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Lecture

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Confidence Intervals

another way of estimating (besides point estimation)

most often you don't know how precise the single sample mean as an estimator (ex.

smaller sample sizes)

place interval around the sample mean, and calculate the probability of the true

population mean falling within this interval

can say, with a measurable level of confidence, the interval contains the true population

parameter

interval approach: our population parameter falls within this interval that we created

around our sample mean

ex. say with 90% confidence the interval range containes the population mean

our population mean is between 90%

in a graph, bell curve, 5% on the neg and 5% on the pos (because it equals 10%) where

we're not interested in

on either side of the mean, there is 45% of where we are looking at (90% divide by two)

look at the z score - you get 1.65 value for 90%

find the one that is close to .45 as close as you can which is .4505 on the z score table

x(bar) ± 1.65(lower right - sigma x bar)

if we have a 90% of confidence, our significance level is 10%

1-∝ (where ∝ = significance level)

x(bar over top) ± z(lower right - sigma ( ) - lower right of this - x bar)σ

x bar = sample mean

z = z value from table

sigma x bar = standard error of the mean

first thing we need to know, what is our z value (probably only 3 or 4 you need to know

for the purposes of intervals and hypothesis testing)

What does it mean if you are 95% confident?

if you constructed 20 interval, each with different sample information, 19 out of 20 would

contain the population parameter , and 1 would notμ

but you can never be sure whether a particular interval contains μ

one is your giving the value (point estimate), the other one is based on my sample

value, my population parameter is WITHIN THE RANGE i have set around

my sample mean (confidence interval)

Choosing Correct Sample Size

total amount of information is due to:

sampling design used (which type determines if there is any bias and allows us to take

a representative sample)

sample size n (bigger sample yields more info and will be more representative of the

population --> central limit theorem)

but how many observations should be included in the sample?

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