STAT 409
Examples for 10/03/2011
Fall 2011
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?
P
(
X
≥
14

p
= 0.60
) = 1 – CDF
(
13

p
= 0.60
) = 1 – 0.750 =
0.250
.
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?
If
p
= 0.60,
then
25%
of all possible samples would have 14 or more patients
cured (out of 20).
Thus, it is
not unusual to see 14 out of 20 patients cured for
a treatment that cures 60% of the patients.
We have no reason to believe that the
new treatment has a better cure rate than the traditional treatment
if
X = 14
.
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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 Fall '11
 STEPHANOV
 Statistics, Statistical hypothesis testing, Statistical significance, new treatment, rejection region, better cure rate

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