1. When variables are used as the basis for a contin- gency table, what scale of measurement must they represent?
2. Differentiate between simple tabulation and cross- tabulation, and give a real or hypothetical example of each.
Note: Exercises 2.48-2.50 can be done by hand, but computer statistical software is preferable, if available.
3. The 30 vehicles operated by a taxi service have been listed according to their engine (1 5 diesel, 2 5 gasoline), transmission (1 5 manual, 2 5 automatic), and whether they have air conditioning (1 5 no air conditioning, 2 5 air conditioning). These characteristics, along with the miles per gallon (mpg) achieved by each vehicle during the past month, are listed here. The data are also provided in file XR02048.
a. Construct a simple tabulation in which the counts are according to the type of engine.
b. Construct a cross-tabulation describing the fleet, using type of engine and type of transmission as the categorization variables.
c. Construct a display showing the average mpg accord- ing to type of engine and type of transmission. Do the categorization variables seem to be related to mpg? If so, how?
|
Engine
|
Trans
|
AC
|
mpg
|
Engine
|
Trans
|
AC
|
mpg
|
|
1
|
1
|
1
|
36.4
|
1
|
1
|
2
|
38.6
|
|
1
|
1
|
1
|
37.7
|
1
|
1
|
2
|
34.8
|
|
1
|
1
|
1
|
38.2
|
1
|
2
|
2
|
30.8
|
|
1
|
1
|
1
|
41.8
|
1
|
2
|
2
|
26.4
|
|
1
|
1
|
1
|
34.8
|
1
|
2
|
2
|
31.6
|
|
1
|
2
|
1
|
35.4
|
1
|
2
|
2
|
28.3
|
|
1
|
2
|
1
|
31.3
|
1
|
2
|
2
|
29.5
|
|
1
|
2
|
1
|
32.2
|
2
|
1
|
2
|
23.0
|
|
2
|
1
|
1
|
26.2
|
2
|
1
|
2
|
21.5
|
|
2
|
1
|
1
|
25.5
|
2
|
1
|
2
|
19.5
|
|
2
|
1
|
1
|
27.7
|
2
|
2
|
2
|
18.3
|
|
2
|
2
|
1
|
22.0
|
2
|
2
|
2
|
19.1
|
|
2
|
2
|
1
|
23.3
|
2
|
2
|
2
|
20.8
|
|
1
|
1
|
2
|
34.8
|
2
|
2
|
2
|
21.8
|
|
1
|
1
|
2
|
34.0
|
2
|
2
|
2
|
18.4
|