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

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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.

Page 2 of 7

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( −

+

−

+−

## 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).