• Inference about a population proportion p from an SRS of size n is based on the sample proportion . When n is large, has approximately the Normal distribution with mean p and standard deviation .
• For large samples, the margin of error for confidence level C is
where the critical value z* is the value for the standard Normal density curve with area C between −z* and z*, and the standard error of is
• The level C large-sample confidence interval is
We recommend using this interval for 90%, 95%, and 99% confidence whenever the number of successes and the number of failures are both at least 10. When sample sizes are smaller, alternative procedures such as the plus four estimate of the population proportion are recommended.
• The sample size required to obtain a confidence interval of approximate margin of error m for a proportion is found from
where p* is a guessed value for the proportion and z* is the standard Normal critical value for the desired level of confidence. To ensure that the margin of error of the interval is less than or equal to m no matter what may be, use
• Tests of H0: p = p0 are based on the z statistic
with P-values calculated from the N(0, 1) distribution. Use this procedure when the expected number of successes, np0, and the expected number of failures, n(1 − p0), are both greater than 10.
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• Software can be used to determine the sample sizes for significance tests.