Hello and welcome back. In the past, we've talked a little bit about testing hypothesis, and today we're going to start delving into what that really means. So, to begin, why do we want to do hypothesis test? Well, typically we have a question, and that question could be, could the value of the parameter be blank? So, we could have some idea of what it could be but we're not sure if that's correct or not. Then, with that question we use data to try and support that claim or maybe go against that claim. For today's lecture, we're going to look at an example and run through a one proportion hypothesis test of a CS Mott Children's Hospital Poll. So, in this poll, there was a national poll on the issue of children's health and particularly sleep habits. So, we'll be looking at an example of lack of sleep in teens or teenagers. Our research question, we were given the background information of in previous years 52 percent of parents believed that electronics and social media was the cause of their teenagers lack of sleep. Do more parents today believe that their teenagers lack of sleep is caused due to electronics and social media? So, with this background, we first want to define what our parameter of interest is and our population. So, we have a population of parents with a teenager and that's ages 13 to 18, and our parameter of interest here is going to be p or the population proportion. The main goal is we want to test for a significant increase in the proportion of parents with a teenager who believe that electronics and social media is the cause for lack of sleep. So, with any hypotheses test, you first want to start with your hypothesis, so you make these before you even collect any data and so that's to say you not influenced in what you believe. So, the first hypothesis is the called null hypotheses, H naught, and for us in that background it said that in previous years 52 percent believed that the lack of sleep was caused by electronics. So, we're going to have H naught being p equals 0.52. The second hypothesis is going to be the alternative and that will be p and then something 0.52. So, this question mark here could be less than greater than or not equal to, which one would it be. So, our alternative will be greater than and the reasoning for that is in the previous slide, the background info said significant increase, and so that means we're looking for if p is we're actually going to be greater than 0.52. A nice concluding statement and on the hypothesis is to state what p really is. If you just gave those hypotheses to someone they'd ask well what is p. So, p is the population proportion of parents with a teenager who believe that electronics and social media is the cause of their teen's lack of sleep. Finally, we want to set a Alpha or a significance level which typically this is 0.05. This is basically the cut-off point of when we've found something to be significant. If we get a p-value, which we'll talk about later, that is less than 0.05. Now, we go out and collect our data. So, the Mott poll came back and said that a random sample of 1,018 parents with the teenager was taken and 56 percent said they believe electronics and social media was the cause of their teenager's lack of sleep. Before we go any further with this, we first need to check some assumptions. So, the first assumption we need to check is we need a random sample of parents, and the second one that will be checking is if our sample size is large enough and that ensures that we have our sample proportions being a normal distribution. How we check a large enough sample size is we want to see if n times p is at least 10, and n times one minus p is at least 10. So, it's like were there at least 10 people that said yes, and were there at least 10 people that said no to the question. Of course we don't know what p is exactly. So, instead of using p we're going to use a pseudo p, which is p naught and that is the null population proportion. So, under the null hypothesis, we believe our population proportion to be this, which for our case is 0.52 and our n again was 1,018. So now, we check these assumptions, so our random sample in our problem statement it was given to us so we've got a nice check there and then the next two n times p naught n times one minus p naught, we want to see if these are at least 10 with p naught being 0.52. So, we go in and we calculate it out we get 529 and 489. So, with a sample size of 1,018. That's a pretty large sample but you might have a smaller sample of like 30 and then you would want to make sure that these are satisfied to be at least 10, and again that ensures we have a normal distribution of our sample proportions. So now, we've set up our hypotheses, we've checked our assumptions, and now we can go on to actually running the tests and seeing if we have significant results or not.
