Hello and welcome back. My name is Mark Rulkowski and I'm a lecturer here in the Department of Statistics. Today, we're going to be learning about the assumptions necessary for a confidence interval, specifically for a single population proportion. Just a quick refresher on confidence intervals and what we use them for. We use confidence intervals to give us a good estimate of a population proportion. So in order to do this, we're going to create a confidence interval where the midpoint or center of the interval is going to be our best estimate. This best estimate will be our sample proportion or point estimate from sample and then we're going to add, and subtract a margin of error onto both ends of this midpoint. This margin of error can be thought of as kind of wiggle room for our estimate and this wiggle room or margin of error is going to reflect the variability that is expected within these sample estimates. When creating a confidence interval, we need to check a couple assumptions first and the first of those is to make sure that our sample of data is a simple random sample. A simple random sample is a representative subset of the population of interest. With this, we need to make sure that each of the observations or each of the subjects has an equal probability of being chosen. If we can get a simple random sample, then we'll have a reliable representation of our population of interest and that will give us a good midpoint for our interval. The second assumption that we need, we need to make sure that we have a large enough sample size. Why do we need this large enough sample size? Well, if we have a large enough sample size, then we can approximate our sampling distribution with a normal curve. In the calculation of our margin of error, we use a critical z-value or a z multiplier and this is taken from a standard normal curve. So if we have a large enough sample size for our data, then we can approximate our sampling distribution or our distribution of sample proportions with a normal curve. But what exactly is large enough? There are a lot of different viewpoints on the subject on what is deemed large enough. Regardless, the larger the sample size we have, the better approximation we're going to get. As our N increases, our sampling distribution is going to become more and more bell shaped and that's really what we're after. For us with a single population proportion and a confidence interval, we're going to define large enough as at least ten of each response outcomes. This is generally yes's and no's, so we'd need at least ten yes's and at least ten no's within our sample. So how do we check these two assumptions? To make sure that we have a simple random sample, what we're going to do is analyze how the sample was collected. We need to make sure that this sample is representative of the population of interest. For this course, generally, we're just going to have a simple random sample and make this assumption. But oftentimes, you can have more complex sampling designs and this can be taken account for with waiting and other various techniques. But again, for this course generally, we'll have simple random samples. To make sure that we have a large enough sample size, we just need to make sure that we have at least ten of each response outcomes. And again, as we've said previously that just means simple ten yeses and ten no's within our sample. If both of these assumptions are met, we can move forward with creating our confidence interval and this confidence interval is going to give us a good estimate of the true population proportion.