7.3 Flashcards
Error due to sampling
P^-p
!!!!See why larger n is better- probability (SC)
Probability that x% (this is not percentile, but x-value)
So that THOSE at this value (this value is a proportion that contains multiple ppl) or above/ less will TOI
- if they only give success #, put it into the p^ equation for its. %on the line ofc
P(p^ >_ x% in deci) = probability as percent
- !!!! inequality: >_ is more (is that p^ and above it too)
<_ is less
- remember this is p^_ sample proportionSSS have multiples and so we are using these DIFF p^ values for this equation
- it is an average (the ppl within aren’t as important as how the SE makes it more accurate towards p or farther away)
What to do
Sketch normal graph
Place mean (p)
Get SE
+ and - SE
Find p^ if its not explicit
Find its place on graph
Shade less or more (“that value or fewer”= that p^ and less)
* round to two decimal places for graph and equation
SC for what exact the area shaded is in percentage form (that out of 100%/ the whole graph,not percentile) REVIEW: ER
BETWEEN-> “77% to 85% continue/ TOI verb” <- !!! This is the central limit that determines TOI (2 SEs away)
Shading rules from previous chapters
SC: P( .77 < p^ < .85) = probability
Probability that you get at less/more (# of successes) in your sample
Just plug in to find p^ -> (p^ >< whatever you get)= shade
Language: at least -> more sign
!!! % of sample we expect to TOI
Translates to sample proportion
But wont give us successes, just parameter and n
If its random (unbiased) it will be same as parameter
Plug this number into SE (its p)
Like p^ has the ability to = p since it varies so much, therefore it CAN be this number but it also so many more
!!! According to ER, there is 95% prob that the sample proportion will fall between what TWO VALUES
Translation to equation: x% <_ p^ <_ x% = 95% (kinda like CI)
So sketch graph and use SEs for tick marks, UP TO the second tick mark on both sides
Those last two are the values you place for x
!!! AND they inquire about SAMPLE proportions because those represent the tick marks for ER stuff !!
SC probability
Stat-> calculator -> normal
P^ = parameter (mentality I had before where I just knew that p is the one in middle (not p^)
Find SE (n and p are given)
Look at language for inequality
Help
If a given value is less than parameter, and sampling distribution is normal -> probability will be greater than (since its less than the middle, probability of successes will be greater than it- p is general probability of success)
!!! Then when GENERALLY putting in SC remember to leave SE as three deci places
