Suppose a researcher is studying a population in which 57% of the population has a certain trait. Round your answer to the nearest tenth of a percent if needed.

Question

daniellelovee · Answer

The researcher wants a sampling distribution
with a standard deviation that is less than 6%.
Would a sample size of 50 give a standard
 deviation that is less than 6%? How about a
sample size of 100?

daniellelovee · Answer

@Directrix

directrix · Answer

I am still working on the other problem. Oh, well.

daniellelovee · Answer

lol yeah im sure the other problem is 9 or at least 97percent sure

directrix · Answer

I can't be of any help at the present because I need to review the central limit theorem. I can't find a formula that makes sense for these problems.

daniellelovee · Answer

look at what the one I gave you on the last problem

daniellelovee · Answer

alright :)

daniellelovee · Answer

@ganeshie8

ganeshie8 · Answer

$$s.d = \dfrac{\sigma}{\sqrt{n}}$$

daniellelovee · Answer

would it be 6/50?

ganeshie8 · Answer

as you can see, the standard deviation of the sampling distribution decreases quadratically as the sample size increases

daniellelovee · Answer

yes but the thing is that im not too sure about the formula that Im supposed to follow and the different percentages confuse me

daniellelovee · Answer

0.36=0.84

daniellelovee · Answer

I think im doing something wrong

ganeshie8 · Answer

You want $s.d$ of the sampling distribution to be less than 6% of the population standard deviation. That is, $s.d\lt 0.06\sigma$. So we can solve : 

$$0.06\sigma=\dfrac{\sigma}{\sqrt{n}}$$

ganeshie8 · Answer

$$\sqrt{n} = \dfrac{1}{0.06} = \dfrac{100}{6}$$

square both sides and round

daniellelovee · Answer

ok so then that will be a yes for 100 sample

ganeshie8 · Answer

nope, what do you get for $n$ when you solve

daniellelovee · Answer

50/3

daniellelovee · Answer

and you said to square root therefore 4.08

ganeshie8 · Answer

you need to square it

ganeshie8 · Answer

$\sqrt{n} = \dfrac{50}{3}$

$n = (\dfrac{50}{3})^2 =277.77 $

ganeshie8 · Answer

that means, you need a sample size of at least 278 to make the standard deviation go below 6%

daniellelovee · Answer

oh then neither 50 nor 100 percent sample would work right?

ganeshie8 · Answer

they are less than 278, so none of them work

daniellelovee · Answer

ok thank you sooo much :)

ganeshie8 · Answer

yw