37
D)1.96

Accepted Answer

The answer of The critical F value with 6 numerator...

Question 19

In a completely randomized design involving four treatments, the following information is provided.  The overall mean (the grand mean) for all treatments is
A)40.0
B)37.3
C)48.0
D)37.0

Accepted Answer

Since the mean is not provided for each individual treatment, we must use the overall mean (grand mean) as an estimate for the true population mean. Therefore, the best choice for the overall mean is the sample mean, which is equal to 37.3 (assuming that the sample size is large enough to provide a reliable estimate).

Question 20

In an analysis of variance problem if SST = 120 and SSTR = 80, then SSE is
A)200
B)40
C)80
D)120

Accepted Answer

SSE = SST - SSTR
SSE = 120 - 80
SSE = 40

Quiz 10: Comparisons Involving Means, Experimental Design and Analysis of Variance

The mean square is the sum of squares divided by

A term that means the same as the term "variable" in an ANOVA procedure is

In a completely randomized design involving three treatments, the following information is provided: The overall mean for all the treatments is

In an analysis of variance, one estimate of $\sigma$ ² is based upon the differences between the treatment means and the

An ANOVA procedure is applied to data obtained from 6 samples where each sample contains 20 observations. The degrees of freedom for the critical value of F are

An ANOVA procedure is used for data obtained from four populations. Four samples, each comprised of 30 observations, were taken from the four populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are

The F ratio in a completely randomized ANOVA is the ratio of

An ANOVA procedure is used for data that was obtained from four sample groups each comprised of five observations. The degrees of freedom for the critical value of F are

In ANOVA, which of the following is not affected by whether or not the population means are equal?

If we are interested in testing whether the mean of items in population 1 is significantly smaller than the mean of items in population 2, the

Which of the following is not a required assumption for the analysis of variance?

In order to determine whether or not the means of two populations are equal,

If we are interested in testing whether the mean of population 1 is significantly larger than the mean of population 2, the correct null hypothesis is

An ANOVA procedure is used for data obtained from five populations. five samples, each comprised of 20 observations, were taken from the five populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are

The required condition for using an ANOVA procedure on data from several populations is that the

The critical F value with 8 numerator and 29 denominator degrees of freedom at $\alpha$ = 0.01 is

Which of the following is not a required assumption for the analysis of variance?

The critical F value with 6 numerator and 60 denominator degrees of freedom at $\alpha$ = .05 is

In a completely randomized design involving four treatments, the following information is provided. The overall mean (the grand mean) for all treatments is

In an analysis of variance problem if SST = 120 and SSTR = 80, then SSE is

Quiz 10: Comparisons Involving Means, Experimental Design and Analysis of Variance

The mean square is the sum of squares divided by

A term that means the same as the term "variable" in an ANOVA procedure is

In a completely randomized design involving three treatments, the following information is provided: The overall mean for all the treatments is

In an analysis of variance, one estimate of σ\sigmaσ 2 is based upon the differences between the treatment means and the

An ANOVA procedure is applied to data obtained from 6 samples where each sample contains 20 observations. The degrees of freedom for the critical value of F are

An ANOVA procedure is used for data obtained from four populations. Four samples, each comprised of 30 observations, were taken from the four populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are

The F ratio in a completely randomized ANOVA is the ratio of

An ANOVA procedure is used for data that was obtained from four sample groups each comprised of five observations. The degrees of freedom for the critical value of F are

In ANOVA, which of the following is not affected by whether or not the population means are equal?

If we are interested in testing whether the mean of items in population 1 is significantly smaller than the mean of items in population 2, the

Which of the following is not a required assumption for the analysis of variance?

In order to determine whether or not the means of two populations are equal,

If we are interested in testing whether the mean of population 1 is significantly larger than the mean of population 2, the correct null hypothesis is

An ANOVA procedure is used for data obtained from five populations. five samples, each comprised of 20 observations, were taken from the five populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are

The required condition for using an ANOVA procedure on data from several populations is that the

The critical F value with 8 numerator and 29 denominator degrees of freedom at α\alphaα = 0.01 is

Which of the following is not a required assumption for the analysis of variance?

The critical F value with 6 numerator and 60 denominator degrees of freedom at α\alphaα = .05 is

In a completely randomized design involving four treatments, the following information is provided. The overall mean (the grand mean) for all treatments is

In an analysis of variance problem if SST = 120 and SSTR = 80, then SSE is

In an analysis of variance, one estimate of $\sigma$ ² is based upon the differences between the treatment means and the

The critical F value with 8 numerator and 29 denominator degrees of freedom at $\alpha$ = 0.01 is

The critical F value with 6 numerator and 60 denominator degrees of freedom at $\alpha$ = .05 is