PS296 Chapter Notes - Chapter 12: Central Limit Theorem, Sampling Distribution, Unimodality
Chapter 12: Hypothesis Tests Applied to Means: One Sample
Sampling Distribution of the Mean:
-the sampling distribution of any statistic is the distribution of values we would expect to
obtain for that statistic if we drew an infinite number of samples from the population in
question and calculated the statistic on each sample
Central limit theorem:
-the distribution will approach the normal distribution as N, the sample size, increases
-sampling distribution of the mean and variance will be equal to the mean and variance of
the population
-the rate at which the sampling distribution of the mean approaches normal is a function of
the shape of the parent population
-if population is symmetric but nonnormal, sampling distribution of the mean will be nearly
normal even for quite small samples (esp if population is unimodal)
-if population is markedly skewed, we may require sample sizes of 30 or more before the
means closely approximate a normal distribute
Testing Hypotheses About Means When σ is Known:
-from the CLT, we know all important characteristics of sampling didstribution of the mean
(its shape, mean, and its standard deviation) even without drawing a single on of those
samples
Document Summary
Chapter 12: hypothesis tests applied to means: one sample. The sampling distribution of any statistic is the distribution of values we would expect to obtain for that statistic if we drew an infinite number of samples from the population in question and calculated the statistic on each sample. The distribution will approach the normal distribution as n, the sample size, increases. Sampling distribution of the mean and variance will be equal to the mean and variance of the population. The rate at which the sampling distribution of the mean approaches normal is a function of the shape of the parent population. If population is symmetric but nonnormal, sampling distribution of the mean will be nearly normal even for quite small samples (esp if population is unimodal) If population is markedly skewed, we may require sample sizes of 30 or more before the means closely approximate a normal distribute. Testing hypotheses about means when is known:
