Determining sample size based on confidence and margin of error | AP Statistics | Khan Academy

Determining sample size based on confidence level and margin of error.

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[zhushuncai]

For people who don't know why p hat needs to be 0.5. The issue is we do not know the value of p hat before the researcher conducts the study. It could be 0.4, 0.3, or 0.01 based on the result. So if we want the margin of error to be no more than +-2%, we need to calculate the worst-case scenario in which p hat is 0.5. For reason I don't know, 0.5 * 0.5 is bigger than any other combination such as 0.4 * 0.6, 0.2 * 0.8, etc.
Let's say we use 0.4 as p hat, and we get a sample size of 1537. We use this sample size and conduct the study, and we find out the p hat is 0.5. We do not have the sample size we need which is 2401 and the margin of error is more than +-2% which is not the result we want.

[FM-kzvq]

I didn’t learn ANY of this in class & it’s on my stats test 🤦🏻‍♂️ thank you !!

[irakozenaftari]

Thank you for great content but the formula could have been simplified to this n=(Z^2*p*q)/E^2 (1.96^2*0.5*0.5)/.02^2 = n=2401

[wtenho]

Neat trick to calculate square numbers near 50: use (a + b)^2 = a^2 + 2ab + b^2, so (50 + b)^2 equals 2500 + 100b + b^2. In this case b = -1 => 49^2 = 2500 - 100 + 1 = 2401

[noutalenezi]

Thank you so much this makes a lot more

[jonhadley]

because we don't have P-Hat, just use N = 1 / ME^2
pick the closest answer it will be off but close

[laurencooper]

confusing introduction of p=0.5. why??

[MrArtbyart]

I would expect that the sample size would vary with the population size. What if the total population is less than 2, 000? Thanks

[valdesito]

Hello, does anyonw know if there is a similar way to calculate stratified sample size? (without knowing the population size for each stratum)

[jeevanrana]

Can we take margin of error 2% when confidence interval 95%?

[noellecook]

Why does p hat have to be maximized? And why does .5 maximize it? Would using .5 apply to any margin of error percentage in which the p hat is unknown?

[junglecat]

Who made the formula? what is it called?

[joaovitorcampos]

what if my population is lesser than 2401??

[fallout]

What if there's no margin of error available?

[adeyeyeoluwafemi]

please what is my samlpe size if my population is 3500

[marianpalko]

Might be a stupid question, but is this not at all affected by the total number of all of the community members?

[pelasgeuspelasgeus]

So, you found the sample without caring about the population size. Does it make sense to you? It sounds like pseudoscience to me.

[anthonycarbonaro]

You made a total mess out of something very simple.
n=(z alpha/2 * theta/E)squared.