in this movie we're going to discuss the behavior of sample proportions by investigating these two questions when we collect random samples what patterns emerge more specifically what is the shape Center and spread of the distribution of sample proportions to investigate these questions we're going to return to the familiar context of the previous example and look at the population of all part-time college students we're assuming that 60% of this population is female now what we're going to be investigating in this movie is what happens as we begin to take random samples from this population I'm going to be collecting random samples of 25 students at a time you will see the sample here and to the right you will see the number of females out of the 25 randomly selected part-time college students in this case 17 out of 25 is 68 this is our P hat value our sample proportion we will graph each P hat above to generate a graph of the sampling distribution of sample proportions let's collect a second random sample and see what happens this time we got 18 out of 25 of the students being female which is a sample proportion of 72 we see that graphed here let's collect another random sample we see this time we got 64 16 of the 25 randomly selected students are female we can begin to see as we collect more random samples that there is going to be variability as we might expect each random sample will have a different proportion of females what we're interested in is what is going to happen when we begin to collect many random samples while we run the simulation we're going to pause the movie and have you make some predictions we want you to think about if we collect many many random samples what will be the shape and center and spread of the distribution that results let's see what happened I collected over 2,000 random samples each sample had 25 part-time college students in it and for each sample I calculated the proportion that were female and I recorded that here did you predict correctly what looks like happened over the long run is that many of the samples had proportions that were close to the population proportion of 6 we can also see that as we moved further away from point 6 we had fewer samples with sample proportions in that range we can get a more accurate sense of the variability in Sample proportions by looking at the standard deviation here the standard deviation is roughly 10% that tells me that typical samples had proportions that fell between about 0.5 and 7 here in the graph I have marked one standard deviation below and one standard deviation above the mean of 6 another thing we notice is that the shape is approximately normal I have used a mathematical formula here to graph a normal curve on top of the sampling distribution and we can see that the normal distribution models the sample proportions well this is encouraging it tells me that a normal model will be a good probability model for the sampling distribution of simple proportions now in the next movie we're going to investigate this issue of variability in Sample proportions in more detail and look specifically at the impact of sample size we'll see you then