1. Section 9.2: Sample Proportions
AP Statistics
Section 9.2: Sample Proportions

2. 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

3. 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?