03 Jun Question 1. A drug manufacturer conducted an experiment to e
Question
1. A drug manufacturer conducted an experiment to evaluate the eectiveness of a new anti-depressant drug. Ten depressed patients were given a test to
measure levels of depression before and after treatment with the new drug. The results (low scores indicate less depression) were as follows:
Before: 23 21 20 23 20 21 25 24 22 21
After: 11 10 14 16 20 23 15 10 11 10
(a) Do these data provide su cient evidence to indicate that the drug is eective in relieving depression? Perform a parametric test at level = :01 (list the hypotheses, compute the statistic and indicate the reasoning behind your decision).
(b) Brie indicate under what assumptions on the distribution of the scores y
is the parametric test in (a) valid?
(c) Suppose that you do not have much faith in the accuracy of the numbers for the scores, but believe that they are indicative only of the direction of change in level of depression (less or more depressed, or no change). Propose a test (state the hypotheses, suggest a suitable statistic, decision rule) and perform
the proposed test.
2. The data that Rutherford and Geiger (1910) examined to test whether radioactive decay of polonium ts the Poisson distribution is given below. They counted the number of scintillations in 1/8 min. intervals.
# of scintillations # of time intervals, ni 0
57
1
203
2
383
3
525
4
532
5
408
6
273
7
139
8
45
9
27
10
10
11
4
12
0
13
1
14
1
(a) State the hypothesis and test.
1
(b) The last three entries are small and the researchers combined them into one (tail of distribution) cell with n12 = 0 + 1 + 1 = 2 and performed the test correspondingly. Do so and compare with your answer to (a).
3. A survey of 320 families with 5 children provided the following data number of boys and girls 5 boys, 0 girls 4 boys, 1 girls 3 boys, 2 girls 2 boys, 3 girls number of families
18
56
110
88
1 boys, 4 girls 0 boys, 5 girls total
40
8
320
Is this consistent with the hypothesis that male and female births are equally probable?
4. The table below shows the numbers of students passed and failed by three instructors, X,Y and Z.
X Y Z Total
passed 50 47 56 153
failed 5 14 8
27
total 55 61 64 180
Test the hypothesis that the proportions of failures are the same for the three instructors.
5. Consider the following data for comparing the height of NYU students by gender.
Source of variation
SS
d.f. MSS
between
127:9 ?
?
within
?
14
?
total
539:4 48
Complete the table and test whether males and females among NYU students
dier in height.
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