# Thread: [SOLVED] Sample St. Dev &amp; Mean

1. ## [SOLVED] Sample St. Dev &amp; Mean

Okay, so I took Data Analysis I over half a year ago and now I'm in II and the Prof isn't really reviewing things in a way that is helping me. He's using software to teach so I don't really get what is going on (yeah, it's easy but come on...not good for learning) and I don't have my old book to review with since I left it at home over the summer. I feel so nervous, I can't recall this stuff and I don't have the software to breeze through it anyways. Here is what I'm stuck on:

A random sample is to be selected from a population that has a proportion of successes π = 0.61. Determine the mean and standard deviation of the sampling distribution of p for each of the following sample sizes. (Round the answers for μp to two decimal places, the answers for σp to four decimal places.)

1. n = 30
μp =
σp =

If someone can help me figure out that one there, hopefully it'll come back to me and I can do the rest. I just can't remember this for the life of me.

2. I have trouble understanding this notation, but here goes.

In estimating the true proportion or say the probability of an event, p.
Which I think is your $\pi$...

You sample n data points.
The proportion of successes from the data is

$\hat P={Y\over n}$

where Y is a binomial random variable with n number of trials and success probability our p.

$\hat P={Y\over n}$ is unbiased meaning that $E(\hat P)={E(Y)\over n}={np\over n}=p$

and variance of $\hat P$ is ${p(1-p)\over n}$

SO plug in that value of Pi for my p and also the value for n.
Note that a standard deviations is the square root of the variance.