# lecture9 - Handout 5 Sampling Distribution of the...

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Handout 5: Sampling Distribution of the Proportion Reading Assignment: Chapter 6 Suppose we conduct a binomial experiment with n trials and get successes on X of the trials. Or sup- pose we measure a categorical variable for a representative sample of n individuals, and X of them have responses in a certain category. In each case, we can compute the sample proportion , the proportion of trials resulting in success, or the proportion in the sample with responses in the specified category, as follows: ˆ p = X n = number of successes total number of observations in the sample If we repeated the binomial experiment or collected a new sample, we would probably get a different value for the sample proportion. Since X is expected to be around n · p with a standard deviation of p n · p · (1 - p ), then X n is expected to be around n · p n with a standard deviation of n · p · (1 - p ) n , or p with a standard deviation of q p · (1 - p ) n .

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