Question 1

The one-way ANOVA test involves assuming that the population variances are equal.

Accepted Answer

The one-way ANOVA test assumes that the population variances are equal. This assumption is necessary for the F-test used in ANOVA to be accurate. If the population variances are not equal, then the results of the ANOVA test may be incorrect.

Question 2

In a one-way analysis of variance design,there is a single factor of interest but there may be multiple levels of the factor.

Accepted Answer

A one-way analysis of variance design involves a single factor with multiple levels, and compares the means of the groups created by these levels.

Question 3

In a completely randomized analysis of variance design,the observations from each factor are selected in an independent and random fashion.

Accepted Answer

In a completely randomized analysis of variance design, the selection of observations from each factor is independent and random, meaning that participants are assigned to different groups randomly, giving no preference or selection bias to any group.

Question 4

Prior to performing a one-way analysis of variance test,the analysts were interested in determining whether the population variances were equal.The design had one factor with 3 levels and a balanced design with sample size equal to 6.Among others,the following summary statistics were computed:  = 50,  = 80,  = 40.Based on these statistics,the calculated F-value for performing a Hartley's F-test for equality of population variances is F = 2.00.

Accepted Answer

The answer of Prior to performing a one-way analysis of...

Question 5

In conducing one-way analysis of variance,the population distributions are assumed normally distributed.

Accepted Answer

One of the assumptions of conducting one-way analysis of variance is that the population distributions of the groups being compared are normal.

Question 6

Recently,a company tested three different machine types to see if there was a difference in the mean thickness of products produced by the three.A random sample of ten products was selected from the output from each machine.Given this information,the proper design to test whether the means are equal is a one-way ANOVA balanced design.

Accepted Answer

A one-way ANOVA is used to compare the means of three or more groups, which is appropriate in this case since there are three different machine types being tested. A balanced design means that each group (machine type) has the same sample size (ten products in this case). Therefore, a one-way ANOVA balanced design is the proper design to test whether the means are equal.

Question 7

The within sample variation is the dispersion that exists because the sample means for the various factor levels are not all equal.

Accepted Answer

The within-sample variation refers to the dispersion of individual observations around their respective sample means, not the differences between the sample means themselves.

Question 8

Prior to performing a one-way analysis of variance test,the analysts were interested in determining whether the population variances were equal.The design had one factor with 3 levels and a balanced design with sample size equal to 6.Among others,the following summary statistics were computed: = 50, = 80, = 40.Based on this information,the Hartley F_max critical value is 10.8 if the significance level for the test is 0.05.

Accepted Answer

The answer of Prior to performing a one-way analysis of...

Question 9

The term one-way analysis of variance refers to the fact that in conducting the test,there is only one way to set up the null and alternative hypotheses.

Accepted Answer

The term one-way analysis of variance refers to the fact that there is only one independent variable or factor being tested, but there are multiple levels or categories within that factor. However, there can be several different ways to set up the null and alternative hypotheses depending on the research question and hypothesis being tested.

Question 10

A study was recently conducted to see whether the mean starting salaries for graduates of engineering,business,healthcare,and computer information systems majors differ.A random sample of 8 graduates was selected from each major.The following chart shows some of the results of the ANOVA computations; however,some of the output is missing.If it had been included,the calculated test statistic would be F = 8.33.
Anova: Single Factor
SUMMARY  ANOVA

Accepted Answer

The missing information in the ANOVA output is the degrees of freedom (df) for between-groups and within-groups, as well as the p-value. However, based on the given information that the calculated test statistic (F) is 8.33, we can conclude that the null hypothesis (that the means of the four majors are equal) is rejected at the 0.05 significance level. Therefore, we can answer that the statement "the mean starting salaries for graduates of engineering, business, healthcare, and computer information systems majors differ" is supported by the data.

Question 11

In conducting one-way analysis of variance,the sample size for each group must be equal.

Accepted Answer

In one-way ANOVA, the sample sizes for each group do not need to be equal, although having equal sample sizes can increase the power of the test.

Question 12

Under the basic logic of one-way analysis of variance,if the within variation is large relative to the between variation,it is an indication that the population means are likely to be different.

Accepted Answer

In one-way analysis of variance (ANOVA), if the within-group variation is large relative to the between-group variation, it suggests that the differences among the group means are not statistically significant, implying that the population means are likely to be similar, not different.

Question 13

A study was recently conducted to see whether the mean starting salaries for graduates of engineering,business,healthcare,and computer information systems majors differ.A random sample of 8 graduates was selected from each major.The following shows the results of the ANOVA computations.However,the degrees of freedom column has been omitted.The correct number of degrees of freedom for the within variation is 28.
Anova: Single Factor
SUMMARY  ANOVA

Accepted Answer

The statement is correct, the correct number of degrees of freedom for the within variation is 28.

Question 14

In a one-way analysis of variance design,the total variation in the data across the various factor levels can be partitioned into two parts,the within sample variation and the between sample variation.

Accepted Answer

This is true as the ANOVA model aims to explain the variation in the dependent variable with respect to the independent variable(s) by separating the total variation into two components: the variation within the groups (within sample variation) and the variation between the groups (between sample variation).

Question 15

In conducting a one-way analysis of variance,if the null hypothesis is true then the variance between groups (MSB)should be approximately equal to the variance within groups (MSW).

Accepted Answer

This is a fundamental assumption of the one-way ANOVA. If the null hypothesis is true, there should be no significant difference between the means of each group, resulting in similar variances between and within groups.

Question 16

A study was recently conducted to see whether the mean starting salaries for graduates of engineering,business,healthcare,and computer information systems majors differ.A random sample of 8 graduates was selected from each major.Based upon this information,the appropriate null hypothesis to be tested is  :  -  -  -  = 0.

Accepted Answer

The answer of A study was recently conducted to see...

Question 17

A study was recently conducted to see whether the mean starting salaries for graduates of engineering,business,healthcare,and computer information systems majors differ.A random sample of 8 graduates was selected from each major.If the test is to be conducted using an alpha = 0.05 level,the critical value will be F = 3.838.

Accepted Answer

The answer of A study was recently conducted to see...

Question 18

In a one-way analysis of variance test,the following null and alternative hypotheses are appropriate:

Accepted Answer

The answer of In a one-way analysis of variance test,the...

Question 19

In one-way analysis of variance,the within-sample variation is not affected by whether the null hypothesis is true on not.

Accepted Answer

In one-way analysis of variance, the within-sample variation or the error variance is solely dependent on the variability of the individuals within each group, and is not affected by whether the null hypothesis is true or not. Thus, the within-sample variation remains constant irrespective of the hypothesis being tested.

Question 20

In a recent one-way ANOVA test,SSW was equal to 15,900 and the SSB was equal to 3,100.Therefore,SST is equal to 12,800.

Accepted Answer

SSW + SSB = SST, therefore SST should be 19,000 not 12,800.

Quiz 12: Analysis of Variance