STAT 210 Lecture 14: Sampling Distribution of p-hat
Document Summary
Consider a random variable x that can take only two possible values: a success or a. The shape of it does not follow a normal distribution. A sampling distribution of a statistic is the distribution of values taken by the statistic in a large number of simple random samples of the same size n taken from the same population. To theoretically describe a sampling distribution we must describe the (1) shape, (2) center, (3) spread, and (4) unusual features of the distribution. Assumptions: the data being used to make inferences must be a simple random sample from the population, the population distribution must be known to be normal, or the sample size must be. Large enough for the central limit theorem to apply. N: shape: the shape will be normal, unusual features: there will be no unusual features. We can summarize the sampling distribution by writing: p ~ n( , (cid:4666) (cid:4667) (cid:4667)
