Problem 14.10 in Keller 5, p.495 - Single Factor (one-Way)
Analysis of Variance: Independent Samples
The IRS is looking for ways to improve the wording and
format of its tax return forms. Three
new forms have been developed recently.
To determine which, if any, are superior to the current form, 120
individuals were asked to participate in an experiment. Each of the three new forms and the
currently used form were filled out by 30 different people. The amount of time (in minutes) taken by
each person to compete the task was recorded and stored in columns 1 through 4
in file XR14-10.
a) What conclusions can be drawn from these data (use alpha
= .05)?
Answer: F=2.94 (p-value = .036), a difference
exists.
Problem 15.19 in Keller, p.608 - Single-Factor Analysis of
Variance: Randomized Blocks
In recent years, lack of confidence in the US Postal Service
has led many companies to send all of their correspondence by private
courier. A large company is in the
process of selecting one of 3 possible couriers to act as its sole delivery
method. To help in making the decision,
an experiment was performed whereby letters were sent using each of the 3
couriers 10 different times of the day to a delivery point across town. The number of minutes required for delivery
was recorded and listed below and store in file XR14-26. (columns 2-4 list the delivery times of
couriers 1, 2, and 3 and column 1 contains codes representing the time of day)
a) Can we conclude at the 5% significance level that there
are differences in delivery times among the 3 couriers?
b) Did we choose the correct design? Explain.
|
Time of day |
Courier1 |
Courier2 |
Courier3 |
|
9:00 |
75 |
63 |
62 |
|
9:30 |
82 |
80 |
67 |
|
10:00 |
74 |
61 |
60 |
|
10:30 |
59 |
55 |
53 |
|
11:00 |
60 |
63 |
51 |
|
11:30 |
63 |
61 |
57 |
|
12:00 |
69 |
68 |
62 |
|
12:30 |
63 |
69 |
73 |
|
1:00 |
59 |
58 |
63 |
|
1:30 |
64 |
58 |
65 |
|
2:00 |
71 |
72 |
70 |
|
2:30 |
75 |
70 |
61 |
How would the data look stacked?
|
Delivery (response) |
Courier (treatment) |
Time-day (block) |
|
75 |
1 |
1 |
|
82 |
1 |
2 |
|
74 |
1 |
3 |
|
59 |
1 |
4 |
|
60 |
1 |
5 |
|
63 |
1 |
6 |
|
69 |
1 |
7 |
|
63 |
1 |
8 |
|
59 |
1 |
9 |
|
64 |
1 |
10 |
|
71 |
1 |
11 |
|
75 |
1 |
12 |
|
63 |
2 |
1 |
|
80 |
2 |
2 |
|
61 |
2 |
3 |
|
55 |
2 |
4 |
|
63 |
2 |
5 |
|
61 |
2 |
6 |
|
68 |
2 |
7 |
|
69 |
2 |
8 |
|
58 |
2 |
9 |
|
58 |
2 |
10 |
|
72 |
2 |
11 |
|
70 |
2 |
12 |
|
62 |
3 |
1 |
|
67 |
3 |
2 |
|
60 |
3 |
3 |
|
53 |
3 |
4 |
|
51 |
3 |
5 |
|
57 |
3 |
6 |
|
62 |
3 |
7 |
|
73 |
3 |
8 |
|
63 |
3 |
9 |
|
65 |
3 |
10 |
|
70 |
3 |
11 |
|
61 |
3 |
12 |
We are given the following sum of squares:
SS(Total) = 1,849.6
SST = 204.2
SSB = 1,150.2
Answers:
a)
F = 4.54, p-value = .022, yes
b)
F = 4.65, p-value = .001, yes