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Proportion
Author(s)
David M. Lane
Prerequisites
Introduction
to the Normal Distribution, Normal
Approximation to the Binomial, Sampling
Distribution of the Mean,
Sampling Distribution
of a Proportion, Confidence
Intervals, Confidence Interval on the Mean
Learning Objectives
- Estimate the population proportion from sample proportions
- Apply the correction for continuity
- Compute a confidence interval
The confidence interval for a proportion is computed
based on the mean and standard deviation of the sampling distribution of a proportion. The formulas for these
two parameters are shown below
μp = π
Since we do not know the population parameter π, we use
the sample proportion p as an estimate. The estimated standard error of p is therefore
To correct for the fact that we are approximating
a discrete
distribution with a continuous
distribution (the normal distribution), we subtract 0.5/N from
the lower limit and add 0.5/N to the upper limit of the interval.
Therefore the confidence interval is
Please answer the questions:
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