Lecture 7. Sampling Distributions.
Statistical Inference: Using statistics calculated from samples to estimate the values of population parameters. Select Random Sample Sample for (statistic) Calculate to estimate Becomes Population Parameter.
BASIC Example: Soft Drink Bottler μ=600, σ=10. Normal Distribution. What is P(X>598)? p(x<598) .
Sampling Dist.of the Mean – Distribution of all Possible Sample Means if you select a sample of a certain size. μX= μ. μ = i=1NXiN (formula for mean) . σ = i=1N(Xi-μ)2N Although you do not know how close the sample mean of any particular sample selected comes to the pop mean, you know that the mean of all possible sample means that could have been selected = the pop mean.
Standard error is calculating the probability of a certain amount of error. EXAMPLE:
Standard error is .
As n increases decreases.

CENTRAL LIMIT THEOREM: Regardless of shape of individual values in distribution; as long as sample size is large enough the sampling distribution of the mean will be approximately normally distributed with μX= μ and σX= σ . For most population distributions n ≥ 30 will be large enough. For symmetric population distributions, n ≥ 5 is sufficient. For normal population distributions, the sampling distribution of the mean is always normally distributed
EXAMPLE:

SAMPLING DISTRIBUTION OF THE PROPORTION. π is the proportion of items in the population with a characteristic of interest. p is the sample proportion and provides an estimate of π.

Underlying Sample distribution is binomial and can be approximated by normal if: nπ ≥ 5 and n(1- π) ≥ 5.
With resulting mean equal to μp=π and standard error equal to σp=π(1-π)n Therefore:

WEEK 8 CONFIDENCE INTERVALS:
CONFIDENCE INTERVAL FOR μ (σ Known): Assume standard deviation is known, population is normally distributed. If not