Question 1

In one-way analysis of variance,within-treatments variation is measured by:

Accepted Answer

A)  sum of squares for error. 
B)  sum of squares for treatments. 
C)  total sum of squares. 
D)  standard deviation. 
A)  sum of squares for error. 
B)  sum of squares for treatments. 
C)  total sum of squares. 
D)  standard deviation.

Question 2

The distribution of the test statistic for analysis of variance is the:

Accepted Answer

A)  normal distribution. 
B)  Student t-distribution. 
C)  F-distribution. 
D)  None of these choices. 
A)  normal distribution. 
B)  Student t-distribution. 
C)  F-distribution. 
D)  None of these choices.

Question 3

The within-treatments variation provides a measure of the amount of variation in the response variables that is caused by the treatments.

Accepted Answer

A) True 
 B)False

Question 4

In a two-factor ANOVA,there are 5 levels for factor A,4 levels for factor B,and 3 observations for each combination of factor A and factor B levels.The number of treatments in this experiment equals 20.

Accepted Answer

A) True 
 B)False

Question 5

The randomized block design with exactly two treatments is equivalent to a two-tail:

Accepted Answer

A)  independent samples z-test. 
B)  independent samples equal-variances t-test. 
C)  independent samples unequal-variances t-test. 
D)  matched pairs t-test. 
A)  independent samples z-test. 
B)  independent samples equal-variances t-test. 
C)  independent samples unequal-variances t-test. 
D)  matched pairs t-test.

Question 6

Health Inspectors' Ages
In order to examine the differences in ages of health inspectors among five counties,a Health Department statistician took random samples of six inspectors' ages in each county.The data are listed below.An F-test using ANOVA showed that average age differs for at least two counties.
 $$\begin{array}{l}
\text { Ages of hipectors among Five sehoal Districts }\
\begin{array} { | c c c c c | } 
\hline 1 & 2 & 3 & 4 & 5 \
\hline 41 & 39 & 36 & 45 & 53 \
53 & 48 & 28 & 37 & 55 \
28 & 41 & 29 & 46 & 49 \
45 & 51 & 33 & 48 & 56 \
40 & 49 & 27 & 51 & 48 \
59 & 50 & 26 & 49 & 61 \
\hline
\end{array}
\end{array}$$
-{Health Inspectors' Ages Narrative} Did Tukey's method and Fisher's LSD method in the previous two questions yield the same results? Will this always be the case?

Accepted Answer

For this data set bo

Question 7

If we square the t-statistic for two means,the result is the ____________________-statistic.

Accepted Answer

A) True 
 B)False

Question 8

The average cost of remodeling one room in a house was compared for four different remodeling companies.A random sample of 10 rooms remodeled by each company were selected all with the same square footage,and cost of remodeling each room was recorded.(Rooms were randomly chosen from different houses. )The data are shown below.An F-test using ANOVA concluded that average costs differ for at least two of the remodeling companies.
 $$\begin{array}{l}
\text { Remodeling Company }\
\begin{array} { | c c c c | } 
\hline 1 & 2 & 3 & 4 \
\hline 610 & 404 & 599 & 272 \
354 & 663 & 426 & 405 \
234 & 521 & 429 & 197 \
399 & 518 & 621 & 363 \
278 & 499 & 426 & 297 \
358 & 374 & 414 & 538 \
379 & 562 & 322 & 181 \
548 & 505 & 460 & 318 \
196 & 375 & 494 & 412 \
444 & 438 & 637 & 499 \
\hline
\end{array}
\end{array}$$ Use Tukey's and LSD multiple comparison methods to determine which remodeling companies differ in their average cost.Compare the results and discuss.(Keep the experimentwise Type I error at or close to 5%. )

Accepted Answer

Computer output showing Tukey's analysis

Question 9

The Bonferroni adjustment decreases the experimentwise Type I error rate,but it increases the probability of a Type II error.

Accepted Answer

A) True 
 B)False

Question 10

Tukey's multiple comparison method is ____________________ (more/less)powerful than Fisher's LSD method.

Accepted Answer

The answer of Tukey's multiple comparison method is ____________________ (more/less)powerful...

Question 11

When the problem objective is to compare more than two populations,the experimental design that is the counterpart of the matched pairs experiment is called the randomized ____________________ design.

Accepted Answer

The answer of When the problem objective is to compare...

Question 12

The sum of squares for error (SSE)measures the amount of variation that is explained by the ANOVA model,while the sum of squares for treatments (SST)measures the amount of variation that remains unexplained.

Accepted Answer

A) True 
 B)False

Question 13

Which of the following statements is true?

Accepted Answer

A)  F = t2 
B)  The F-test can be used instead of a two tail t-test when you compare two population means. 
C)  Doing three t-tests is statistically equivalent to doing one F-test when you compare three population means. 
D)  All of these choices are true. 
A)  F = t2 
B)  The F-test can be used instead of a two tail t-test when you compare two population means. 
C)  Doing three t-tests is statistically equivalent to doing one F-test when you compare three population means. 
D)  All of these choices are true.

Question 14

In the one-way ANOVA where k is the number of treatments and n is the number of observations in all samples,the number of degrees of freedom for error is:

Accepted Answer

A)  k - 1 
B)  n - 1 
C)  n - k 
D)  n - k + 1 
A)  k - 1 
B)  n - 1 
C)  n - k 
D)  n - k + 1

Question 15

One-way ANOVA is applied to independent samples taken from three normally distributed populations with equal variances.Which of the following is the null hypothesis for this procedure?

Accepted Answer

A)  $\mu$1 + $\mu$2 + $\mu$3 = 0 
B) $\mu$1 + $\mu$2 + $\mu$3 $\neq$ 0 
C)  $\mu$1 = $\mu$2 = $\mu$3 = 0 
D)  $\mu$1 = $\mu$2 = $\mu$3 
A)  $\mu$1 + $\mu$2 + $\mu$3 = 0 
B) $\mu$1 + $\mu$2 + $\mu$3 $\neq$ 0 
C)  $\mu$1 = $\mu$2 = $\mu$3 = 0 
D)  $\mu$1 = $\mu$2 = $\mu$3

Question 16

The F-test of a randomized block design of the analysis of variance has the same requirements as the independent samples design;that is,the random variable must be ____________________ distributed and the population ____________________ must be equal.

Accepted Answer

normally;v

Question 17

Tukey's multiple comparison method is based on the Studentized range statistic.

Accepted Answer

A) True 
 B)False

Question 18

In one-way analysis of variance,if all the sample means are equal,then the:

Accepted Answer

A)  total sum of squares is zero. 
B)  sum of squares for treatments is zero. 
C)  sum of squares for error is zero. 
D)  sum of squares for error equals sum of squares for treatments. 
A)  total sum of squares is zero. 
B)  sum of squares for treatments is zero. 
C)  sum of squares for error is zero. 
D)  sum of squares for error equals sum of squares for treatments.

Question 19

The techniques used to detect which population means differ are called multiple ____________________ methods.

Accepted Answer

The answer of The techniques used to detect which population...

Question 20

Which of the following components in an ANOVA table is not additive?

Accepted Answer

A)  Sum of squares 
B)  Degrees of freedom 
C)  Mean squares 
D)  All of these choices are additive. 
A)  Sum of squares 
B)  Degrees of freedom 
C)  Mean squares 
D)  All of these choices are additive.

Exam 14: Analysis of Variance

In one-way analysis of variance,within-treatments variation is measured by:

The distribution of the test statistic for analysis of variance is the:

The within-treatments variation provides a measure of the amount of variation in the response variables that is caused by the treatments.

In a two-factor ANOVA,there are 5 levels for factor A,4 levels for factor B,and 3 observations for each combination of factor A and factor B levels.The number of treatments in this experiment equals 20.

The randomized block design with exactly two treatments is equivalent to a two-tail:

If we square the t-statistic for two means,the result is the ____________________-statistic.

The Bonferroni adjustment decreases the experimentwise Type I error rate,but it increases the probability of a Type II error.

Tukey's multiple comparison method is ____________________ (more/less)powerful than Fisher's LSD method.

When the problem objective is to compare more than two populations,the experimental design that is the counterpart of the matched pairs experiment is called the randomized ____________________ design.

The sum of squares for error (SSE)measures the amount of variation that is explained by the ANOVA model,while the sum of squares for treatments (SST)measures the amount of variation that remains unexplained.

Which of the following statements is true?

In the one-way ANOVA where k is the number of treatments and n is the number of observations in all samples,the number of degrees of freedom for error is:

One-way ANOVA is applied to independent samples taken from three normally distributed populations with equal variances.Which of the following is the null hypothesis for this procedure?

The F-test of a randomized block design of the analysis of variance has the same requirements as the independent samples design;that is,the random variable must be ____________________ distributed and the population ____________________ must be equal.

Tukey's multiple comparison method is based on the Studentized range statistic.

In one-way analysis of variance,if all the sample means are equal,then the:

The techniques used to detect which population means differ are called multiple ____________________ methods.

Which of the following components in an ANOVA table is not additive?

What Is Statistics

Graphical Descriptive Techniques I

Graphical Descriptive Techniques II

A: Numerical Descriptive Techniques

B: Numerical Descriptive Techniques

C: Numerical Descriptive Techniques

Data Collection and Sampling

Probability

A: Random Variables and Discrete Probability Distributions

B: Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Introduction to Estimation

Introduction to Hypothesis Testing

Inference About a Population

Inference About Comparing Two Populations

Chi-Squared Tests

A: Simple Linear Regression and Correlation

B: Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Statistics

Time-Series Analysis and Forecasting

Statistical Process Control

Decision Analysis

Conclusion

Filters

The F-test of a randomized block design of the analysis of variance has the same requirements as the independent samples design;that is,the random variable must be distributed and the population must be equal.