 Hi, this is Dr. Don. I have a problem out of Chapter 8 where we're dealing with the difference in two population proportions. In this problem, we're told that we have a study about the effectiveness of using magnetic insoles to treat a form of heel pain, and it tells us that 53 subjects wore the insoles. 48 did not wear the magnetic insoles. We're given an alpha, and we want to answer the question, can you support the claim that there is a difference in the proportion of subjects who felt better? We assume the random samples are independent. When we look at this information, one thing that should jump out to you given these pie charts, that we're dealing with two categorical variables, which we have counts. And when we're given counts and a categorical variables, those are proportions, all proportion hypothesis tests that we run use the z-test. First thing we have to do is identify the null and alternative. Here it says, can you support the claim there is a difference? If there's a difference, that means that the two proportions are not equal. So the proportions of the two groups are different. And if we look at the options there, we would find over here that proportion one equal portion two, and the claim is that the two proportions are not equal. The first thing we need to do is to find the critical values and rejection regions. But we're going to do this using an Excel calculator I built on my website. Let me show you that now. Okay, I've navigated to my website and to the calculator. The link to the calculator is in the page below. There are two forms of the calculator. One version, the one that comes up, you enter the proportions and the n. The one we want, scroll down here, we've got the sample x is given, which means we can put in the counts and the number, the opportunities. So here the count for the first sample was 17, the opportunities were 53. The second sample had a success of 22, and the opportunities were 48. The alpha is 0.07. Now we scroll down here, you can see that this calculator checks to make sure that we can use a normal approximation, which is appropriate because we need to check that in actuality. And as we drop down, we need to select the claim operator. And we just click the drop down button. And in this case, the claim was not equal. So that tells us that the claim is the alternative. And it shows that the null is p1 equal p2, claim is p1 not equal p2. We have a two-tailed test. And as we scroll down, we get our critical value of z plus and minus 1.812. It gives us the rejection region. Any standardized test statistic z less than minus 1.81 or greater than positive 1.81 would begin the rejection region. It calculates the test statistic, which is just the difference in the two proportions. It gives you the confidence interval around that test statistic. It gives us our standardized test statistic minus 1.42. And it gives us the p-value 0.15. Now you would remember that you need to check to see if this standardized test statistic is in the rejection region. Or if the p-value is greater than alpha, this calculator does that for you. It tells us this standardized test statistic is not in the rejection region. p-value is not less than alpha. It gives you a decision that we fail to reject the null because z not in the rejection, p not less than alpha. And it gives us conclusion. At the 7% significance level, there is not enough evidence to support the claim that the two proportions are not equal. So I hope this helps. And if it does help, please consider subscribing to my YouTube channel, Stats Files. Just click the big red subscribe button.