STAT 100 Lecture Notes - Lecture 18: Sampling Distribution, Normal Distribution

• School: University of Maryland
• Department: Statistics and Probability
• Course: STAT 100
• Professor: Cremins

Document Summary

When the sampling distribution of (x-bar) is close to normal, we can nd probabilities involving (x-bar) by standardizing: z = (x-bar) m s / n. When we don"t know , we can estimate it using the sample standard deviation sx. This new statistic does not have a normal distribution! When we do not know the population standard deviation (which is usually the case), we must estimate it with the sample standard deviation s. When the standard deviation of a statistic is estimated from data, the result is called the standard error of the statistic. The standard error of the sample mean is: s n. When we standardize based on the sample standard deviation sx, our statistic has a new distribution called a t distribution. It has a different shape than the standard normal curve: It is symmetric with a single peak at 0, however it has much more area in the tails.