chapter 8 z intervals

point estimator

a statistic that provides an estimate of a population parameter

* is a phat or xbar

margin of error

describes how far, at mose, we expect the estimate to vary from the true population value.\`

decreases

a smaller confidence level _____ the margin of error

decreases

a larger sample size _____ the margin of error

critical value

a multiplier that makes the interval wide enough to have the stated capture rate

random condition

to be sure that phat is a valid point estimate, we check the random conditions: the data come from a random sample from the population of interest

large counts

when met, can use a normal distribution to calculate the critical value z for any confidence level

* nphat > 10 and n(1-phat0) > 10

10% condition

whenever we are sampling without replacement, which is nearly always, we need to check this.

* n > .10N

standard error

when the standard deviation of a statistic is estimated from data

z\*

invnorm of 100-confidence interval / 2

state

one sample z interval for p = true proportion of context

plan

check conditions

* random
* 10%
* large counts

do

* find phat
* z\*
* SEphat
* find interval

two sample

(phat1-phat2) +/- z\* root of (phat1)(1-phat1)/ n1 + (phat2)(1-phat2)/n2

0

for a two sample error, this number can not be in the interval to have convincing evidence of a difference

formula

conditions

other