Question 1

You are testing the equality of two population means using samples of size 10.The F_stat value for your ANOVA is 4.0.If, instead of an F test, you had conducted a t test to test the "no difference in population means" null hypothesis, the t_stat value would be 16.0.

Accepted Answer

The t-statistic is related to the F-statistic by the square root, so if the F-statistic is 4.0, the t-statistic would be the square root of 4.0, which is 2.0, not 16.0.

Question 2

The computed F value (F_stat) in a one-way analysis of variance is the ratio of the between groups sum of squares (SSB) to the within groups sum of squares (SSW).

Accepted Answer

The computed F value in a one-way analysis of variance is the ratio of the between groups mean square (MSB) to the within groups mean square (MSW), not the sum of squares.

Question 3

You are testing the equality of two population means using ANOVA.The critical value F_c for your test is 3.634.If, instead of an F test, you had conducted a t test to test the "no difference in population means" null hypothesis, the t_c value would be 1.906.

Accepted Answer

In hypothesis testing, when comparing two population means, the square of the t-statistic (t^2) from a t-test is equal to the F-statistic from an ANOVA test when the ANOVA is comparing these two groups. Given the F-statistic is 3.634, taking the square root gives a value close to 1.906, which matches the provided t-statistic value.

Question 4

In an experimental study, the investigator has the ability to directly influence or manipulate one or more of the elements involved in the investigation.

Accepted Answer

In an experimental study, the investigator manipulates one or more independent variables to determine their effect on one or more dependent variables, thus directly influencing elements of the investigation.

Question 5

The computed F value (F_stat) in a one-way analysis of variance is the ratio of the within groups mean square (MSW) to the between groups mean square (MSB).

Accepted Answer

The computed F value in a one-way analysis of variance is the ratio of the between groups mean square (MSB) to the within groups mean square (MSW).

Question 6

The computed F value (F_stat) in a one-way analysis of variance is the ratio of the between groups mean square (MSB) to the within groups mean square (MSW).

Accepted Answer

In a one-way ANOVA, the F value is calculated as the ratio of the variance between the groups (MSB) to the variance within the groups (MSW).

Question 7

One of the assumptions for the one-way analysis of variance is that the standard deviations - and so the variances - are not the same for all the populations.

Accepted Answer

One of the assumptions for the one-way analysis of variance (ANOVA) is that the populations have equal variances, known as the assumption of homogeneity of variances.

Question 8

The F distribution can be used to describe how the ratio of two sample variances behaves when the two samples have been independently selected from normal populations with the same variance.

Accepted Answer

The F distribution is indeed used to describe the ratio of two sample variances, especially in the context of ANOVA (Analysis of Variance) tests, where it helps in determining if the variances from two independent samples (assumed to be drawn from normal populations with the same variance) significantly differ from each other.

Question 9

In a completely randomized design, experimental units are arranged into similar groups based on extraneous factors in an effort to reduce error variation in experimental results.

Accepted Answer

In a completely randomized design, experimental units are not arranged into similar groups based on extraneous factors; instead, all units have an equal chance of receiving any treatment, and grouping is not based on similarity.

Question 10

You are testing the equality of population means using ANOVA.The partial ANOVA table appears below.If the samples used in the ANOVA are all the same size, that sample size must be 15.

Accepted Answer

The answer of You are testing the equality of population...

Question 11

You are testing the equality of population means using ANOVA.The partial ANOVA table appears below.The between-groups mean square value is 1540.

Accepted Answer

The answer of You are testing the equality of population...

Question 12

You are testing the equality of population means using ANOVA and a 5% significance level.If the p-value for the F_stat that you produce is .0212, you should conclude that the population means are not equal.

Accepted Answer

Since the p-value (.0212) is less than the significance level (0.05), we reject the null hypothesis, concluding that there is a significant difference among the population means.

Question 13

You are testing the equality of population means using one-way ANOVA and a 5% significance level.If the p-value for the F_stat that you produce is .0711, you should conclude that the population means are not equal.

Accepted Answer

A p-value of .0711 is greater than the 5% significance level (0.05), meaning there is not enough evidence to reject the null hypothesis of equal population means.

Question 14

The within groups mean square in a one-way analysis of variance is the within groups sum of squares divided by (n-1) degrees of freedom.

Accepted Answer

The within groups mean square in a one-way ANOVA is calculated by dividing the within groups sum of squares by the within groups degrees of freedom, which is the total number of observations minus the number of groups (N - k), not (n - 1).

Question 15

You are testing the equality of three population means using samples of size 5.The F_stat value for your ANOVA is 3.256.At a 5% significance level, you should reject the null hypothesis that the population means are equal.

Accepted Answer

The decision to reject the null hypothesis in ANOVA depends on comparing the F-statistic to the critical value from the F-distribution table, not directly on the F-statistic value itself. Without knowing the critical value for the specific degrees of freedom associated with the test, we cannot determine whether to reject the null hypothesis based solely on the F-statistic value provided.

Question 16

You are testing the equality of population means using ANOVA.The partial ANOVA table appears below.According to the table, four population means are involved in the test.

Accepted Answer

The answer of You are testing the equality of population...

Question 17

In a randomized block design, experimental units are arranged into similar groups based on extraneous factors in an effort to reduce error variation in experimental results.

Accepted Answer

In a randomized block design, experimental units are grouped (or blocked) based on extraneous factors that are not of primary interest but are thought to affect the response variable, with the aim of reducing error variation and increasing the experiment's sensitivity to detect differences among treatments.

Question 18

The within groups mean square in a one-way analysis of variance is the within groups sum of squares (SSW) divided by the between groups sum of squares (SSB).

Accepted Answer

The within groups mean square in a one-way analysis of variance is the within groups sum of squares (SSW) divided by the degrees of freedom for the within groups, not the between groups sum of squares (SSB).

Question 19

The within groups mean square in a one-way analysis of variance is the within groups sum of squares divided by its corresponding degrees of freedom.

Accepted Answer

The within groups mean square in a one-way ANOVA is calculated by dividing the within groups sum of squares by its corresponding degrees of freedom, which represents the average variation within each of the groups.

Question 20

You are testing the equality of four population means with four samples of size six.To compute the within-groups mean square, you should divide the total sum of squares by 3.

Accepted Answer

To compute the within-groups mean square, you should divide the sum of squares within groups by the degrees of freedom within groups, which is calculated as the total number of observations minus the number of groups. With four samples of size six, there are 24 total observations and 4 groups, so the degrees of freedom within groups would be 24 - 4 = 20, not 3.

Quiz 13: F Tests and Analysis of Variance

You are testing the equality of two population means using samples of size 10.The Fstat value for your ANOVA is 4.0.If, instead of an F test, you had conducted a t test to test the "no difference in population means" null hypothesis, the tstat value would be 16.0.

The computed F value (Fstat) in a one-way analysis of variance is the ratio of the between groups sum of squares (SSB) to the within groups sum of squares (SSW).

You are testing the equality of two population means using ANOVA.The critical value Fc for your test is 3.634.If, instead of an F test, you had conducted a t test to test the "no difference in population means" null hypothesis, the tc value would be 1.906.

In an experimental study, the investigator has the ability to directly influence or manipulate one or more of the elements involved in the investigation.

The computed F value (Fstat) in a one-way analysis of variance is the ratio of the within groups mean square (MSW) to the between groups mean square (MSB).

The computed F value (Fstat) in a one-way analysis of variance is the ratio of the between groups mean square (MSB) to the within groups mean square (MSW).

One of the assumptions for the one-way analysis of variance is that the standard deviations - and so the variances - are not the same for all the populations.

The F distribution can be used to describe how the ratio of two sample variances behaves when the two samples have been independently selected from normal populations with the same variance.

In a completely randomized design, experimental units are arranged into similar groups based on extraneous factors in an effort to reduce error variation in experimental results.

You are testing the equality of population means using ANOVA.The partial ANOVA table appears below.If the samples used in the ANOVA are all the same size, that sample size must be 15.

You are testing the equality of population means using ANOVA.The partial ANOVA table appears below.The between-groups mean square value is 1540.

You are testing the equality of population means using ANOVA and a 5% significance level.If the p-value for the Fstat that you produce is .0212, you should conclude that the population means are not equal.

You are testing the equality of population means using one-way ANOVA and a 5% significance level.If the p-value for the Fstat that you produce is .0711, you should conclude that the population means are not equal.

The within groups mean square in a one-way analysis of variance is the within groups sum of squares divided by (n-1) degrees of freedom.

You are testing the equality of three population means using samples of size 5.The Fstat value for your ANOVA is 3.256.At a 5% significance level, you should reject the null hypothesis that the population means are equal.

You are testing the equality of population means using ANOVA.The partial ANOVA table appears below.According to the table, four population means are involved in the test.

In a randomized block design, experimental units are arranged into similar groups based on extraneous factors in an effort to reduce error variation in experimental results.

The within groups mean square in a one-way analysis of variance is the within groups sum of squares (SSW) divided by the between groups sum of squares (SSB).

The within groups mean square in a one-way analysis of variance is the within groups sum of squares divided by its corresponding degrees of freedom.

You are testing the equality of four population means with four samples of size six.To compute the within-groups mean square, you should divide the total sum of squares by 3.

You are testing the equality of two population means using samples of size 10.The F_stat value for your ANOVA is 4.0.If, instead of an F test, you had conducted a t test to test the "no difference in population means" null hypothesis, the t_stat value would be 16.0.

The computed F value (F_stat) in a one-way analysis of variance is the ratio of the between groups sum of squares (SSB) to the within groups sum of squares (SSW).

You are testing the equality of two population means using ANOVA.The critical value F_c for your test is 3.634.If, instead of an F test, you had conducted a t test to test the "no difference in population means" null hypothesis, the t_c value would be 1.906.

The computed F value (F_stat) in a one-way analysis of variance is the ratio of the within groups mean square (MSW) to the between groups mean square (MSB).

The computed F value (F_stat) in a one-way analysis of variance is the ratio of the between groups mean square (MSB) to the within groups mean square (MSW).

You are testing the equality of population means using ANOVA and a 5% significance level.If the p-value for the F_stat that you produce is .0212, you should conclude that the population means are not equal.

You are testing the equality of population means using one-way ANOVA and a 5% significance level.If the p-value for the F_stat that you produce is .0711, you should conclude that the population means are not equal.

You are testing the equality of three population means using samples of size 5.The F_stat value for your ANOVA is 3.256.At a 5% significance level, you should reject the null hypothesis that the population means are equal.