 Hi, this is Dr. Don. I have a problem out of Chapter 8, Section 8.3 on dependent samples, which are also known as paired samples. I have another video on this same problem using StatCrunch. This one, I want to show you how to use the Excel calculator I have on my website. In this problem, a company wants to know whether or not its consumer product ratings have changed from year to year. They give us a table of data. They say, Alpha is 0.05, and they ask, is there enough evidence to conclude the ratings have changed? Okay, that language have changed tells me that the claim is that they have changed, which is a non-equal operator, which means that the claim must be the alternative, and we have a two-tail test. Meaning down here, the claim is, as I said, ratings have changed, and looking, we see that the correct statement of the two hypotheses, the null is the mean difference, mean before or last year minus mean this year is 0, and the claim is that the mean difference is not equal to 0. We need to find a critical value. We need to find the D-bar, the mean of the differences, S of D, the standard deviation, and the standard eye test statistic, and of course, make a decision and a conclusion. We're going to use the Excel calculators I have on my website. We'll go there now. This is my website, drdonright.com. When you get to the website, just click on Business 233. It will bring up a page and list a number of calculators I have there. We want the paired sample t-test, and we'll bring up that calculator and let it load. Now, I'm going to scroll down here a bit. I actually have two calculators, one for the summary data, which is what came up. We want the raw data in this case, and I have to admit this part is not as easy as I'd like it, but you have to do actually is to key in the data. This is the before, six, enter, eight, enter, five for the before, and the after is three, enter, eight, enter, three. That's not too bad with that group of data. I'm going to scroll back over here, and as quickly as that, just entering the data, we need to put in the alpha level, which is this one is 0.05, and the difference in this case is zero. We just want to know if there's a change. We need to select the alternative or the claim operator, which is not equal, and it tells us the claim as the alternative. It gives us the statement of the hypotheses, tells us the two-tailed tests, gives us the degrees of freedom, the critical values, plus and minus 2.365, and the rejection regions. We get the test statistic, which is D bar, use of D, 0.625, and the standardized test statistic, which is 1.106. We get the p-value, which is 0.3, which is greater than 0.05, which tells us we do not reject, but down here it gives us the decision, we fail to reject, and the conclusion is at the 5% level, there is not enough evidence support to claim. I might also mention that this calculator will give you the confidence interval for the test statistic. Hope this helps.