 Given a specific confidence level and a desired margin of error, we're now going to practice calculating the sample size needed to predict a population proportion. You wish to estimate a proportion within a 0.015 margin of error at a 95% confidence level. With no prior knowledge, what sample size should you gather? So the key here is we're trying to predict a proportion, a population proportion. Since we have no prior knowledge, meaning we didn't do a study and calculate a sample proportion, we have to use the following formula. Our sample size will be our critical value, squared, times 0.25 divided by margin of error squared. Well since I'm dealing with a 95% confidence level, the critical value is actually going to be 1.96. And the margin of error, as I give it to you in the question, is going to be 0.015. Plug these pieces of information into our formula. You'll have 1.96 squared times 0.25 over 0.015 squared. So now you'll go through and use your calculator. Do not round until your final answer. So I got 4268.4. I will round this up. You will always round up when you're calculating sample size. You get 4269.4269. Now let's calculate the sample size needed in the instance where we have information on a sample proportion. So we went out and we did a little bit of a study, or we looked at a previous study and we found the sample proportion, p hat equals 0.225. Well when you know information such as the sample proportion, there's a different formula you can use. You still take the critical value and square it, but you now multiply by p hat and q hat, then you divide by the margin of error squared, or the error bound squared. In this instance, since I have a 95% confidence level, I know that the critical value is 1.96, probably the most common critical value that's often used in statistics. We know that p hat is 0.225, which would mean q hat, which is always 1 minus p hat is going to be 1 minus 0.225. That means 0.775. And the error bound as they gave you in the question is 0.015. Plug this information into the formula. You have 1.96 times 0.225 times 0.775, all divided by 0.015 raised to the second power. Plug all of this into your calculator. And at the end of the day, because of the fact that we had information about the sample proportion, I now only need a sample size of 2,977.24, which you always round up, because 2,977 isn't quite going to get you where you want to be. So I'm going to round up to about 2,978. That is the sample size that we'll need here. It's important that you try to wait until your final answer to do any sort of rounding, otherwise your sample size that you need could be way off. So once again, wait until your final answer to round. And honestly, the more decimal places you keep for your critical value, the more accurate your answer is going to be. Typically, you can do two to three decimal places on the critical value, but you can definitely keep more if you want. Well, that's all I have for you today. Thanks for watching.