7.2 Flashcards
Graph for sampling proportions and SE (mean differences)
Largest estimate (chance out of size proportion) at end, smallest at beginning, mean in middle (x_)
Largest ERROR from any of the samples-> largest error (SE) = x_ - M
Sample mean= largest proportion
Parameter mean= given
Goes to show: more sample-> more normal, more centered mean
The estimate value gets a dot on the POPULATION dot plot to show how far away from the PARAMETER it is (then SE)
Really know the difference between parameter and statistic
Statistic comes FROM the estimate
Look for key words (go back to other cards)
Using parameter and statistic and SAMPLING ERROR
“Find the error in the estimate”
Look at both the percentages
If they are close, the error is small -> SAMPLING error between proportions: estimate - parameter (p^ - p)
Can be a negative distance
Standard error and GIST (bigger n= normal)
SQUARE ROOT p(1 - p) / n
The AVERAGE sampling error
When n> = SE small
When n> = more sample units, SMALLER variability, SMALLER SEs (more condensed in middle), more normal
- smaller SEs= SAMPLE proportion is closer to the parameter (p) -> p^-p where p^ is getting smaller/ closer so if its even smaller itself (!!!!from a bigger n- 6/36 is not 36/6), it will have greater chances)
Here its all about what we can more accurately pinpoint as true WITHIN 2 SEs (95% chance)
Either 95% chance where each sample unit’s percentage value is close to 95% (1/2 = 50%), and so the sample units chances are more spread out and leave plenty of room for gaps (SEs) (PARAMETER DOESN’T CHANGE WITH HER)
Or 95% where all sample units are close so there’s no room for error (more confident in 95%)
Find the mean and SE of sampling distribution of p^ and GIVE OR TAKE
See if values on it are unusual (not analyzing shape)
If take RANDOM sample, We EXPECT (parameter) the parameter to TOI, give or take ONE SE negative or positive (the SE result you calculate more simply) IN DECI FORM !!!
Mean- will be p (not p^) because we are trying to see how sample values match up to its truth on the graph
Look for solid words like “are”
SE= SQRROOT mean (1- mean) / sample size * and the mean is p
Sketch= normal with +- SE
CONT. would it be unusual to get x% that are TOI
See if more or less than 2 SEs from the PARAMETER
Instead of saying “within” say more or less
P^ is never going to be mean on graph
Because it CHANGES with every sample size and TOI size, so its the values on the line (2/100, 5/100, 8/100)
Whereas parameter doesn’t change, its set and only has ONE value (p^ has multiple)
Sample proportion (p^)
Will always equal parameter if the sample is random (unbiased)
UD sample proportions for sample distributions
The whole graph is meant to put all the possible p^s seperated by SEs, but find which samples in the lineup are are successes (meet TOI)
“ get random sample hoping to get at least a majority of units that are successes (meet TOI) “
If this sample is small
IMP!!!! UD width of CI
Wider ones are unstable (less confident because when the m +_ the p^ is bigger (m is bigger) there is more margin for error, hence bigger values for you to add onto either sides of the p^)
