1.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 an 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.6 in the numerator, 15 in the denominator
The answer is C because there are 3 Treatment (categories) so F(k-1,n-k) should where k=3 and n=18 so F(3-1,18-3) critical must be found.
2.The college of business was interested in comparing the attendance for three different class times for a business statistics class. The data follow.
What is the treatment variable?
A.Day.
B.Class time.
C.Tuesday.
D.8:00 am class.
Answer should be classtime. There are 3 categories (treatments).
3.A manufacturer of automobile transmissions uses two different processes. Management ordered a study of the production costs to see if there is a difference among the two 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.4.41
D.4.38
The total sample is 10 + 10 = 20, there are 2 treatments so k=2. Therefore F(2-1,20-2)=F(1,18)=4.41.
4.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
MST=1116/2=558. MSE=1068/(3x6-3)=1068/15=71.12 F statistic=MST/MSE=558/71.12=7.83
5.Given the following Analysis of Variance table for three treatments each with six observations.
What is the decision regarding the null hypothesis?
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.
Reject if F statistic > F critical->F(2,15), that is 7.83 >3.68.
6.Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results:
What is H0?
A.Option A
Note that null always has some kind of equality.
7.What is H1?
B.Option B
Can be derived once the null is set.
8.What are the degrees of freedom for the numerator of the F ratio?
A.8
B.9
C.10
D.18
Since the exams are graded both forthe same number of students n1= n2= 10.
IS THERE A WAY OF CALCULATING THE SST (SUM OF SQUARES OF TREATMENTS) WITHOUT FIRST FINDING THE TOTAL AND THAN FINDING THE ERROR SUM OF SQUARES AND THAN SUBTRACTING THE SECOND FROM THE FIRST ?
YES, and here is the table (In Excel).
Treatment1 / Treatment2 / Treatment3 / Treatment4MEAN / 87.25 / 78.2 / 72.86 / 69 / 75.64
COLMean-Grand Mean / 11.61 / 2.56 / -2.78 / -6.64
SQUARES / 134.7921 / 6.5536 / 7.7284 / 44.0896 / 193.1637
EACH MULTIPLIED BY NUMBER OF OBS IN THE COLUMN / 539.1684 / 32.768 / 54.0988 / 264.5376 / 890.6 / SST
NOTE THAT WHAT MAKES THE SST A BIG NUMBER IS THE DIFFERENCE OF THE COLUMN MEAN FROM THE GRAND MEAN. THAT IS IF THE DEVIATION OF THE EACH COLUMN MEAN FORM THE OVERALL MEAN IS GREATER, IT INCREASES THE CHANCES OF GETTING A BIG F STATISTIC SO AS TO REJECT THE NULL EASILY.