STAT 409
Examples for 10/05/2009
Fall 2009
CDF @
x
p
n
x
0.60
20
0
0.000
1
0.000
2
0.000
3
0.000
4
0.000
5
0.002
6
0.006
7
0.021
8
0.057
9
0.128
10
0.245
11
0.404
12
0.584
13
0.750
14
0.874
15
0.949
16
0.984
17
0.996
18
0.999
1.
A scientist wishes to test if a new treatment has a better
cure rate than the traditional treatment which cures only
60% of the patients.
In order to test whether the new
treatment is more effective or not, a test group of 20
patients were given the new treatment.
Assume that
each personal result is independent of the others.
Trying to decide:
cure rate
p
≤
0.60
vs.
p
> 0.60.
a)
If the new treatment has the same success rate as the
traditional, what is the probability that at least 14 out
of 20 patients (14 or more) will be cured?
b)
Suppose that 14 out of 20 patients in the test group
were cured.
Based on the answer for part (a), is there
a reason to believe that the new treatment has a better
cure rate than the traditional treatment?
19
1.000
c)
If the new treatment has the same success rate as the traditional, what is the
probability that at least 17 out of 20 patients (17 or more) will be cured?
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 Spring '11
 Stepanov
 Null hypothesis, Cure, Statistical hypothesis testing, new treatment, P0

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