9.1 And 9.2 Flashcards
Language for p vs sample
It will say “mean”, but you HAVE to look at if this “mean” is from a sample (study) or a population.
!!!! Sometimes the population is from a study, but it will include “ALL”
SUP IMP!!! Estimate / probability (p^)- SAMple
Estimate/ statistic(percent form) = success guess (shouldn’t be a %) / SAMPLE size
This is all estimation- because we dont “sample” the WHOLE pop (what makes it a statistic)
BUT if it comes from this one sample (yes, considering the above), its a PROBABILITY/ Statistic (p^)
!!!
USED to estimate the parameter (guessing if their thoughts will match up with ACTUAL outcome of votes (p))
Sampling error
Guessing from small portion mistake
Missing some of the MOST imp factors to what will lead to the parameter
!!!
Probability - parameter = p^ - p
Will give negative # -> off by this much BUT depends on how big the sample was (if big then distance of tick marks (SE) will be smaller, making this negative value even riskier
POP parameter (outcome) vs SAMPLE statistic (guess of outcome)
POP(parameter) sample( statistic)
Mean = MU x_
SD= sigma o- s !!! SE !!!
PROPORTION of successes-> p (parameter) p^ - estimate
Number of units (pop)= N n - sample size
Standard error = SE- o- / SQR n
KW!!- LOOK OUT FOR “ALL” - ALL is the parameter/ actual outcome of EVERYONE, not just outcome of a SAMPLE
Parameter
Isn’t exclusively the p or proportion
Its anything that comes from population (SE, mean, or proportion)
Same with anything coming from a sample
OH
What does SD mean in context again? Like if its big, what does that imply on the mean or the population and TOI in particular?
Shapes of sampling distributions (central limit theorem)
It’ll say from multiple “means”, but it’s actually just proportions, so the “this sample TOI process was repeated 36 times” is basically 36 means.
N= 36 but each mean is different.
As you repeat, the distribution gets more normal
- low variability
- small SD
The parameter distribution isn’t a concern here.
The “each from a sample of 50 cars” is the sample size within each sample, and each sample makes up the sample size
WO4- when sample is just one sample and not multiple, its just a sampling distribution
!!!The first sample size matters more than the “many”-> if small, then each “many means” mean is going to be based from a proportion with that as the denominator!
Small n -> wider variability/ big SD
Left skewed
!!! When a sampling distribution comes from a population that is skewed
The three distributions you’ll see
Sampling distribution from a !!! population !!
Sampling distribution of many means each from sample of 5 (small)
Of many means each from sample of 25 (big)
- Are taken straight from a pop, so it will be raw and there will be mulitple outliers (largest SD)
- Will be SLIGHTLY skewed, and NEITHER largest nor smallest SD
- Smallest SD, looks normal
Sample mean and population mean in context with each other
Context- population distribution and stamping distribution is small sample size, but not “smaller”, because teh population size isn’t comparable to sample size
Sample mean is an unbiased estimator of the population mean ALWYAS
Basically because sampling distributions revolve around Mu always even if that number is insanely larger than their sample size could ever give
Standard error (p) and SE (s)
SQUARE ROOT p(1 - p) / n
The AVERAGE sampling error
When n> = SE small
Standard error of a sample
Populations !!!! Only have SDs and samples only have SEs based on how close they are to those SDs (hence the errors)
!! o- / SQR n !!
Determine about population distributions
Look for the SDDDD
If its small -> low variability
You have to use context and logic
And think about the !!VALUES !!!!
When values are assumed to be mostly small -> very few large ones (right skewed)
Showers cannot be less than 0 so ofc all the minutes piles up at the beginning and fade out as ppl turn to prunes
So when we sample more times (no matter the n within) it’ll get more normal because we have so many more perspectives to even out outliers
The sample size does matter if its like 5 people in each sample tho
Probability on these guys
Just find tick mark.
Less or more
Use ER
“Probability that sample mean will be at least # bigger or smaller than pop mean?”
Equation: “How many SDs is that?” Is what z score rlly asks for -> take diff between mean and value (x), then see how many SDs fit in this difference ->
X-(x-) <- distance from mean
———
SD <- how many SDs can first in that distance
BUT NOW SINCE ITS STATISTICS ->
- x- minus Mu
________
SE —- NOT pop SD
I guess just use SC, z score not reliable
!!! It will say “least or bigger than pop mean” so you have to add and subtract this number from mean and use the BETWEEN on SC
!
SCCC
Stat calculators normal
Put mena
SD
And input value or values for BTWEEN -> p( 4<x< 6) = probability
When it asks for “many means” you use the SE formula and input the new sample size
This is actually the t distribution (when there are more samples)
