Finding the sample size needed to estimate a confidence interval on a population mean

Intro

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to find the sample size needed to estimate a confidence interval on a population mean.  Here's our problem statement: An IQ test is designed so that the mean is 100 and the standard deviation is 20 for a population of normal adults.  Find the sample size necessary to estimate the mean IQ scores of statistics students such that it can be said with 99% confidence that the sample mean is within 6 IQ points of the true mean.  Assume that σ = 20, and determine the required sample size using technology.  Then determine if this is a reasonable sample size for a real world calculation.

Part 1

OK, to get the sample size for a confidence interval, the easy way to do that is to go into StatCrunch.  Notice there's no icon here for me to click on to dump data into StatCrunch.  All the data, so to speak, that I need is actually here in the problem statement.  So I'm going to go up here and click on Question help and then click StatCrunch.  And if I click on this arrow button here, it'll actually pull the window out of the window where the homework problem is listed so I can actually move this around and I can resize it as needed, which is actually really helpful when you're making a video.  It's also helpful when you're actually working the problem out because you're going to get an answer here, and then you can just transfer it over without having to cover up anything.

Anywho, here we go to get the sample size.  I'm going to go to Stat --- do I go to Z Stats or T Stats next?  Well, I'm going to go to Z Stats because remember the key question is "Do we know what the population standard deviation is?"  In this case, we do know what the population standard deviation is. They tell us right here in the problem σ = 20.  That is the problem --- the population standard deviation.  And so we're going to use Z Stats.  We have only one sample, and then I want to click down here on Width sample size because we're using the width of a confidence interval to calculate sample size.

Down here in my input fields, I'm going to select the confidence interval we want is 99%.  Our standard deviation we said here was 20.  The width is going to be the width of the confidence interval that we're looking for, and that is twice the margin of error.  So the margin of error we have here is 6 IQ points.  So that means my width is going to be 12, because 12 is twice 6. I hit Compute!, and it gives me my required sample size.  So no need to do that asinine little hand calculation, although you could do it that, you know, old school way if you want to.  But hey, I prefer joining the 21st century.  I check my answer and I'm told, "Well done!"

Part 2

And there's one more part to the problem, and it asks us, "Would it be reasonable to sample this number of students?"  Well, this is the minimum required, and it's not a very large number.  So yeah, I mean, you could reasonably --- well, I mean, one person could reasonably sample 74 people.  So yeah, it's a fairly small number. It should be pretty simple to get out.  Fantastic!

And that's how we do it at Aspire Mountain Academy.  Be sure to leave your comments below, let us know how good a job we did or how we can improve.  And if your stats teacher is boring or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see.  Thanks for watching!  We'll see you in the next video.