Question 1

In one-way ANOVA,the test statistic is defined as the ratio of the mean square for error (MSE)and the mean square for treatments (MST),namely,F = MSE / MST.

Accepted Answer

A) True 
 B)False

Question 2

In which case can an F-test be used to compare two population means?

Accepted Answer

A)  For one tail tests only. 
B)  For two tail tests only. 
C)  For either one or two tail tests. 
D)  None of these choices. 
A)  For one tail tests only. 
B)  For two tail tests only. 
C)  For either one or two tail tests. 
D)  None of these choices.

Question 3

The distribution of the test statistic for analysis of variance is the F-distribution.

Accepted Answer

A) True 
 B)False

Question 4

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} Use Tukey's multiple comparison method to determine which means differ.

Accepted Answer

@#LAT-DLM& = 10.847
 @#IMG-DLM& The mean age of inspectors

Question 5

Number of observation for a particular combination of treatments is called a replicate.

Accepted Answer

A) True 
 B)False

Question 6

Sub Sandwich Customers
The marketing manager of a Sub Shop chain is in the process of examining some of the demographic characteristics of her customers.In particular,she would like to investigate the belief that the ages of the customers of Sub Shops,hamburger emporiums,and fast-food chicken restaurants are different.The ages of eight randomly selected customers of each of the restaurants are recorded and listed below.From previous analyses we know that the ages are normally distributed with equal variances for each group.
 $$\begin{array}{l}
\text { Customers' Agas }\
\begin{array} { | c c c | } 
\hline \text { Subs } & \text { Hamburaer } & \text { Chicken } \
\hline 23 & 26 & 25 \
19 & 20 & 28 \
25 & 18 & 36 \
17 & 35 & 23 \
36 & 33 & 39 \
25 & 25 & 27 \
28 & 19 & 38 \
31 & 17 & 31 \
\hline
\end{array}
\end{array}$$
-{Sub Sandwich Customers Narrative} Set up the ANOVA Table.Use $\alpha$= 0.05 to determine the critical value.

Accepted Answer

\[\begin{array} { | l | c c c c c c | }

Question 7

Number of observation for particular combination of treatments is called a(n)________________.

Accepted Answer

The answer of Number of observation for particular combination of...

Question 8

In one-way ANOVA,the amount of total variation that is unexplained is measured by the:

Accepted Answer

A)  sum of squares for treatments. 
B)  degrees of freedom. 
C)  total sum of squares. 
D)  sum of squares for error. 
A)  sum of squares for treatments. 
B)  degrees of freedom. 
C)  total sum of squares. 
D)  sum of squares for error.

Question 9

A(n)____________________ experiment requires that the sample size for each treatment be equal.

Accepted Answer

The answer of A(n)____________________ experiment requires that the sample size...

Question 10

We can use the F-test to determine whether $\mu$1 is greater than $\mu$2.

Accepted Answer

A) True 
 B)False

Question 11

One example of a blocking variable is the dosage level that each subject is assigned to in a randomized experiment.

Accepted Answer

A) True 
 B)False

Question 12

Which of the following is true regarding SSB?

Accepted Answer

A)  SSB stands for sum of squares for blocks. 
B)  SSB can help to reduce SSE. 
C)  SSB can help make it easier to determine whether differences exist between the treatment means. 
D)  All of these choices are true. 
A)  SSB stands for sum of squares for blocks. 
B)  SSB can help to reduce SSE. 
C)  SSB can help make it easier to determine whether differences exist between the treatment means. 
D)  All of these choices are true.

Question 13

How does conducting multiple t-tests compare to conducting a single F-test?

Accepted Answer

A)  Multiple t-tests increases the chance of a Type I error. 
B)  Multiple t-tests decreases the chance of a Type I error. 
C)  Multiple t-tests does not affect the chance of a Type I error. 
D)  This comparison cannot be made without knowing the number of populations. 
A)  Multiple t-tests increases the chance of a Type I error. 
B)  Multiple t-tests decreases the chance of a Type I error. 
C)  Multiple t-tests does not affect the chance of a Type I error. 
D)  This comparison cannot be made without knowing the number of populations.

Question 14

The value of the test statistic in a completely randomized design for ANOVA is F = 6.29.The degrees of freedom for the numerator and denominator are 5 and 10,respectively.Using an F table,the most accurate statements to be made about the p-value is that it is:

Accepted Answer

A)  greater than 0.05 
B)  between 0.001 and 0.010. 
C)  between 0.010 and 0.025. 
D)  between 0.025 and 0.050. 
A)  greater than 0.05 
B)  between 0.001 and 0.010. 
C)  between 0.010 and 0.025. 
D)  between 0.025 and 0.050.

Question 15

In the one-way ANOVA where there are k treatments and n observations,the degrees of freedom for the F-statistic are equal to,respectively:

Accepted Answer

A)  n and k. 
B)  k and n. 
C)  n - k and k -1. 
D)  k - 1 and n - k. 
A)  n and k. 
B)  k and n. 
C)  n - k and k -1. 
D)  k - 1 and n - k.

Question 16

In one-way ANOVA,the total variation SS(Total)is partitioned into two sources of variation: the sum of squares for treatments (SST)and the sum of squares for error (SSE).

Accepted Answer

A) True 
 B)False

Question 17

Migraine Treatments
The following data were generated from a 2*2 factorial experiment with 3 replicates,where factor A levels represent two different injection procedures of an anesthetic to the occipital nerve (located in the back of the neck),and factor B levels represent two different drugs,which physicians recommend to increase the effectiveness of the injections.Three migraine patients were randomly selected for each combination of injection and drug.
 $$\begin{array} { | c | c c | } 
 &\text { Factor B }\
\hline \text { Factor A } & 1 & 2 \
\hline 1 & 7 & 13 \
& 10 & 11 \
& 8 & 12 \
2 & 10 & 10 \
& 11 & 15 \
& 0 & 11 \
\hline
\end{array}$$
-{Migraine Treatments Narrative} Test at the 5% significance level to determine if differences exist among the four treatment means.

Accepted Answer

\[\begin{array} { | l | c c c c c c | }

Question 18

Sub Sandwich Customers
The marketing manager of a Sub Shop chain is in the process of examining some of the demographic characteristics of her customers.In particular,she would like to investigate the belief that the ages of the customers of Sub Shops,hamburger emporiums,and fast-food chicken restaurants are different.The ages of eight randomly selected customers of each of the restaurants are recorded and listed below.From previous analyses we know that the ages are normally distributed with equal variances for each group.
 $$\begin{array}{l}
\text { Customers' Agas }\
\begin{array} { | c c c | } 
\hline \text { Subs } & \text { Hamburaer } & \text { Chicken } \
\hline 23 & 26 & 25 \
19 & 20 & 28 \
25 & 18 & 36 \
17 & 35 & 23 \
36 & 33 & 39 \
25 & 25 & 27 \
28 & 19 & 38 \
31 & 17 & 31 \
\hline
\end{array}
\end{array}$$
-{Sub Sandwich Customers Narrative} Do these data provide enough evidence at the 5% significance level to infer that there are differences in ages among the customers of the three restaurants?

Accepted Answer

H₀: @#LAT-DLM&₁ = @#LAT-DLM&₂

Question 19

When the variation associated with blocks is removed from the data,SSE increases.

Accepted Answer

A) True 
 B)False

Question 20

Which of the following statements is true?

Accepted Answer

A)  A fixed-effects ANOVA refers to the analysis which includes all possible levels of a factor. 
B)  A random-effects ANOVA refers to the analysis where the levels included in the study represent a random sample of all levels that exist. 
C)  A multifactor experiment is one where there are two or more factors that define the treatments. 
D)  All of these choices are true. 
A)  A fixed-effects ANOVA refers to the analysis which includes all possible levels of a factor. 
B)  A random-effects ANOVA refers to the analysis where the levels included in the study represent a random sample of all levels that exist. 
C)  A multifactor experiment is one where there are two or more factors that define the treatments. 
D)  All of these choices are true.

Exam 14: Analysis of Variance

In one-way ANOVA,the test statistic is defined as the ratio of the mean square for error (MSE)and the mean square for treatments (MST),namely,F = MSE / MST.

In which case can an F-test be used to compare two population means?

The distribution of the test statistic for analysis of variance is the F-distribution.

Number of observation for a particular combination of treatments is called a replicate.

Number of observation for particular combination of treatments is called a(n)________________.

In one-way ANOVA,the amount of total variation that is unexplained is measured by the:

A(n)____________________ experiment requires that the sample size for each treatment be equal.

We can use the F-test to determine whether μ\muμ 1 is greater than μ\muμ 2.

One example of a blocking variable is the dosage level that each subject is assigned to in a randomized experiment.

Which of the following is true regarding SSB?

How does conducting multiple t-tests compare to conducting a single F-test?

The value of the test statistic in a completely randomized design for ANOVA is F = 6.29.The degrees of freedom for the numerator and denominator are 5 and 10,respectively.Using an F table,the most accurate statements to be made about the p-value is that it is:

In the one-way ANOVA where there are k treatments and n observations,the degrees of freedom for the F-statistic are equal to,respectively:

In one-way ANOVA,the total variation SS(Total)is partitioned into two sources of variation: the sum of squares for treatments (SST)and the sum of squares for error (SSE).

When the variation associated with blocks is removed from the data,SSE increases.

Which of the following statements is true?

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

We can use the F-test to determine whether $\mu$ ₁ is greater than $\mu$ ₂.