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When use Normal approximation
 When n is large, coefficients hard to calculate
 lots of possible values for Y
 and p isn't close to 0 or 1

Normal approximation equations
 u = np
 o = √np(1p)
 as long as np and n(1p) are both at least 5

Proportion of success in Normal approximation
 phat = Y/n
 µ = p
 sd = √p(1p)/n

Continuity correction
interval is y  .5 and y + .5

Standard error
 SE = s/√n
 'average' deviation when using the sample means as an estimate for the population mean
 description of the mean as applies to population mean


Confidence interval formulas
 ybar +/ t_{a/2}(o/√n)
 that area will contain (1a)100% of all samples

tdistribution
 heavier tail
 more to z curve with larger samples
 had df

ttable
 gives t values in the table
 zvalues on bottom
 alpha/2 is the given on top as the area to the right

cofidence interval contains the population...
x% of the time, and ybar is always the middle value

Validity of CI construction models
 must be random samples
 if n is small the pop. needs to be normal
 if n is large the pop. can be t'whatever

observational study v. controlled experiment
observational  less certain of results

Pool v. unpooled
 pool when sd_{1} = sd_{2}
 usually use unpooled, easier




Tvalue Calc
(Ybar  µ) / (s/√n)

if 95% CI contains Zero:
"no significant difference" btw µ1 and µ2 at 5% level of significance

If 95% CI does not contain zero
it implies statistical difference btw µ1 and µ2 at 5% level of significance.

Conditions for validity of hypothesis testing
 same for CI
 two independent random samples
 normal or large samples

H_{0}
 null hypothesis
 default state (innocent)

H_{A}
alternate hypothesis

Hypothesis
 either fail to reject H_{0}
 or
 reject H0

Errors with hypo decision
 Type I error: rejected, when it was true
 low upper limit = alpha
 statements have = signs
 Type II error: fail to reject when Ha is true
 upper limit = beta
 Power of a test Pr(reject H0  Ha is true)
 statements ≠ or < >

