Population One Simple Random All Simple Random Samples of size n Sample y1, y2, ... , yn of size n Y Y Associated Random Variable The population for is all simple random samples of size n from Y. The value of for a particular simple random sample is the sample mean for that sample. Y a normal The sample is the The distribution of is called the Associated has from Sampling Distribution distribution. (normal) distribution of The theorem tells us that the Distribution. Y. sampling distribution is normal. Associated Population mean Sample mean Since it’s a random variable, also has a µ, also called mean, E(). The theorem tells us that E() = µ. Mean(s) = (y1+ y2+ ... + yn)/n E(Y), or the (In other words, the random variables Y expected value and have the same mean i.e., E() = E(Y) – It’s an estimate of µ. of Y, or the = µ.) expectation of Y Associated Population Sample standard Sampling distribution standard deviation. Standard The theorem tells us that the standard standard deviation s = deviation of the sampling standard deviation Deviation deviation s is an estimate of the is . population standard deviation
Population One Simple Random Sample y1, y2, ... , yn of size n All Simple Random Samples of size n Associated Random Variable Y Y The population for is all simple random samples of size n from Y. The value of for a particular simple random sample is the sample mean for that sample. Associated Distribution Y has a normal distribution. The sample is from the (normal) distribution of Y. The distribution of is called the Sampling Distribution. The theorem tells us that the sampling distribution is normal. Associated Mean(s) Population mean µ, also called E(Y), or the expected value of Y, or the expectation of Y Sample mean = (y1+ y2+ ... + yn)/n It’s an estimate of µ. Since it’s a random variable, also has a mean, E(). The theorem tells us that E() = µ. (In other words, the random variables Y and have the same mean – i.e., E() = E(Y) = µ.) Associated Standard Deviation Population standard deviation Sample standard deviation s = s is an estimate of the population standard deviation Sampling distribution standard deviation. The theorem tells us that the standard deviation of the sampling standard deviation is .
WorkshopSlidesDayTwo2017-part2.docx