Question 1

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 given by:

Accepted Answer

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

Question 2

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

Accepted Answer

A) True 
 B)False

Question 3

In a completely randomised design, 12 experimental units were assigned to the first treatment, 15 units to the second treatment, and 18 units to the third treatment. A partial ANOVA table is shown below: $$\begin{array} { | l | c | c | c | c | } 
\hline \text { Source of Variation } & \text { SS } & d f & M S & F \
\hline \text { Treatments } & * & * & * & 9 \
\hline \text { Error } & * & * & 35 & \
\hline \text { Total } & * & * & & \
\hline
\end{array}$$ Fill in the blanks (identified by asterisks) in the above ANOVA table.

Accepted Answer

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

Question 4

Which of the following best describes an experimental design model where the treatments are defined as the levels of one factor, and the experimental design specifies independent samples?

Accepted Answer

A)  Randomised block design 
B)  Two way ANOVA 
C)  One way ANOVA 
D)  All of these choices are correct. 
A)  Randomised block design 
B)  Two way ANOVA 
C)  One way ANOVA 
D)  All of these choices are correct.

Question 5

Which of the following is the primary interest of designing a randomised block experiment?

Accepted Answer

A)  Reduce the variation among blocks. 
B)  Reduce the within-treatments variation to more easily detect differences among the treatment means. 
C)  Increase the between-treatments variation to more easily detect differences among the treatment means. 
D)  Increase the total sum of squares. 
A)  Reduce the variation among blocks. 
B)  Reduce the within-treatments variation to more easily detect differences among the treatment means. 
C)  Increase the between-treatments variation to more easily detect differences among the treatment means. 
D)  Increase the total sum of squares.

Question 6

The following data are drawn from three normal populations. $$\begin{array} { | c | c | c | } 
\hline A & B & C \
\hline 5 & 8 & 16 \
\hline 16 & 13 & 5 \
\hline 13 & 12 & 10 \
\hline 14 & 15 & 13 \
\hline 10 & 23 & \
\hline & 11 & \
\hline
\end{array}$$ Set up the ANOVA table and test at the 5% level of significance to determine whether differences exist among the population means. Assume that the random variable is normally distributed.

Accepted Answer

Ho: µ₁= µ₂ = µ₃ H_A: At least two means diffe

Question 7

Two samples of 10 each have been taken from the male and female workers of a large company. The data involve the wage rate of each worker. To test whether there is any difference in the average wage rate between male and female workers, a pooled-variances t-test will be considered. Another test option to consider is ANOVA. The most likely ANOVA to fit this test situation is one way ANOVA.

Accepted Answer

A) True 
 B)False

Question 8

A randomised block design with 4 treatments and 5 blocks produced the following sum of squares values: SS(Total) = 2000, SST = 400, SSE = 200. The value of MSB must be 350.

Accepted Answer

A) True 
 B)False

Question 9

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

Accepted Answer

A) True 
 B)False

Question 10

Is it possible to have a randomised block design of the analysis of variance in which SSE = 0 and SSB is not equal to zero? Explain.

Accepted Answer

No, since if there i

Question 11

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

Accepted Answer

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

Question 12

In a completely randomised design, 12 experimental units were assigned to the first treatment, 15 units to the second treatment, and 18 units to the third treatment. A partial ANOVA table is shown below: $$\begin{array} { | l | c | c | c | c | } 
\hline \text { Source of Variation } & \text { SS } & d f & M S & F \
\hline \text { Treatments } & * & * & * & 9 \
\hline \text { Error } & * & * & 35 & \
\hline \text { Total } & * & * & & \
\hline
\end{array}$$ Test at the 5% significance level to determine if differences exist among the three treatment means.

Accepted Answer

@#LAT-DLM& . @#LAT-DLM& At least two means differ.

Question 13

Which of the following is a correct formulation for the null hypothesis in one-way ANOVA?

Accepted Answer

A)  $\mu _ { 1 } + \mu _ { 2 } + \mu _ { 3 } = 0$ . 
B)  $\mu _ { 1 } + \mu _ { 2 } + \mu _ { 3 } \neq 0$ . 
C)  $\mu _ { 1 } = \mu _ { 2 } = \mu _ { 3 }$ . 
D)  $\mu _ { 1 } \neq \mu _ { 2 } \neq \mu _ { 3 }$ . 
A)  $\mu _ { 1 } + \mu _ { 2 } + \mu _ { 3 } = 0$ . 
B)  $\mu _ { 1 } + \mu _ { 2 } + \mu _ { 3 } \neq 0$ . 
C)  $\mu _ { 1 } = \mu _ { 2 } = \mu _ { 3 }$ . 
D)  $\mu _ { 1 } \neq \mu _ { 2 } \neq \mu _ { 3 }$ .

Question 14

In order to examine the differences in age of teachers among five school districts, an educational statistician took random samples of six teachers' ages in each district. The data are listed below. $\text { Ages of teachers among five school districts }$
$\begin{array}{|c|c|c|c|c|}
\hline 1 & 2 & 3 & 4 & 5 \
\hline 42 & 23 & 45 & 31 & 37 \
\hline 22 & 52 & 48 & 45 & 40 \
\hline 33 & 32 & 50 & 33 & 45 \
\hline 32 & 44 & 45 & 38 & 61 \
\hline 26 & 39 & 37 & 29 & 50 \
\hline 24 & 33 & 49 & 46 & 50 \
\hline
\end{array}$ Assume that ages of teachers are normally distributed.
Test at the 5% significance level to determine whether differences in teachers' ages exist among the five districts.

Accepted Answer

@#LAT-DLM& @#LAT-DLM& At least two means differ. \[\begin{ar

Question 15

If we examine two or more independent samples to determine if their population means could be equal, we are performing one-way analysis of variance (ANOVA).

Accepted Answer

A) True 
 B)False

Question 16

Which of the following is not a required condition for one-way ANOVA?

Accepted Answer

A)  The populations are normally distributed. 
B)  The population variances are equal. 
C)  The samples are selected independently of each other. 
D)  The population means are equal. 
A)  The populations are normally distributed. 
B)  The population variances are equal. 
C)  The samples are selected independently of each other. 
D)  The population means are equal.

Question 17

Automobile insurance appraisers examine cars that have been involved in accidental collisions and estimate the cost of repairs. An insurance executive claims that there are significant differences in the estimates from different appraisers. To support his claim he takes a random sample of six cars that have recently been damaged in accidents. Three appraisers then estimate the repair costs of all six cars. From the data shown below, can we infer at the 5% significance level that the executive's claim is true? $\quad $$\quad $$\quad $$\quad $$\quad $$\text { Estim ated repair cost }$
$\begin{array}{|c|c|c|c|}
\hline \text { Car } & \text { Appraiser 1 } & \begin{array}{c}
\text { Appraiser2 } \
\end{array} & \text { Appraiser 3 } \
\hline 1 & 650 & 600 & 750 \
\hline 2 & 930 & 910 & 1010 \
\hline 3 & 440 & 450 & 500 \
\hline 4 & 750 & 710 & 810 \
\hline 5 & 1190 & 1050 & 1250 \
\hline 6 & 1560 & 1270 & 1450 \
\hline
\end{array}$

Accepted Answer

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

Question 18

In ANOVA, a factor is an independent variable.

Accepted Answer

A) True 
 B)False

Question 19

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 one-way analysis of variance.

Accepted Answer

A) True 
 B)False

Question 20

Which of the following is not true of Tukey's multiple comparison method?

Accepted Answer

A)  It is based on the studentised range statistic q to obtain the critical value needed to construct individual confidence intervals. 
B)  It requires that all sample sizes are equal, or at least similar. 
C)  It can be employed instead of the analysis of variance. 
D)  All of these choices are correct. 
A)  It is based on the studentised range statistic q to obtain the critical value needed to construct individual confidence intervals. 
B)  It requires that all sample sizes are equal, or at least similar. 
C)  It can be employed instead of the analysis of variance. 
D)  All of these choices are correct.

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 given by:

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

Which of the following best describes an experimental design model where the treatments are defined as the levels of one factor, and the experimental design specifies independent samples?

Which of the following is the primary interest of designing a randomised block experiment?

The following data are drawn from three normal populations. A B C 5 8 16 16 13 5 13 12 10 14 15 13 10 23 11 Set up the ANOVA table and test at the 5% level of significance to determine whether differences exist among the population means. Assume that the random variable is normally distributed.

A randomised block design with 4 treatments and 5 blocks produced the following sum of squares values: SS(Total) = 2000, SST = 400, SSE = 200. The value of MSB must be 350.

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

Is it possible to have a randomised block design of the analysis of variance in which SSE = 0 and SSB is not equal to zero? Explain.

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

Which of the following is a correct formulation for the null hypothesis in one-way ANOVA?

If we examine two or more independent samples to determine if their population means could be equal, we are performing one-way analysis of variance (ANOVA).

Which of the following is not a required condition for one-way ANOVA?

In ANOVA, a factor is an independent variable.

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 one-way analysis of variance.

Which of the following is not true of Tukey's multiple comparison method?

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

Exam 16: Analysis of Variance

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 given by:

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

Which of the following best describes an experimental design model where the treatments are defined as the levels of one factor, and the experimental design specifies independent samples?

Which of the following is the primary interest of designing a randomised block experiment?

The following data are drawn from three normal populations. A B C 5 8 16 16 13 5 13 12 10 14 15 13 10 23 11 Set up the ANOVA table and test at the 5% level of significance to determine whether differences exist among the population means. Assume that the random variable is normally distributed.

A randomised block design with 4 treatments and 5 blocks produced the following sum of squares values: SS(Total) = 2000, SST = 400, SSE = 200. The value of MSB must be 350.

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

Is it possible to have a randomised block design of the analysis of variance in which SSE = 0 and SSB is not equal to zero? Explain.

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

Which of the following is a correct formulation for the null hypothesis in one-way ANOVA?

If we examine two or more independent samples to determine if their population means could be equal, we are performing one-way analysis of variance (ANOVA).

Which of the following is not a required condition for one-way ANOVA?

In ANOVA, a factor is an independent variable.

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 one-way analysis of variance.

Which of the following is not true of Tukey's multiple comparison method?

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters