Variability in estimates proportions

Proportions are for

Categorical data

Proportions are written as

%, decimal, or fraction (x/n)

Sample proportion is called

P-hat

What is p-hat written as

%, decimal, Or fraction

P-hat is written as

^

P

P-hat without hat is

Population sample

Sample stats estimate

Population parameters

Sample stat is also known as

Point estimate

Sample stat should be ____ to pop parameter

very close

Sampling distribution

Average of all p-hats (point estimates)

Standard error

Variation or standard deviation in point estimates

SE vs SD

SE= categorical

SD= numerical

can a graph be curved for categorical data

No— not continuous data

Larger sample size = ___ SE

Smaller

Central Limit Theorem**

If observations are independent and sample size is sufficiently large, sample proportion will be nearly normally distributed (mean = p aka population proportion)

How to verify independence

Random sample less than 10% of pop

How to verify sufficiently large sample

Must meet success failure condition

(Np>=10) and n(1-p)>= 10

If p is not known, you can use

P-hat

Confidence interval

range of plausible values where we are likely to find population parameter

CI written as

(60%, 70%)

What do you need in confidence interval

Parenthesis!!

More commonly used confidence intervals

A- 90% = significance level, 1-0 confidence level

Leftover = alpha

95%

99%

Cutoff scores for critical values

90%+-1.65

95% +-1.96

98$ +-2.33

99%+2.58

(Given)

How to calculate confidence level

Point estimate +- ME

Or x* points estimate +- z* (SE)

what do you use to calculate uncertainty of point estimate

standard error

variables in SE formula

n= sample #

x= observed stat

p= point estimate/sample state

how to get point estimate from confidence interval problem

average it

how to get margin of error

distance from middle to endpoint

steps to solve confidence interval question

1. check conditions

2. find point estimate/sample stat (aka phat) and z score (on chart)

3. calculate with formula

4. put into words

parameter is also known as

population proportion

success failure condition

np>10 and (1-p)n>10

point estimate

sample value use to estimate population parameter

example of point estimates

sample mean, sample proportion, sample standard deviation

error

difference between observations and the parameter

when conditions are not met distribution is

discrete (not continuous)

skewed

why do we need a confidence interval?

cuz point estimates will likely not exactly hit population proportions

margin of error formula in confidence interval

z*+-SE

why do you need to check conditions

to make sure distribution will be near normal