Question 1

Three different advertisements were used to sell a popular toy. In computing F, how many degrees of freedom are there in the numerator?

Accepted Answer

A)  0 
B)  1 
C)  2 
D)  3 
E)  None of these statements are true

Question 2

Analysis of variance is used to:

Accepted Answer

A)  compare nominal data. 
B)  compute t test. 
C)  compare population proportion. 
D)  simultaneously compare several population means. 
E)  None of these statements are true.

Question 3

i. If we want to determine which treatment means differ, one method is confidence intervals. 
ii. If the confidence interval includes 0, there is a difference in the pair of treatment means.
Iii) If both end points of a confidence interval are of the same sign, it indicates that the treatment means are not different.

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)  (i) is a correct statement but not (ii) or (iii). 
E)  All statements are false

Question 4

Given the following Analysis of Variance table for three treatments each with six observations.  What is the critical value of F at the 5% level of significance?

Accepted Answer

A)  3.29 
B)  3.68 
C)  3.59 
D)  3.20 
E)  None of these statements are true

Question 5

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 sum of squares for the treatment?

Accepted Answer

A)  67.80 
B)  58.07 
C)  149.34 
D)  23.47 
E)  None of these statements are true

Question 6

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. Is there a difference in the performance between the four grades of gas?  If you were to use Excel to assist in your solution to this problem, which test would you use?

Accepted Answer

A)  ANOVA: Single Factor 
B)  ANOVA: Two-Factor with Replication 
C)  ANOVA: Two-Factor without Replication 
D)  F-Test Two Sample for Variances 
E)  t-Test: Paired Two Sample for Means

Question 7

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 sum of squares of the error?

Accepted Answer

A)  67.80 
B)  58.07 
C)  149.34 
D)  23.47 
E)  None of these statements are true

Question 8

When comparing the mean annual incomes for executives with a High School education or less and Undergraduate Degree, the 95% confidence interval shows an interval of 11.7 to 42.7 for the difference. This result indicates that:

Accepted Answer

A)  There is no significant difference between the two incomes. 
B)  The interval contains a difference of zero. 
C)  Executives with and Undergraduate Degree earn significantly more than executives with a High School education or less. 
D)  Executives with and Undergraduate Degree earn significantly less than executives with a High School education or less.

Question 9

Suppose we select 20 observations from each of five treatments. The appropriate degrees of freedom are:

Accepted Answer

A)  4 and 15 
B)  5 and 20 
C)  4 and 19 
D)  4 and 20 
E)  Not of these are correct.

Question 10

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 is H0?

Accepted Answer

A)  ?21= ? 22 
B)  ?2 1 ? ? 22 
C)  µ1 = µ2 
D)  µ1 ? µ2 
E)  None of these statements are true

Question 11

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:  The calculated F ratio is:

Accepted Answer

A)  3.484 
B)  1.867 
C)  3.18 
D)  5.35 
E)  None of these statements are true

Question 12

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) Not rejecting the null hypothesis in ANOVA indicates that the population means are equal.

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

Question 13

If the confidence interval for the difference in treatment means contains zero, then:

Accepted Answer

A)  We can conclude that there is a significant difference in the selected treatment means. 
B)  We can conclude that there is no significant difference in the selected treatment means. 
C)  We can conclude that the selected treatment means both equal zero. 
D)  We can conclude that at least one of the selected treatment means equals zero.

Question 14

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 is H1?

Accepted Answer

A)  ?2 1 = ? 22 
B)  ?21 ? ? 22 
C)  µ1 = µ2 
D)  µ1 ? µ2 
E)  None of these statements are true

Question 15

An electronics company wants to compare the quality of their cell phones to the cell phones from three competitors. They sample 10 phones from each company and count the number of defects for each phone. Using Excel, what test is used to compare the average number of defects?

Accepted Answer

A)  ANOVA: Single Factor 
B)  ANOVA: Two-Factor with Replication 
C)  ANOVA: Two-Factor without Replication 
D)  F-Test Two Sample for Variances 
E)  t-Test: Paired Two Sample for Means

Question 16

i. The statistical technique used to test the equality of three or more population means is called analysis of variance (ANOVA)
ii. To employ ANOVA, the populations should have approximately equal standard deviations. 
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

Question 17

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. A technique that is efficient when simultaneously comparing more than two population means is known as analysis of variance (ANOVA)

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

Question 18

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

Accepted Answer

A)  Reject H0--there is a difference in treatments 
B)  Fail to reject H0--there is a difference in treatments 
C)  Reject H0--there is a difference in errors 
D)  Fail to reject H0--there is a difference in errors 
E)  None of these statements are true

Question 19

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 symmetrical. 
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

Question 20

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:  Using Excel to assist in the comparison, what test would be used?

Accepted Answer

A)  ANOVA: Single Factor 
B)  ANOVA: Two-Factor with Replication 
C)  F-Test Two Sample for Variances 
D)  t-Test: Paired Two Sample for Means 
E)  We need the raw data in order to use the F-test in Excel

Exam 11: Analysis of Variance

Three different advertisements were used to sell a popular toy. In computing F, how many degrees of freedom are there in the numerator?

Analysis of variance is used to:

Given the following Analysis of Variance table for three treatments each with six observations. What is the critical value of F at the 5% level of significance?

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 sum of squares for the treatment?

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 sum of squares of the error?

When comparing the mean annual incomes for executives with a High School education or less and Undergraduate Degree, the 95% confidence interval shows an interval of 11.7 to 42.7 for the difference. This result indicates that:

Suppose we select 20 observations from each of five treatments. The appropriate degrees of freedom are:

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 is H0?

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: The calculated F ratio is:

If the confidence interval for the difference in treatment means contains zero, then:

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 is H1?

An electronics company wants to compare the quality of their cell phones to the cell phones from three competitors. They sample 10 phones from each company and count the number of defects for each phone. Using Excel, what test is used to compare the average number of defects?

i. The statistical technique used to test the equality of three or more population means is called analysis of variance (ANOVA) ii. To employ ANOVA, the populations should have approximately equal standard deviations. iii. The least number of sources of variation in ANOVA is two.

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

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 symmetrical. iii. Like Student's t distribution, a change in the degrees of freedom causes a change in the shape of the F distribution.

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: Using Excel to assist in the comparison, what test would be used?