Question 1

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 C The test statistic was computed to be 4.91. What can we conclude at the 0.05 level?

Accepted Answer

The test statistic of 4.91 suggests that there is a significant difference in mean hourly wages among the areas at the 0.05 level, indicating that at least two areas have different mean wages.

Question 2

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:

Accepted Answer

The treatments in an ANOVA test refer to the different groups being compared, which in this case are the four companies.

Question 3

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

Accepted Answer

The answer of i. For the population means, the alternate...

Question 4

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

Accepted Answer

(i) and (ii) are true because rejecting the null hypothesis in ANOVA only indicates that there is a significant difference among the population means, but it does not identify which specific populations differ significantly. Not rejecting the null hypothesis indicates that there is no significant difference among the population means. (iii) is false because the null hypothesis for an ANOVA is that all population means are equal, not that µ1 - µ2 = µ3.

Question 5

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

Accepted Answer

The answer of Given the following Analysis of Variance table...

Question 6

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

Accepted Answer

The answer of i. If the computed value of F...

Question 7

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

The computed F value being greater than the critical value means we reject the null hypothesis, indicating not all population means are equal. Rejecting the null hypothesis in ANOVA suggests the means are not equal. The null hypothesis for ANOVA is that all population means are equal, not μ1 - μ2 ≠ μ3.

Question 8

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

The answer of A manufacturer of automobile transmissions uses three...

Question 9

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

Accepted Answer

The answer of Suppose we select 20 observations from each...

Question 10

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

Accepted Answer

The answer of Several employees have submitted different methods of...

Question 11

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?

Accepted Answer

The answer of In an effort to determine the most...

Question 12

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

Accepted Answer

The answer of i. The alternate hypothesis for ANOVA states...

Question 13

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

The alternate hypothesis in ANOVA states that not all population means are equal, not that they are equal. Rejection of the null hypothesis in ANOVA indicates that at least one population mean is different, but it does not specify which one. Not rejecting the null hypothesis suggests that there is no significant evidence to say the means are different, implying they are equal.

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

Accepted Answer

The answer of A manufacturer of automobile transmissions uses three...

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

ANOVA: Single Factor is the appropriate test for comparing the means of multiple groups. In this case, the one factor is the company, and there are four levels (the focal company and the three competitors).

Question 16

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

The alternate hypothesis in ANOVA states that at least one population mean is different, not that they are all equal. Rejection of the null hypothesis in ANOVA indicates that there is a difference, but it does not specify which means differ. If the computed F value is greater than the critical value, we reject the null hypothesis, meaning not all means are equal.

Question 17

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

The answer of A manufacturer of automobile transmissions uses three...

Question 18

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?

Accepted Answer

The answer of A manufacturer of automobile transmissions uses three...

Question 19

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

The answer of Suppose that an automobile manufacturer designed a...

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

The answer of A manufacturer of automobile transmissions uses three...

Quiz 11: Analysis of Variance

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 C The test statistic was computed to be 4.91. What can we conclude at the 0.05 level?

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:

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

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

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

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

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 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?

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

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

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 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?

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 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 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 are the degrees of freedom for the numerator of the F ratio?