Module 12

Exhibit 13-1 SSTR = 6,750H0: μ1 = μ2 = μ3 = μ4SSE = 8,000Ha: At least one mean is differentnT = 20 ​ ​ Refer to Exhibit 13-1. The mean square within treatments (MSE) equals _____.

500

An experimental design where the experimental units are randomly assigned to the treatments is known as _____.

completely randomized design

Exhibit 13-3 To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the three treatments. You are given the results below. Treatment Observation A 20 30 25 33 B 22 26 20 28 C 40 30 28 22 ​ Refer to Exhibit 13-3. The null hypothesis _____.

should not be rejected

Exhibit 13-3 To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the three treatments. You are given the results below. Treatment Observation A 20 30 25 33 B 22 26 20 28 C 40 30 28 22 ​ Refer to Exhibit 13-3. The test statistic to test the null hypothesis equals _____.

1.059

In an analysis of variance problem involving three treatments and 10 observations per treatment, SSE = 399.6. The MSE for this situation is _____.

14.8

The independent variable of interest in an ANOVA procedure is called _____.

a factor

The number of times each experimental condition is observed in a factorial design is known as a(n) _____.

replication

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

within-samples estimate of σ2

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

2.25

Exhibit 13-1 SSTR = 6,750H0: μ1 = μ2 = μ3 = μ4SSE = 8,000Ha: At least one mean is differentnT = 20 ​ ​ Refer to Exhibit 13-1. The test statistic to test the null hypothesis equals _____.

4.5

In a completely randomized design involving three treatments, the following information is provided: Treatment 1 Treatment 2 Treatment 3 Sample size 5 10 5 Sample mean 4 8 9 ​ The overall mean for all the treatments is _____.

7.25

Exhibit 13-3 To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the three treatments. You are given the results below. Treatment Observation A 20 30 25 33 B 22 26 20 28 C 40 30 28 22 ​ Refer to Exhibit 13-3. The null hypothesis is to be tested at the 1% level of significance. The critical value from the table is _____.

8.02

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

MSTR/MSE

In an analysis of variance where the total sample size for the experiment is nT and the number of populations is k, the mean square within treatments is _____.

SSE/(nT - k)

An experimental design that permits statistical conclusions about two or more factors is a _____.

factorial design

The ANOVA procedure is a statistical approach for determining whether the means of _____.

two or more populations are equal

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

3 and 16

In the ANOVA, treatment refers to _____.

different levels of a factor

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

factor

In factorial designs, the response produced when the treatments of one factor interact with the treatments of another in influencing the response variable is known as _____.

interaction

The mean square is the sum of squares divided by _____.

its corresponding degrees of freedom

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

sampled populations have equal variances

Exhibit 13-1 SSTR = 6,750H0: μ1 = μ2 = μ3 = μ4SSE = 8,000Ha: At least one mean is differentnT = 20 ​ ​ Refer to Exhibit 13-1. The mean square between treatments (MSTR) equals _____. Correct!

2,250

In the analysis of variance procedure (ANOVA), factor refers to _____.

the independent variable

Exhibit 13-3 To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the three treatments. You are given the results below. Treatment Observation A 20 30 25 33 B 22 26 20 28 C 40 30 28 22 ​ Refer to Exhibit 13-3. The null hypothesis for this ANOVA problem is _____.

μ1 = μ2 = μ3