Question 1

Given the following Analysis of Variance table for three treatments each with six observations.   What are the degrees of freedom for the numerator and denominator?

Accepted Answer

A)  3 and 18 
B)  2 and 17 
C)  3 and 15 
D)  2 and 15 
E)  None of these statements are true 
A)  3 and 18 
B)  2 and 17 
C)  3 and 15 
D)  2 and 15 
E)  None of these statements are true D

Question 2

i. To employ ANOVA, the populations should have approximately equal standard deviations. 
ii. To employ ANOVA, the populations being studied must be approximately normally distributed. 
iii. The least number of sources of variation in ANOVA is two.

Accepted Answer

A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and (ii) are correct statements, but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  All statements are false 
A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and (ii) are correct statements, but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  All statements are false A

Question 3

Two accounting professors decided to compare the variation of their grading procedures. To accomplish this they each graded the same 10 exams with the following results:   What are the degrees of freedom for the denominator of the F ratio?

Accepted Answer

A)  20 
B)  18 
C)  10 
D)  9 
E)  8 
A)  20 
B)  18 
C)  10 
D)  9 
E)  8 D

Question 4

What distribution does the F distribution approach as the sample size increases?

Accepted Answer

A)  Binomial 
B)  Normal 
C)  Poisson 
D)  Exponential 
E)  None of these is correct 
A)  Binomial 
B)  Normal 
C)  Poisson 
D)  Exponential 
E)  None of these is correct

Question 5

i. If the computed value of F is 4.01 and the critical value is 2.67, we would conclude that all the population means are equal.F5
Ii) Rejecting the null hypothesis in ANOVA indicates that the population means are equal.
Iii) The null hypothesis for an ANOVA is μ1 - μ2 ≠ μ3

Accepted Answer

A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and (ii) are correct statements, but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  All statements are false 
A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and (ii) are correct statements, but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  All statements are false

Question 6

ii. The calculated F value must be equal to or greater than one (1) iii. The shape of the F distribution is symmetrical. i. The test statistic used in ANOVA is t

Accepted Answer

A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and (ii) are correct statements, but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  All statements are false 
A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and (ii) are correct statements, but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  All statements are false

Question 7

Suppose that an automobile manufacturer designed a radically new lightweight engine and wants to recommend the grade of gasoline to use. The four grades are: below regular, regular, premium, and super premium. The test car made three trial runs on the test track using each of the four grades. Assuming any grade can be used at the 0.05 level, what is the critical value of F using 0.05 level of significance?

Accepted Answer

A)  1.96 
B)  4.07 
C)  2.33 
D)  12.00 
E)  None of these statements are true 
A)  1.96 
B)  4.07 
C)  2.33 
D)  12.00 
E)  None of these statements are true

Question 8

i. For the population means, the alternate hypothesis used in the analysis of variance test states that µ1 = µ2 = µ3.
Ii) For an ANOVA test, rejection of the null hypothesis does not identify which populations differ
Significantly.
Iii) If the computed value of F is 4.01 and the critical value is 2.67, we would conclude that all the population means are equal.

Accepted Answer

A)  (i), (ii) and (iii) are all correct statements 
B)  (ii) is a correct statement, but not (i) or (iii). 
C)  (iii) is a correct statements but not (i) or (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  All statements are false 
A)  (i), (ii) and (iii) are all correct statements 
B)  (ii) is a correct statement, but not (i) or (iii). 
C)  (iii) is a correct statements but not (i) or (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  All statements are false

Question 9

i. The F distribution is positively skewed and its values may range from 0 to plus infinity. 
ii. The F distribution's curve is positively skewed
Iii) Like Student's t distribution, a change in the degrees of freedom causes a change in the shape of the F distribution.

Accepted Answer

A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and (ii) are correct statements, but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  All statements are false 
A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and (ii) are correct statements, but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  All statements are false

Question 10

i. The shape of the F distribution is determined by the degrees of freedom for the F-statistic, one for the numerator and one for the denominator.
Ii) Like Student's t distribution, a change in the degrees of freedom causes a change in the shape of the
F distribution.
Iii) The calculated F value must be equal to or greater than zero (0)

Accepted Answer

A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and (ii) are correct statements, but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  All statements are false 
A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and (ii) are correct statements, but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  All statements are false

Question 11

An F statistic is:

Accepted Answer

A)  a ratio of two means. 
B)  a ratio of two variances. 
C)  the difference between three means. 
D)  a population parameter. 
A)  a ratio of two means. 
B)  a ratio of two variances. 
C)  the difference between three means. 
D)  a population parameter.

Question 12

A random sample of 30 executives from companies with assets over $1 million was selected and asked for their annual income and level of education. The ANOVA comparing the average income among three levels of education rejected the null hypothesis. The Mean Square Error (MSE) was 243.7. The following table summarized the results:   When comparing the mean annual incomes for executives with Undergraduate and Master's Degree or more, the following 95% confidence interval can be constructed:

Accepted Answer

A)  2.0 ± 2.052*6.51 
B)  2.0 ± 3.182*6.51 
C)  2.0 ± 2.052*42.46 
D)  None of these statements are true 
A)  2.0 ± 2.052*6.51 
B)  2.0 ± 3.182*6.51 
C)  2.0 ± 2.052*42.46 
D)  None of these statements are true

Question 13

In ANOVA analysis, when the null hypothesis is rejected, we can find which means are different by:

Accepted Answer

A)  constructing confidence intervals. 
B)  adding another treatment. 
C)  doing an additional ANOVA. 
D)  doing a t test. 
E)  None of these statements are true. 
A)  constructing confidence intervals. 
B)  adding another treatment. 
C)  doing an additional ANOVA. 
D)  doing a t test. 
E)  None of these statements are true.

Question 14

A manufacturer of automobile transmissions uses three different processes. The management ordered a study of the production costs to see if there is a difference among the three processes. A summary of the findings is shown below.   What is the mean square for error?

Accepted Answer

A)  2.511 
B)  2.151 
C)  33.9 
D)  29.035 
E)  None of these statements are true 
A)  2.511 
B)  2.151 
C)  33.9 
D)  29.035 
E)  None of these statements are true

Question 15

Which of the following is NOT a characteristic of the F distribution?

Accepted Answer

A)  It is based on two sets of degrees of freedom 
B)  It is positively skewed. 
C)  As the values of X increase, the F curve approaches the X-axis and eventually equals zero. 
D)  It is asymptotic. 
A)  It is based on two sets of degrees of freedom 
B)  It is positively skewed. 
C)  As the values of X increase, the F curve approaches the X-axis and eventually equals zero. 
D)  It is asymptotic.

Question 16

A random sample of 30 executives from companies with assets over $1 million was selected and asked for their annual income and level of education. The ANOVA comparing the average income among three levels of education rejected the null hypothesis. The Mean Square Error (MSE) was
243.7. 
 The following table summarized the results:  
 When comparing the mean salaries to test for differences between treatment means, the t statistic is based on:

Accepted Answer

A)  The treatment degrees of freedom. 
B)  The total degrees of freedom. 
C)  The error degrees of freedom 
D)  The ratio of treatment and error degrees of freedom 
A)  The treatment degrees of freedom. 
B)  The total degrees of freedom. 
C)  The error degrees of freedom 
D)  The ratio of treatment and error degrees of freedom

Question 17

Given the following Analysis of Variance table for three treatments each with six observations.   What is the mean square for treatments?

Accepted Answer

A)  71.2 
B)  71.4 
C)  558 
D)  534 
E)  None of these statements are true 
A)  71.2 
B)  71.4 
C)  558 
D)  534 
E)  None of these statements are true

Question 18

The components of an ANOVA table include:

Accepted Answer

A)  Sum of squares total. 
B)  Mean Squares. 
C)  Degrees of freedom. 
D)  All of these components are part of an ANOVA table. 
A)  Sum of squares total. 
B)  Mean Squares. 
C)  Degrees of freedom. 
D)  All of these components are part of an ANOVA table.

Question 19

A manufacturer of automobile transmissions uses three different processes. The management ordered a study of the production costs to see if there is a difference among the three processes. A summary of the findings is shown below.   What are the total degrees of freedom?

Accepted Answer

A)  27 
B)  28 
C)  29 
D)  30 
E)  None of these statements are true 
A)  27 
B)  28 
C)  29 
D)  30 
E)  None of these statements are true

Question 20

A manufacturer of automobile transmissions uses three different processes. The management ordered a study of the production costs to see if there is a difference among the three processes. A summary of the findings is shown below.   What are the degrees of freedom for the numerator of the F ratio?

Accepted Answer

A)  2 
B)  3 
C)  10 
D)  27 
E)  None of these statements are true 
A)  2 
B)  3 
C)  10 
D)  27 
E)  None of these statements are true

Given the following Analysis of Variance table for three treatments each with six observations. What are the degrees of freedom for the numerator and denominator?

i. To employ ANOVA, the populations should have approximately equal standard deviations. ii. To employ ANOVA, the populations being studied must be approximately normally distributed. iii. The least number of sources of variation in ANOVA is two.

Two accounting professors decided to compare the variation of their grading procedures. To accomplish this they each graded the same 10 exams with the following results: What are the degrees of freedom for the denominator of the F ratio?

What distribution does the F distribution approach as the sample size increases?

i. If the computed value of F is 4.01 and the critical value is 2.67, we would conclude that all the population means are equal.F5 Ii) Rejecting the null hypothesis in ANOVA indicates that the population means are equal. Iii) The null hypothesis for an ANOVA is μ1 - μ2 ≠ μ3

ii. The calculated F value must be equal to or greater than one (1) iii. The shape of the F distribution is symmetrical. i. The test statistic used in ANOVA is t

i. The F distribution is positively skewed and its values may range from 0 to plus infinity. ii. The F distribution's curve is positively skewed Iii) Like Student's t distribution, a change in the degrees of freedom causes a change in the shape of the F distribution.

An F statistic is:

In ANOVA analysis, when the null hypothesis is rejected, we can find which means are different by:

A manufacturer of automobile transmissions uses three different processes. The management ordered a study of the production costs to see if there is a difference among the three processes. A summary of the findings is shown below. What is the mean square for error?

Which of the following is NOT a characteristic of the F distribution?

Given the following Analysis of Variance table for three treatments each with six observations. What is the mean square for treatments?

The components of an ANOVA table include:

A manufacturer of automobile transmissions uses three different processes. The management ordered a study of the production costs to see if there is a difference among the three processes. A summary of the findings is shown below. What are the total degrees of freedom?

A manufacturer of automobile transmissions uses three different processes. The management ordered a study of the production costs to see if there is a difference among the three processes. A summary of the findings is shown below. What are the degrees of freedom for the numerator of the F ratio?

What Is Statistics

Describing Data: Frequency Distributions and Graphic Presentation

Describing Data: Numerical Measures

A Survey of Probability Concepts

Discrete Probability Distributions

The Normal Probability Distribution

Sampling Methods and the Central Limit Theorem

Estimation and Confidence Intervals

One-Sample Tests of a Hypothesis

Two-Sample Tests of Hypothesis

Linear Regression and Correlation

Multiple Regression and Correlation Analysis

Chi-Square Applications for Nominal Data

Index Numbers

Time Series and Forecasting

An Introduction to Decision Theory

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Exam 11: Analysis of Variance

Given the following Analysis of Variance table for three treatments each with six observations. What are the degrees of freedom for the numerator and denominator?

i. To employ ANOVA, the populations should have approximately equal standard deviations. ii. To employ ANOVA, the populations being studied must be approximately normally distributed. iii. The least number of sources of variation in ANOVA is two.

Two accounting professors decided to compare the variation of their grading procedures. To accomplish this they each graded the same 10 exams with the following results: What are the degrees of freedom for the denominator of the F ratio?

What distribution does the F distribution approach as the sample size increases?

i. If the computed value of F is 4.01 and the critical value is 2.67, we would conclude that all the population means are equal.F5 Ii) Rejecting the null hypothesis in ANOVA indicates that the population means are equal. Iii) The null hypothesis for an ANOVA is μ1 - μ2 ≠ μ3

ii. The calculated F value must be equal to or greater than one (1) iii. The shape of the F distribution is symmetrical. i. The test statistic used in ANOVA is t

i. The F distribution is positively skewed and its values may range from 0 to plus infinity. ii. The F distribution's curve is positively skewed Iii) Like Student's t distribution, a change in the degrees of freedom causes a change in the shape of the F distribution.

An F statistic is:

In ANOVA analysis, when the null hypothesis is rejected, we can find which means are different by:

A manufacturer of automobile transmissions uses three different processes. The management ordered a study of the production costs to see if there is a difference among the three processes. A summary of the findings is shown below. What is the mean square for error?

Which of the following is NOT a characteristic of the F distribution?

Given the following Analysis of Variance table for three treatments each with six observations. What is the mean square for treatments?

The components of an ANOVA table include:

A manufacturer of automobile transmissions uses three different processes. The management ordered a study of the production costs to see if there is a difference among the three processes. A summary of the findings is shown below. What are the total degrees of freedom?

A manufacturer of automobile transmissions uses three different processes. The management ordered a study of the production costs to see if there is a difference among the three processes. A summary of the findings is shown below. What are the degrees of freedom for the numerator of the F ratio?

What Is Statistics

Describing Data: Frequency Distributions and Graphic Presentation

Describing Data: Numerical Measures

A Survey of Probability Concepts

Discrete Probability Distributions

The Normal Probability Distribution

Sampling Methods and the Central Limit Theorem

Estimation and Confidence Intervals

One-Sample Tests of a Hypothesis

Two-Sample Tests of Hypothesis

Linear Regression and Correlation

Multiple Regression and Correlation Analysis

Chi-Square Applications for Nominal Data

Index Numbers

Time Series and Forecasting

An Introduction to Decision Theory

Filters