Question 1

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 denominator?

Accepted Answer

A)  3 
B)  10 
C)  27 
D)  30

Question 2

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. The F distribution's curve is positively skewed.
iii. Unlike Student's t distribution, there is only one 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)  (i), (ii), and (iii) are all false statements.

Question 3

i. One characteristic of the F distribution is that F cannot be negative. ii. One characteristic of the F distribution is that computed F can only range between -1 and +1.
iii. The shape of the F distribution is positively skewed.

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)  (i), (ii), and (iii) are all false statements.

Question 4

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:  At the 1% level of significance, what is the decision?

Accepted Answer

A)  Reject the null hypothesis and conclude the variance is different. 
B)  Fail to reject the null hypothesis and conclude the variance is different. 
C)  Reject the null hypothesis and conclude the variance is the same. 
D)  Fail to reject the null hypothesis and conclude the variance is the same.

Question 5

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. There is one, unique F distribution for a F-statistic with 29 degrees of freedom in the numerator and 28 degrees of freedom in the denominator.

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)  (i), (ii), and (iii) are all false statements.

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?  Using the printout given by Excel, what to you conclude?

Accepted Answer

A)  Since the calculated F-value is smaller than the F-critical value, there is a difference in the performance of these four grades of gas. 
B)  Since the calculated F-value is smaller than the F-critical value, there is no significant difference in the performance of these four grades of gas. 
C)  Since the calculated F-value is larger than the F-critical value, there is no significant difference in the performance in the four grades of gas. 
D)  There is no significant difference in the performance of these four grades of gas as indicated by the calculated F-value being smaller than the F-critical value, and the P-value is large at 0.899, there is an 89% chance of these results happening.

Question 7

The components of an ANOVA table include:

Accepted Answer

A)  sum of squares total. 
B)  mean squares. 
C)  degrees of freedom. 
D)  sum of squares total, mean squares and degrees of freedom are all components of an ANOVA table.

Question 8

i. For the population means, the alternate hypothesis used in the analysis of variance test states thatµ1=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)  (i), (ii), and (iii) are all false statements.

Question 9

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 need not have equal standard deviations.
iii. To employ ANOVA, the populations being studied must be approximately normally distributed.

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)  (i), (ii), and (iii) are all false statements.

Question 10

In a study of low tar cigarettes, five cigarettes from each of three brands were tested to see if the mean amount of tar per cigarette differs among the brands. i. The F critical value for alpha = 0.05 is 3.89.
ii. If F calculated is 4.75, the decision if $\alpha$ = 0.05 is to reject H0.
iii. If the calculated F is 4.74, the decision if $\alpha$ = 0.01 is to not reject H0.

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)  (i), (ii), and (iii) are all false statements.

Question 11

i. The alternate hypothesis for ANOVA states that not all the means are equal. ii. Not rejecting the null hypothesis in ANOVA indicates that the population means are equal.
iii. The null hypothesis for an ANOVA isµ1-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)  (i), (ii), and (iii) are all false statements.

Question 12

If an ANOVA test is conducted and the null hypothesis is rejected, what does this indicate?

Accepted Answer

A)  Too many degrees of freedom. 
B)  No difference between the population means. 
C)  A difference between at least one pair of population means.

Question 13

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 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 an Undergraduate Degree earn significantly more than executives with a High School education or less. 
D)  executives with an Undergraduate Degree earn significantly less than executives with a High School education or less.

Question 14

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)  (i), (ii), and (iii) are all false statements.

Question 15

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

Question 16

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)  (i), (ii), and (iii) are all false statements.

Question 17

i. If the computed value of F is 0.99 and the critical value is 3.89, we would not reject the null hypothesis. ii. When comparing two population variances we use the F distribution.
iii. A one way ANOVA is use to compare several treatment means.

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)  (i), (ii), and (iii) are all false statements.

Question 18

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

Question 19

Using the Excel printout below to compare the mean annual incomes for executives with Undergraduate and Master's Degree or more, the following statements can be made:

Accepted Answer

A)  since the calculated F-value is smaller than the F-critical value, there is no significant difference in the incomes of these two groups. 
B)  since the calculated F-value is smaller than the F-critical value, there is a significant difference in the incomes of these two groups. 
C)  since the P-value is 0.62, there is a 62% chance of these results happening when there is no significant difference in the incomes of these two groups. 
D)  since the calculated F-value is larger than the F-critical value, and the P-value is so small, there is strong evidence to suggest that both groups with different levels of education have the same incomes. 
E)  since the calculated F-value is smaller than the F-critical value, there is no significant difference in the incomes of these two groups; also, since the P-value is 0.62, there is a 62% chance of these results happening when there is no significant difference in the incomes of these two groups.

Question 20

In a study of low tar cigarettes, five cigarettes from each of three brands were tested to see if the mean amount of tar per cigarette differs among the brands. i. The F critical value for alpha = 0.05 is 3.74.
ii. If F calculated is 4.75, the decision if $\alpha$ = 0.05 is to reject H0.
iii. If the calculated F is 4.74, the decision if $\alpha$ = 0.01 is to reject H0.

Accepted Answer

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

Exam 11: Analysis of Variance

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 denominator?

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. The F distribution's curve is positively skewed. iii. Unlike Student's t distribution, there is only one F distribution.

i. One characteristic of the F distribution is that F cannot be negative. ii. One characteristic of the F distribution is that computed F can only range between -1 and +1. iii. The shape of the F distribution is positively skewed.

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: At the 1% level of significance, 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 skewed. iii. There is one, unique F distribution for a F-statistic with 29 degrees of freedom in the numerator and 28 degrees of freedom in the denominator.

The components of an ANOVA table include:

i. The alternate hypothesis for ANOVA states that not all the means are equal. ii. Not rejecting the null hypothesis in ANOVA indicates that the population means are equal. iii. The null hypothesis for an ANOVA isµ₁-µ₂=µ₃.

If an ANOVA test is conducted and the null hypothesis is rejected, what does this indicate?

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?

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.

i. If the computed value of F is 0.99 and the critical value is 3.89, we would not reject the null hypothesis. ii. When comparing two population variances we use the F distribution. iii. A one way ANOVA is use to compare several treatment means.

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?

Using the Excel printout below to compare the mean annual incomes for executives with Undergraduate and Master's Degree or more, the following statements can be made:

Exam 11: Analysis of Variance

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 denominator?

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. The F distribution's curve is positively skewed. iii. Unlike Student's t distribution, there is only one F distribution.

i. One characteristic of the F distribution is that F cannot be negative. ii. One characteristic of the F distribution is that computed F can only range between -1 and +1. iii. The shape of the F distribution is positively skewed.

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: At the 1% level of significance, 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 skewed. iii. There is one, unique F distribution for a F-statistic with 29 degrees of freedom in the numerator and 28 degrees of freedom in the denominator.

The components of an ANOVA table include:

i. The alternate hypothesis for ANOVA states that not all the means are equal. ii. Not rejecting the null hypothesis in ANOVA indicates that the population means are equal. iii. The null hypothesis for an ANOVA isµ1-µ2=µ3.

If an ANOVA test is conducted and the null hypothesis is rejected, what does this indicate?

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?

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.

i. If the computed value of F is 0.99 and the critical value is 3.89, we would not reject the null hypothesis. ii. When comparing two population variances we use the F distribution. iii. A one way ANOVA is use to compare several treatment means.

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?

Using the Excel printout below to compare the mean annual incomes for executives with Undergraduate and Master's Degree or more, the following statements can be made:

i. The alternate hypothesis for ANOVA states that not all the means are equal. ii. Not rejecting the null hypothesis in ANOVA indicates that the population means are equal. iii. The null hypothesis for an ANOVA isµ₁-µ₂=µ₃.