 If you find this video helpful, please consider subscribing to my YouTube channel, TheStatsFiles. Just look for the big red button. Hi, this is Dr. Don. I have a problem out of Chapter 7. So let's scan it. And what I want to do is to read the actual problem statement here. We're given a sample of 1,000 home buyers. We find that 443 found their real estate agent through a friend. We're given an alpha, and it says, can you reject the claim that 45% of the home buyers find their real estate agent through a friend? Well, this is a proportion problem. We can see we've got 45% there for our assumed population proportion. And we're given, again, a proportion here, 443 out of 1,000 in our sample. So we can look at this, and very carefully, we see that the claim is that 45%. So the proportion is 45%, tells us this is an equality. And since the claim is in equality, it must be the null. And if we look down here, we find this is the option there. The null, the population proportion P is equal to 45%. And the alternative is the complement, not equal to 45%. We need to find the critical values. We need to get a sketch, and we need to get the standardized test statistic, and then make a decision. So we're going to do this using stat crunch. Over here, I've got stat crunch up. We're going to click on stat. And then we go down. And although we always use the Z distribution, the Z test, for proportions. That crunch has a special Z test for proportions. And it's found under the proportion stats option, one sample with summary. So we bring up the dialog box. We're given the number of successes, which was 443. The observations was 1,000. We're going to make sure that's checked to perform the hypothesis test for the population proportion P. The assumed value is 0.45. And we want to make sure that the alternative is the complement, which is the not equal. And we're going to go ahead and get the P value plot down here. So we click compute, and we bring up our answer dialog box. We've got to expand it just a bit in order to get all the information there. Check it real quickly to make sure you set it up. And we can see we've got our null and alternative set up properly, and we're using a proportions test. Our Z standardized test statistic is minus 0.444, which rounds to two decimal places of minus 0.444, which is the answer they wanted us to give them over here. The stat crunch gives us a P value. And that very large P value, 0.6564, tells us that it is much greater than alpha of 0.08, therefore we would fail to reject as our decision. Let's look at the graph. Here is the graph. It gives us the standardized test statistic minus 0.449, and that's right there. And of course, we check on a two-tail test, we divide the probability in the two-tails. So this is half of 0.6564, and this other red area is the other half of 0.6564. Now we need the critical value. So we go back to stat, and we're going to go on calculators, and we get the normal calculator to come up, and we can just take the defaults, which is the standard normal distribution values, make sure we have the left tail selected to be consistent, and we're going to put our alpha divided by 2.04, and there, and we click compute, and we get the lower side critical value minus 1.75. And by symmetry, we know there's our upper critical value, positive 1.75. So if we look at our chart here, we would know that our critical value is somewhere in here minus 1.75. There's our test statistic minus 0.449. It's definitely not up here in the rejection sum. So again, we get fail to reject. We look over here, there's our answer minus and plus 1.75. And the graphs, we need the two-tail graph there for our two values of critical values of Z. There's our standardized test statistic. The last part is to draw a conclusion. Now we know we failed to reject, and there's two options here that have failed to reject. The first says there's not enough evidence to reject the claim. The other says there is enough evidence to reject the claim. Well, we know that the null is the claim. The second one that was trying to confuse you to think about the alternative, but the null is the claim and there was not enough evidence to reject the claim that 45% buyers find the real estate agents. So I hope this helps. And if it does help, please consider subscribing to my YouTube channel, TheStatsFiles. Just click the big red subscribe button.