Section 9.2: Sample Proportions

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Section 9.2: Sample Proportions AP Statistics Section 9.2: Sample Proportions

Objective: To be able to define and describe the sampling distribution of a sample proportion. Choose an SRS of size n from a large population with population proportion,𝑝, having some characteristic of interest. Let 𝑝 be the proportion of the sample having that characteristic. Then, The mean of the sampling distribution of 𝑝 is 𝑝. 𝜇 𝑝 =𝑝 The standard deviation of the sampling distribution of 𝑝 is 𝑝𝑞 𝑛 . 𝜎 𝑝 = 𝑝𝑞 𝑛

The sampling distribution of 𝑝 : The sampling distribution is approximately normal and closer to normal when n is large. 𝑝 is an unbiased estimator of 𝑝. Rules of Thumb: (Conditions) We may use the formula for standard deviation of 𝑝 when the population size is greater than or equal to 10 times the sample size. (𝑁≥10𝑛) We may use a normal approximation to the sampling distribution of 𝑝 when 𝑛𝑝≥10 and 𝑛𝑞≥10. Q: In general, how big must the sample size be in order to reduce the standard deviation by half?