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Mr. Gregory White, Teacher
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# Statistics (Non-homework, do not move)

OK, stats question: I'm doing a hypothesis test and I want to know when I can stop my test, i.e. I want to know the sample size necessary to reach a certain confidence. However, I care about both type 1 and type 2 errors, and it's a two-sided test. Where can I find a formula for this? And go  easy on me please, stats bends my brain something fierce!

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A couple of questions while looking this prompt over - I will go as "Easy" on you as possible. :-)

1) What is the population size that you are using? This is important to know when looking at sample size. What confidence level are you trying to reach for the test? (90%, 95%, 99%, etc). Of course, the greater the confidence level required, the larger the population that will be required.

2) If you can provide some additional information (such as asked above), I will try to help you put this together using the "formula" you are requesting.

However, if you really just need the formula first and then help working through it, you can let me know that as well. Just want to be sure I know which direction and the type of help you are needing.

:-)

Customer: replied 4 years ago.

I would like to leave confidence level as a variable if at all possible, but if not, we are aiming for 85%

And I'm not sure what you mean about the population size? I think we're assuming that the population is everyone ever...

I am going to put two resources here that I think will be helpful (especially the second one) in your situation. The first is going to be the actual formula but I think the calculator resources I am going to provide secondly will be even better for you as you can manipulate some numbers on it to get a better determination of what you need.

First, the formula used (in research) to determine sample size is

Where

Z = Z value (e.g. 1.96 for 95% confidence level)
Confidence Level/ Value for Z
90% / 1.645
95% / 1.960
99% / 2.575
99.9% / 3.29
You probably would want at least a 90% confidence level for your results.

p = percentage picking a choice, expressed as decimal
(.5 used for sample size needed)
c = confidence interval, expressed as decimal
(e.g., .04 = ±4)

Now, this can get really frustrating for someone who is not really into the "math" side of the formula.

In my own research, I often use the following site which allows you to enter the information (data) and it will give you a good estimate of the sample size you will need

The first box is the confidence level you want (gives options of the 90, 95, and 99). The second box is the confidence interval you want (you enter a whole number - I would use 4 as a good starting point). This then allows a +4/-4 interval on either side of the level in the sample size. Finally, you have to enter a population. It is impossible to determine a sample size without having a "population" that you are drawing from. For example, if looking at ALL high school students, you would need to estimate how many high school students there are and put in that amount. Then based on the level and interval, you would know how many high school students you would need to sample in order to reach the confidence level that is needed.

I hope this helps. If I can be of ANY further assistance, please click on "Reply to Expert"

:-)
Customer: replied 4 years ago.

Thank you most kindly for your help!

You are more than welcome! I hope it helped to work it through.

If you need any further assistance on your efforts, feel free to request me again anytime.

Have a wonderful rest of the week. Hope it is warmer in your area of the country than mine right now.

:-)
Customer: replied 4 years ago.

Most definitely - windows are open and the sun is shining here in Northern California! :)