Inference on Linear Regression
1.
Name___________________________
Is there a linear relationship between the amount of crude oil (in thousands of barrels per day)
produced by the U. S. and the amounts of crude oil (in thousands of barrels per day) imported by the
U.S. for seven years. ( = 0.05)
Produced
Imported
5801
11871
5746
11530
5681
12264
5419
13145
5178
13714
5102
13707
5064
13468
2. Is there a linear relationship between the number of initial public offerings of stock issued in a recent
12-year period and the total proceeds of these offerings (in millions of U.S. Dollars). Use a 1% level of
significance.
# Issues
Proceeds
318
34614
486
64927
382
65088
79
34241
70
22136
67
10068
184
32269
168
28593
162
30648
162
35762
21
22762
43
13307
3. Is there a linear relationship between the caloric contents and the sugar contents (in grams) of 11 highfiber breakfast cereals.
Calories
Sugar
140
6
200
9
160
6
170
9
170
10
190
17
190
13
210
18
190
19
170
10
160
10
4. Use a 90% confidence interval to estimate the average change in test scores for each additional hours
spent studying.
# hours
Test Score
0
40
1
41
2
51
4
48
4
64
5
69
5
73
5
75
6
68
6
93
7
84
7
90
8
95
5. Use a 99% confidence interval to estimate the average change in the number of hours and infant sleeps
in a day for each additional year of age for ten infants.
Age
#Hours
0.1
14.9
0.2
14.5
0.4
13.9
0.7
14.1
0.6
13.9
0.9
13.7
0.1
14.3
0.2
13.9
0.4
14
0.9
14.1
6. The article “Effect of Temperature on the pH of Skim Milk” reported on a study involving x =
temperature (ºC) under specified experimental conditions and y = milk pH. Do these data strongly
suggest that there is a negative linear relationship between temperature and pH? Use a 0.01 level of
significance.
x
y
4
6.85
4
6.79
24
6.63
24
6.65
25
6.72
38
6.62
38
6.57
40
6.52
45
6.5
50
6.48
55
6.42
56
6.41
60
6.38
67
6.34
70
6.32
78
6.34
7. Construct a 90% prediction interval for shopping center sales when the total square footage of shopping
centers.
Footage
Sales
5
893.8
5.1
933.9
5.2
980
5.3
5.5
5.6
5.7
5.8
5.9
6
6.1
1032.4 1105.3 1181.1 1221.7 1277.2 1339.2 1432.6 1530.4
8. In anthropological studies, an important characteristic of fossils is cranial capacity. Frequently, skulls
are at least partially decomposed, so it is necessary to use other characteristics to obtain information
about capacity. One such measure that has been used is the length of the lambda-opisthion chord.
Suppose that from previous evidence, anthropologists had believed that for each 1-mm increase in chord
length, cranial capacity would be expected to increase by 20cm3. Do these new experimental data
strongly contradict prior belief? (Use  = 0.05)
Chord, mm
Capacity, cm
78
850
75
775
78
750
81
975
84
915
86
1015
87
1030