Chapter 18 - Part 2 Sampling Distribution Models for.

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Presentation transcript:

Chapter 18 - Part 2 Sampling Distribution Models for

What about ? Mean (Center) Expect to get on average μ is unbiased for μ

What about ? Standard Deviation (Spread) As n gets larger, gets smaller. Larger samples are more accurate than smaller samples

Example Height of women has a normal distribution N(66,2.5) Sample n women. Calculate mean height. Repeat sampling. What does sampling distribution of mean look like?

What about ? Normal population distribution Three conditions 1. Sample must be random sample 2. Sample must be independent values 3. Sample must be less than 10% of population. Shape is NORMAL DISTRIBUTION! Expressed as

Example Roll a die n times Find mean of n rolls Repeat a lot of times. What does distribution of mean look like?

What about ? Non-normal population distribution Four conditions 1. Sample must be random sample 2. Sample must be independent values 3. Sample must be less than 10% of population. 4. Is n is large (n  30)? Then, the shape is NORMAL!!!

Central Limit Theorem As the sample size n increases, the mean of n independent values has a sampling distribution that tends toward a normal distribution.

Central Limit Theorem If the shape of the population is already normal, then the Central Limit Theorem is not needed. However, the distribution is still