Q1. 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:
Answer these questions.
What is H0?
A) σ21 = σ22
B) σ21 ≠σ22
C) μ1 = μ2
D) μ1 ≠ μ2
- What is H1?
- What are the degrees of freedom for the numerator of the F ratio?
- What are the degrees of freedom for the denominator of the F ratio?
- What is the critical value of F at the 0.01 level of significance?
The calculated F ratio is?
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.
Q2. Given the following Analysis of Variance table for three treatments each with six observations.
Source Sum of squares df Mean square
Treatments 1116
Errors 1068
Total 2184
Answer these questions.
What are the degrees of freedom for the numerator and denominator?
What is the critical value of F at the 5% level of significance?
What is the mean square for treatments?
What is the computed value of F?
A) 7.48
B) 7.84
C) 8.84
D) 8.48
What is the decision?
A) Reject H0 -- there is a difference in treatment means
B) Fail to reject H0 -- there is a difference in treatment means
C) Reject H0 -- there is a difference in errors
D) Fail to reject H0 -- there is a difference in errors
Q3. What is the null hypothesis for an ANOVA?
Q4. In ANOVA, when we do not reject the null hypothesis, what inference do we make about the population means?
Q5. ANOVA requires that the populations should be ________, __________, and ___________.
Q6. What is the shape of the F distribution?
Q7. 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 Discover. Six MasterCard sales, seven Visa and five Discover 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?
Q8. A bottle cap manufacture with four machines and three operators wants to see if variation in hourly production is due to the machines and/or the operators or an interaction effect of machine and operator. Each operator is assigned to each machine and the production of caps from 3 randomly selected hours is recorded. The analysis shows the following Analysis of Variance table.
|
Source
|
Sum of Squares
|
df
|
Mean Square
|
|
Machines
|
114
|
|
|
|
Operators
|
115
|
|
|
|
Interaction
|
100
|
|
|
|
Error
|
54
|
|
|
|
Total
|
383
|
|
|
Answer these questions.
What are the degrees of freedom for the machines, operators, interaction and error?
What is the critical value of F for the machine effect at the 1% level of significance?
What is the mean square for machines, operators, interaction and error?
What is the computed value of F for the machines?
What is the computed value of F for the operators?
Using a 1% significance level, what is the decision for the machines?
Q9. 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?
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
D) None of these is correct
Q10. 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 were 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.