The Practice of Statistics Third Edition Chapter 9: Sampling Distributions Copyright © 2008 by W. H. Freeman & Company Daniel S. Yates

Sample Proportions To estimate the proportion of successes in the population: Take an SRS from the population of interest. phat = count of successes in the sample/size of sample = X/n Note that X and phat are random variables If the population is much larger than the sample, X is distributed binomially

The mean and standard deviation for the sampling distribution of a sample proportion are algebraically derived from what we already know about the mean and standard deviation of a binomial random variable. Note: phat is less variable in larger samples.

Rule of Thumb 1 will be used throughout the course whenever we draw a sample to make an inference about a population. Remember we only sample when a population is large enough to make a census impractical.

This rule should sound familiar. We used it when calculating binomial probabilities with the Normal approximation. Note: The accuracy of the Normal approximation improves as n increases. For a fixed sample size, the normal approximation is most accurate when p is close to.5.

Applying to College SRS of st year college students on whether they applied for admission to any other college. 35% applies to other colleges besides the one they were attending. What is the probability that a random sample of 1500 students will give a result within 2 percentage points of this true value?

Note that these calculations are virtually the same as those done in chapter 2. But now we know the proportion of the area under the Normal curve is the same as the probability.