Solution To Stat1600 Test #2 Form A Math Worksheet With Answers Page 3
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1
2
3
4
5M E = 1.96SE = 1.96
0.010 = 0.020. A 95% confidence interval for the true
proportion is
(0.08
0.020, 0.08 + 0.020) = (0.060, 0.100).
Hence a 95% confidence interval for the true percentage is (6.0%, 10.0%).
4. The table below shows the result of a study of the effectiveness of thalidomide in healing
mouth ulcers in AIDS patients (an announcement by the National Institutes of Health on
October 31, 1995):
ulcers healed?
YES
NO
Treatment
14
9
Placebo
1
21
(a) (10 points) Estimate the difference in heal rates (i.e., difference in proportions) of the
two groups (Treatment versus Placebo).
ANSWER (show your work):
Let group 1 = Treatment and group 2 = Placebo. Then
n
=
14
+
9
= 23;
n
=
1
+
21
= 22.
1
2
It follows
14
1
ˆ p
=
= 0.609; ˆ p
=
= 0.045.
1
2
23
22
The difference in proportions is estimated by ˆ p
ˆ p
= 0.609
0.045 = 0.564.
1
2
(b) (10 points) Calculate a 95% confidence interval for the difference in heal rates. Does
the interval exclude 0? Is the difference statistically significant? ANSWER (show your
work):
3
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