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6-3 Sampling Distributions 6.1 The Sampling Distribution of the Sample Mean 6.2 The Sampling Distribution of the Sample Proportion

6-4 6.1 Sampling Distribution of the Sample Mean The sampling distribution of the sample mean is the probability distribution of the population of sample means obtainable from all possible samples of size n.

6-5 Example: Sampling Distribution of Mean

6-6 Sampling Distribution of the Sample Mean Normal, if the sampled population is normal Has mean Has standard deviation If a random sample of size n is taken from a population with mean  and standard deviation  then the sampling distribution of the sample mean is It should be standard error or standard deviation of sample mean.

6-7 Effect of Sample Size on Sampling Distribution

6-8 Example: Gas Mileage Case Probability that when  = 31.

6-9 The Central Limit Theorem For sample size n sufficiently large, the population of all possible sample means is approximately normally distributed with Sampling Distribution of Sample Mean Population Distribution Random Sample(x 1, x 2, …, x n ) X

6-10 Example: Central Limit Theorem Simulation

6-11 Example: Effect of Sample Size The larger the sample size, the more nearly normally distributed is the population of all possible sample means.

6-12 6.2 Sampling Distribution of Sample Proportion If a random sample of size n is taken from a population  then the sampling distribution of the sample proportion is Approximately normal, if n is large. Has mean Has standard deviation

6-13 Sampling Distributions 6.1 The Sampling Distribution of the Sample Mean 6.2 The Sampling Distribution of the Sample Proportion Summary: