MGEB12H3 Lecture Notes - Lecture 4: Aspirin, Test Statistic, Confidence Interval

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Published on 6 Apr 2019
School
UTSC
Department
Economics for Management Studies
Course
MGEB12H3
Professor
MGEB12: Quantitative Methods in Economics-II
TUTORIAL-4
Question 1: In an attempt to study the relationship between the daily use of aspirin as a
measure to prevent stroke, a researcher has divided a group of 4500 women over 64 years
of age. They were randomly assigned to receive either aspirin or placebo [a pill that looks
exactly like aspirin but has no active ingredients]. The following results were provided:
Stroke Total
Aspirin 95 2220
Placebo 139 2280
a) Test at 1% if there is a difference in taking or not taking aspirin in preventing stroke.
Report the p-value and clearly state your conclusion.
Solution:
( )
[ ]
( )
006.0
745.2
)2280/1(2220/1()052.01(052.0
061.0043.0
061.02280/139
ˆ
,043.02220/95
ˆ
,052.0
22802220
13995
)/1(/1()1(
0
ˆˆ
0:
0:
:
:
21
21
21
211
210
2
1
+
=
===
+
+
=
+
=
=
valuep
Z
ppp
nnpp
pp
Z
ppH
ppH
NoAspirinp
Aspirinp
Reject the null at 1. The p-value is <1% therefore the test is very strong. There is
overwhelming evidence in favor of the null. There is a difference.
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b) Go back to part (a). Find the 95% confidence Interval for the difference in the
population proportions.
Solution:
2280
)061.01(061.0
2220
)043.01(043.0
96.1)061.0043.0(
+
+
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Document Summary

Question 1: in an attempt to study the relationship between the daily use of aspirin as a measure to prevent stroke, a researcher has divided a group of 4500 women over 64 years of age. They were randomly assigned to receive either aspirin or placebo [a pill that looks exactly like aspirin but has no active ingredients]. 2280: test at 1% if there is a difference in taking or not taking aspirin in preventing stroke. Report the p-value and clearly state your conclusion. The p-value is <1% therefore the test is very strong. There is overwhelming evidence in favor of the null. There is a difference: go back to part (a). Find the 95% confidence interval for the difference in the population proportions. In a study, a random sample of 120 college students was selected. Each student was asked whether or not they exercised regularly (at least 30 minutes of aerobic exercise 3 times a week).