Deck 11: Analysis of Variance

Question 1

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.

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

Answer 1

(i), (ii) and (iii) are all correct statements

Question 2

i. One characteristic of the F distribution is that computed F can only range between -1 and +1.
ii. 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.
Iii) The F distribution's curve is positively skewed.

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

Answer 2

(ii) and (iii) are correct statements but not (i).

Question 3

i. One characteristic of the F distribution is that computed F can only range between -1 and +1.
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.

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

Answer 3

(ii) and (iii) are correct statements but not (i).

Question 4

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.

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 5

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 numerator of the F ratio?

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

Question 6

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?

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

Question 7

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)

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 8

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

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 9

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.

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

Which of the following are characteristics of the F distribution?

A) There is a "family" of F distributions
B) The F distribution is continuous.
C) The F distribution cannot be negative.
D) All of the above are characteristics of the F distribution.

Question 11

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

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

Question 12

An F statistic is:

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

Question 13

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

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 14

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.

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 15

Which statement is correct about the F distribution?

A) Cannot be negative
B) Cannot be positive
C) Is the same as the t distribution
D) Is the same as the z distribution
E) None of these is correct

Question 16

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?

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

Question 17

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.

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

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?

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

Question 19

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?

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

Question 20

ii. The calculated F value must be equal to or greater than zero (0) iii. The shape of the F distribution is symmetrical i. The test statistic used in ANOVA is F

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 21

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?

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

Question 22

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.

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 23

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 the critical value of F at the 0.01 level of significance?

A) 5.85
B) 5.35
C) 6.51
D) 4.03
E) None of these statements are true

Question 24

In an effort to determine the most effective way to teach safety principles to a group of employees, four different methods were tried. Some employees were given programmed instruction booklets and worked through the course at their own pace. Other employees attended lectures. A third group watched a television presentation, and a fourth group was divided into small discussion groups. A high of 10 was possible. Samples of five tests were selected from each group. The test grade results were: At the 0.01 level, what is the critical value?

A) 1.00
B) 1.96
C) 3.24
D) 5.29
E) None of these statements are true

Question 25

Which one of the following is not assumed in the use of ANOVA?

A) The populations follow a normal distribution.
B) The samples have equal standard deviations.
C) The populations have equal standard deviations.
D) The populations are independent.

Question 26

i. The rejection region for analysis of variance is in the upper tail of the F distribution ii. In ANOVA, k -1 degrees of freedom are associated with the numerator of the F ratio.
Iii) In ANOVA, k-1 degrees of freedom are associated with the denominator of the F ratio.

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 27

i. To employ ANOVA, the populations being studied must be approximately normally distributed.
ii. A technique that is efficient when simultaneously comparing more than two population means is known as analysis of variance (ANOVA)
iii. The least number of sources of variation in ANOVA is two.

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 28

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:

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

Question 29

A large department store examined a sample of the 18 credit card sales and recorded the amounts charged for each of three types of credit cards: MasterCard, Visa and American Express. Six
MasterCard sales, seven Visa and five American Express sales were recorded. The store used
ANOVA to test if the mean sales for each credit card were equal. What are the degrees of freedom for the F statistic?

A) 18 in the numerator, 3 in the denominator
B) 3 in the numerator, 18 in the denominator
C) 2 in the numerator, 15 in the denominator
D) 0 in the numerator, 15 in the denominator
E) None of these statements are true

Question 30

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.

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 31

i. To employ ANOVA, the populations need not have equal standard deviations.
ii. To employ ANOVA, the populations being studied need not be normally distributed.
Iii) A technique that is efficient when simultaneously comparing more than two population means is known as analysis of deviation.

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 32

Analysis of variance is used to:

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 33

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 the critical value of F at the 0.05 level of significance?

A) 5.85
B) 5.35
C) 3.18
D) 4.03
E) None of these statements are true

Question 34

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)

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 35

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

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

Question 36

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 5% level of significance, what is the decision?

A) Reject the null hypothesis and conclude the variance is different.
B) Fail to reject the null hypothesis and conclude no significant difference in the variance.
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.
E) None of these statements are true

Question 37

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. To employ ANOVA, the populations being studied must be approximately normally distributed.

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 38

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

A) Too many degrees of freedom
B) No difference between the population means
C) A difference between at least one pair of population means
D) None of these statements are true

Question 39

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?

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.
E) None of these statements are true

Question 40

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.

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 41

A preliminary study of hourly wages paid to unskilled employees in three metropolitan areas was conducted. Seven employees were included from Area A, 9 from Area B and 12 from Area

A) Mean hourly wages of unskilled employees all areas are equal
B) Mean hourly wages in at least 2 metropolitan areas are different
C) More degrees of freedom are needed
C) The test statistic was computed to be 4.91. What can we conclude at the 0.05 level?
D) None of these is correct

Question 42

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. If ANOVA is used to compare the average number of defects, the treatments would be defined as:

A) the number of cell phones sampled.
B) the average number of defects.
C) The total number of phones
D) The four companies.

Question 43

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) The null hypothesis for an ANOVA is µ1 - µ2 = µ3

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 44

i. For an ANOVA test, rejection of the null hypothesis does not identify which populations differ significantly.
Ii) Not rejecting the null hypothesis in ANOVA indicates that the population means are equal.
iii. The null hypothesis for an ANOVA is µ1 - µ2 = µ3

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 45

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

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 46

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.
Ii) Not rejecting the null hypothesis in ANOVA indicates that the population means are equal.
iii. The null hypothesis for an ANOVA is µ1 - µ2 = µ3

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 47

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

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 48

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?

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

Question 49

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

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

Question 50

Several employees have submitted different methods of assembling a product. Sample data for each method are: How many treatments are there?

A) 3
B) 4
C) 12
D) 0
E) None of these statements are true

Question 51

In an effort to determine the most effective way to teach safety principles to a group of employees, four different methods were tried. Some employees were given programmed instruction booklets and worked through the course at their own pace. Other employees attended lectures. A third group watched a television presentation, and a fourth group was divided into small discussion groups. A high of 10 was possible. Samples of five tests were selected from each group. The test grade results were: Using Excel to assist in determining if all methods generate the same results, what test would be used?

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 52

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 is µ1 - µ2 = µ3

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 53

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.

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 54

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 critical value of F at the 1% level of significance?

A) 99.46
B) 5.49
C) 5.39
D) 4.61
E) None of these statements are true

Question 55

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?

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 56

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.

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 57

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

Question 58

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 critical value of F at the 5% level of significance?

A) 19.45
B) 3.00
C) 3.35
D) 3.39
E) None of these statements are true

Question 59

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?

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 60

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?

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

Question 61

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 treatments?

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

Question 62

i. If we want to determine which treatment means differ, one method is confidence intervals.
ii. If the confidence interval includes 0, there is no 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.

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 63

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

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 64

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

Question 65

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?

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

Question 66

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

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 67

Based on the comparison between the mean annual incomes for executives with Undergraduate and Master's Degree or more,

A) A confidence interval shows that the mean annual incomes are not significantly different.
B) The ANOVA results show that the mean annual incomes are significantly different.
C) A confidence interval shows that the mean annual incomes are significantly different.
D) The ANOVA results show that the mean annual incomes are not significantly different.

Question 68

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?

A) 3
B) 10
C) 27
D) 30
E) None of these statements are true

Question 69

The components of an ANOVA table include:

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

Question 70

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.

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 71

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. There are 2 degrees of freedom for the numerator.
Ii) There are 12 degrees of freedom for the denominator.
Iii) If the sum of squares for the brands is 0.07, the mean square for brands is 0.035.

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 72

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 calculated F?

A) 0.086
B) 1.168
C) 11.56
D) 13.50
E) None of these statements are true

Question 73

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:

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 74

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) There are 2 degrees of freedom for the numerator.
Ii) There are 14 degrees of freedom for the denominator.
Iii) If the sum of squares for the brands is 0.07, the mean square for brands is 0.035.

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 75

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?

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

Question 76

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

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

Question 77

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:

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 78

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

Question 79

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:

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 80

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

A) 7.48
B) 7.84
C) 8.84
D) 8.48
E) None of these statements are true