 Hi, this is Dr. Don. I have a problem out of Chapter 7 on single sample test of hypotheses. And this sample, we're told that a politician claims the mean salary for managers in his state is more than a national mean $82,000. Assume the population is normally distributed and this population standard deviation sigma is $8,400. And we're given a random sample of 30 managers, a significance level alpha .01, and we need to test that claim. Okay, remember you need to read the problem very carefully and look for the claim. And here it's spelled out for you. The claim is the mean salary for managers in this particular state is more than, another key phrase. More than is a form of inequality as the greater than symbol. So that means it must be the alternative hypothesis because the null must always be a form of equality. We're given the population sigma of $8,400. That means in our intro course that we will use the Z distribution to do the test. Now we're given a lot of raw data here, 30 salaries. You would need to enter that into your technology. Remember if you're in my stat lab, you can click on the little blue rectangle and open this data directly in your technology. I'm going to use Excel. So let's move to Excel now. Okay, I've got Excel open. The raw data is here in column D. I've hidden the grid lines to make it a little bit easier for you to see on this video. The first thing we need to do is to get our sample mean. Now I'm going to click in that cell, start entering equal average because that is the function that Excel gives us to get the mean, double click to select it, and I need to select my data range there and then hit enter. And that gives me a sample mean of 84, 439. While I'm here, I'm going to get my count. Now we know this is 30, but if you had a large amount of data, you can use the count function, start typing count, select that function, and again, we'll select our data and then hit enter. And of course tells us we've got an N of 30. Now I always like to draw a sketch. I'm going to bring up a little sketch I've already drawn here. And on it, I've overlaid the normal distribution. Remember because of the central limit theorem, we know we've got an N 30 or more. That means the sampling distribution is going to be a normal distribution as well. Here is the population mean of 82,000 in the center. And over here, I've plotted our sample mean of 82, 449, but I made a typo. That should be 84, 49, excuse me. We need to know the probability of getting that value or greater. And that's the area in red here and the right tail. Now that jives with the fact that the alternative was the claim. In the alternative, we have a greater than symbol which tells us a right tail test, which means again we need the area in this right tail. Okay, we need to get the standard error of the distribution of sample means. And that's just the population standard division sigma divided by the square of N, so I'm going to click in that cell, equal. And I'm going to go up here and get my sigma in that cell divided by sqrt brings up the square root function. Double click that to select it. I just need my sample size, close it with a parentheses. And that gives me a standard error of 1 by 33.632. The test statistic is this formula. It's always the same, what we measure minus what we think divided by the standard deviation. It's the sample mean x bar minus the assumed population mean of 82,000 divided by the standard error. So I'm going to click in that cell, equal. Now to help Excel do the calculations in the order I want, I'm going to use a parentheses and I want to take my x bar minus my mu, close that, and then divide that by my standard error. And that gives me a standardized test statistic z of 1.5904. Now we're going to use the normal distribution, I start typing normal, N-O-R, and it brings up the number of options here. The one I'm going to use is the norm s disk. I'm going to open that up because that just requires the z that I just calculated, put a comma. And now you need to either give it a true for the cumulative, which is everything from left infinity to the point, or the probability density function. And of course for a continuous probability distribution like this, that doesn't really help us. So we're going to use true, close that, and we get a value of .9441. Now that is the left tail distribution. That's this area here, because that's what you get when you use the standard normal table or the basic Excel functions. To get the right tail, I'm going to click back in that cell, go up here in the edit function bar, and enter 1 minus, and click the enter key, and I get all these decimals, let's format that real quickly. I'm going to get rid of some of those decimals, drop it on down here to 056. Now if we compare that with our alpha up here of .01, .05 is greater than .01. It has to be less than or equal to alpha in order to reject the null. So this relatively large p value there would tell us to fail to reject the null. I hope this helps.