Please place your completed assignment in the box marked for your tutorial group in the basement of BSB.
Analyse the following three data sets. Give appropriate graphs. For each case, state any assumptions you make and do what you can to test the assumptions. State your conclusions.
(a) The following data came from a study of a method for preparing pure alcohol from refinery streams. The independent variable x is volume hourly space velocity and the dependent variable y is the amount of conversion of isobutylene.
x:
1.0
1.0
2.0
4.0
4.0
4.0
6.0
y:
23.0
24.5
28.0
30.9
32.0
33.6
20.0
(b) A new psychological test is intended to measure (in arbitrary units) the emotive response to prescribed stimuli. The table below shows the scores on this test for 9 independent subjects. The test was applied before and after applying a treatment to desensitise them emotionally.
Subject:
1
2
3
4
5
6
7
8
9
Before:
23
189
17
26
29
280
24
22
19
After:
22
59
18
12
8
70
32
12
20
(c) The following table gives the airborne bacteria count (number of colonies/ft3) in a sample of 8 carpeted hospital rooms and an independent sample of 8 uncarpeted hospital rooms.
Carpeted:
11.8
8.2
7.1
13.0
10.8
10.1
14.6
14.0
Uncarpeted:
12.1
8.3
3.8
7.2
12.0
11.1
10.1
13.7
(a) Analyse the following data on the frequencies of audiogenic seizure in mice whose dams had received differing injection treatments during gestation. Suggest how you could improve the experimental design.
No response
Wild running
Clonic seizure
Tonic seizure
Treatment
Thienylalanine:
21
7
24
44
Solvent:
15
14
20
54
Unhandled:
47
13
28
32
(b) Combine categories to collapse the table above into a 2 X 2 table, where the rows are "Injected" and "Unhandled" and the columns are "No response" and "Some response". Compute a 99% confidence interval for the odds ratio and explain what it means.
Analyse the following data which give plasma epinephrine concentration for two different subjects under (1) isoflurane, (2) halothane and (3) cyclopropane anaesthesia. Present your results in a two-way ANOVA table. State your assumptions and your conclusions. Give a 95% confidence interval for s2. If this study is to be done over again, what changes to the design would you recommend?
Subject:
1
1
1
1
1
1
2
2
2
2
2
2
Anaesthesia:
1
1
2
2
3
3
1
1
2
2
3
3
Epinephrine:
0.28
0.36
0.30
0.88
1.07
1.53
0.51
0.32
0.39
0.39
1.35
0.49
The following data come from a paper "Cotton square damage by the plant bug, Lygus hesperus, and abcission rates," with x = age of a cotton plant (days) and y = percent damaged squares.
x:
9
12
12
15
18
18
21
21
27
30
30
33
y:
11
12
23
30
29
52
41
65
60
72
84
93
(a) Fit a straight line to the data by least squares. Plot the data and the fitted line on a graph. Can percent damaged squares be predicted as a linear function of age? Present your analysis in an ANOVA table with F-tests for non-linearity and for the slope of the regression line. State your assumptions and your conclusions.
(b) What percent damaged squares would you predict for ages 2, 20, and 40 days?
(c) Give a 95% confidence interval for s2 = Var(y | x).