Module 23: Proportions: Confidence Intervals and Hypothesis Tests, Two Samples

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Module 23 Proportions Confidence Intervals and
Hypothesis Tests, Two Samples
This module examines confidence intervals and
hypothesis test for two independent random
samples for proportions.
Reviewed 06 June 05 /MODULE 23
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Proportions Two Independent Random Samples
P1 Parameter for population one P2 Parameter
for population two x1 Number in sample one
with the characteristic x2 Number in sample two
with the characteristic n1 Total number in
sample one n2 Total number in sample two p1
x1 / n1, estimate for sample one p2 x2 / n2,
estimate for sample two
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Hypothesis Test Proportions from two samples
H0 P1 P2 vs. H1 P1 ? P2 p2
x2/n2, p1 x1/n1 The test is based on
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Example AJPH, Nov. 1977671033 - 1036
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Proportions for Two Independent samples
1. The hypothesis H0 PM PF vs. H1 PM
? PF 2. The assumptions Independent
random samples 3. The ?-level ? 0.05 4.
The test statistic 5. The rejection region
Reject if z not between ?1.96
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6. The test result 7. The
conclusion Accept H0 PM PF , since z is
between 1.96
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Confidence Interval for PM - PF
? 0.05
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Example Two Vaccines
In testing two new vaccines, for one group 137 of
200 persons became infected. For the second
group, 98 of 150 became ill. Test the hypothesis
that the two vaccines are equally effective. 1.
The hypothesis H0 P1 P2 vs. H1 P1 ?
P2 2. The assumptions Independent random
samples 3. The ?-level ?
0.05 4. The test statistic

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5. The rejection region Reject H0 P1 P2, if
z is not between 1.96 6. The
result 7. The conclusion Accept
H0 P1 P2 , since z is between 1.96

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Example AJPH, Sept. 1998881319 - 1324
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Hypothesis Test
Hypothesis test for proportion of Asthma or
Wheezy Bronchitis in Social Class I vs. Social
Class II nI 191
nII 1,173
pI 0.047
pII 0.078 1. The hypothesis H0 PI
PII vs. H1 PI ? PII 2. The assumptions
Independent Random Samples
Binomial Data 3. The ?-level
? 0.05 4. The test statistic
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5. The rejection region Reject H0 PI PII ,
if z is not between 1.96 6. The result
7. The conclusion Accept H0 PI
PII , since z is between 1.96

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Confidence Interval for PI - PII
  nI 191 nII 1,173

pI 0.047 pII 0.078
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