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Unformatted text preview: Inference about a Difference Between
Population Proportions
Example problem:
Olestra was a fat substitute used in some snack foods.
After some people consuming such snacks reported gastrointestinal
problems an experiment was performed.
Results:
90 of 563 subjects in the olestra treatment group reported problems.
93 of 529 subjects in the control group reported problems.
Inference problem:
Let be the proportion in the treatment group.
Let be the proportion in the treatment group.
Test
versus
with significance level .05.
R Script
x = c( 90, 93 )
n = c( 563, 529 )
prop.test( x, n )
data: x out of n
Fail to Reject
Xsquared = 0.3894, df = 1, pvalue = 0.5326 (Bigger than .05)
alternative hypothesis: two.sided
95 percent confidence interval:
0.0621 0.0302
(95 percent CI includes 0 )
sample estimates:
prop 1 prop 2
0.1599 0.1758 Distribution Results
Let and with
Let and independent. and
estimated by where
For large samples (both m and n)
has an approximate normal distribution so The two sided confidence interval for The case of is is special. If the null hypothesis is true
and we can combined the two sample results to estimate
in variance for each of the two samples. This estimate is a
weighted average individual sample estimates that favors the larger
sample. Alternative Hypothesis Rejection Region prop.test(x, n, p = NULL,
alternative = c("two.sided", "less", "greater"),
conf.level = 0.95, correct = TRUE)
The p argument vector is not used in this class.
The allows null hypothesis proportions to be specified for each sample.
This is beyond the class scope except for the one sample case.
The class uses binom.test() for the one sample case. ...
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 Spring '08
 Staff

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