in this video we're going to look at the requirements for hypothesis testing and we're specifically going to look at the requirements for means and proportions first let's start with the requirements for a mean and we're going to look at a Z test so the first requirement is you're testing a population mean the population is normally distributed or your sample is approximately normally distributed and remember that we actually checked that by checking our sample size being greater than or equal to 30 third the sample comes from a simple random sample so it should say this in the problem and for most of our problems this will be true so we'll just kind of assume that this happens the population standard deviation Sigma is known and then we've got our formula which is our z-score formula z equals the data minus the mean over the standard deviation in this case the data is our X bar or a sample mean our mean is mu our population mean and then divided by the standard deviation which is our Sigma divided by square root of n because we have a sample so later when we actually do a hypothesis test this will be called the test statistic so this is going to be really important the main thing here because we're gonna have two different tests for means a Z and a t-test is that for a Z our Sigma is known so that means population standard deviation is known and for a t-test its unknown so let's look at that one so this requirement for a t-test is still for a mean so you are testing a population mean the population still has to be normally distributed or your sample is approximately normally distributed the sample still needs to come from a simple random sample so so far all the requirements are the same here's the difference the population standard deviation Sigma is unknown but you know the sample standard deviation so this is going to be our difference between our Z test and our t-test so our T value formula is very similar to our z-score the only thing is that right here instead of a Sigma we've gotten s for our sample standard deviation again this is also going to be our test statistic when we do our hypothesis test and then lastly requirements for a proportion test we have to be testing a population proportion the population has to be normally distributed or your sample is approximately normally distributed and for proportions we check n times P times 1 minus P is greater than or equal to 10 and again just like the other ones 4 means the sample needs to come from a simple random sample and then we've got our z-score for proportion which is our P hat minus P divided by the square root of P times 1 minus P over N again this will be our test statistic when we do our hypothesis test for proportions okay so let's just sum this all up which test to use so the first thing you want to ask yourself is what parameter are you testing are you testing a mean or are you testing a proportion if you're testing a mean we have another question to ask do you know the population standard deviation if you do then we're gonna use a z-test with our test statistic of x-bar minus mu over Sigma divided by square root of n if you don't know the population standard deviation but you do know the sample standard deviation s then we're going to use a t-test with our test statistic being again similar x-bar minus mu over s divided by square root of n so those are all four means and you can see the difference here between the Z and the T is just if our population standard deviation is known or not it's very important to distinguish between the two because there are different graphs that we're going to look up so on the tables and it is slightly a different shape between a Z and a tee if you're testing a proportion we don't have any other questions we can just jump right to our proportion test with our test statistic of Z equal P hat minus P divided by the square root of P times 1 minus P over N so in later videos we'll look at our using our calculator but right now this is just a summary of what tests to use with the information that you have