 Here is our problem. The Excel file sales data provides data on a sample of customers. An industry trade publication stated that the average profit per customer for this industry was at least $4,500. Let's pause there and the next sentence is our first question. Using a test of hypothesis, do the data support this claim or not? Okay, let's highlight something. The critical phraseology here is that the industry claims that the average profit was at least, and here they're talking about the profit for the entire population of the customers in this industry. The Excel data that we have is on a sample of the customers, so that is something we need to think about, and they tell us to use a test of hypothesis, do the data support this claim or not? Okay, let's look at our data. This is the Excel Evans file sales data, and we've got a lot of information here. We've got the percentage gross profit, the gross sales gross profit, industry code, and competitive rating. What we want, because the question has to do with profit in terms of dollars, not percentages, is this column for gross profit. And by inspecting the data, we can see, if we scroll down here, we have 60 values in our sample. So we've got an N of 60. To use pH stat, we click on add ends, and then we look over here for pH stat. Click the little triangle to open up the expanded menu, and we're doing a one sample hypothesis test because we just have this one sample of the sales in that industry. And then we have to make a decision. What type of hypothesis test are we going to run? Do we do the Z test for the mean? Well, we're interested in the mean, but we don't know sigma, do we? We have a sample, and we can calculate the standard deviation for the sample, but we don't know the population standard deviation, so we can't use the Z test. We're not talking about the variance, and we're not interested in a proportion. Again, we're interested in the mean, so that leaves the T test for the mean sigma unknown, which is our situation. Click on that, and we bring up the secondary dialogue box. Our no hypothesis was that the mean equaled 4500, and the level of significance was not given, but it's safe to assume that alpha is .05. Now, the next decision. Do we know the sample statistics? We know the sample size, 60, but we haven't calculated the mean or standard deviation, and we can do that using PhStat and Excel, but in PhStat we don't have to do that. We can click on sample statistics unknown, and then we want to enter the sample range. Note that the default is selected that the first cell contains a label until when we select our sample cell range, we will include that label. To select the sample cell range, click on this little box over here, and it opens up another dialogue box, and all we have to do is click on that first cell, the title of the column, Gross Profit, and drag down to the bottom. We've got our range selected. We click on the little icon again, and that puts that range inside the PhStat dialogue box. The next decision is what type of test are we running, a two-tail, upper-tail, or lower-tail? Well, let's go back for a minute and look at our apothesis. Our null has a greater than or equal. The null always has some form of equality. Our alternative is the complement of the null, and the complement of greater than or equal is less than. So we're talking about a left-tail, and you can remember that by looking at the direction that the less than operator points. It points to the left, our lower-tail. So we can go back, and we can click on lower-tail. Now, we can go ahead and I'm going to label this P-A-R Part A, so this is the first part of our question, and I'm going to click OK. And we get this tab open up that summarizes our hypothesis test. The null hypothesis was mu equal to 45. Now that confuses a lot of people because the default there is the mean equal. This just is an artifact of the math behind the hypothesis test. If we conduct the test for the equality of 4500 as opposed to the less than lower-tail, and if that test is significant, then everything greater than 4500 would also be significant, if that difference. So just keep that in mind. We get the level of significance alpha, sample size of 60 as we said. It calculated the sample mean of $4239 and a sample standard deviation S bar of $5,812 roughly. Calculate some intermediate values, gives us the degrees of freedom for the t-test, which is n minus 1 of 59, and calculates our test statistics of minus 3.476. That's less than the mean is to the left, but is it far enough to the left? Well, the critical value for this test, this t-test, is again on the left-hand or lower side, and it's negative 1.67. We can tell that the test statistics, negative 0.3, is not greater than the lower critical value. Therefore, it's not in the rejection region, and that tells us we do not reject the null hypothesis. But we're also given the p-value, the probability associated with this hypothesis, and it's 0.365. That is also greater than the alpha 0.05. It's not less than the alpha. Therefore, it also tells us to do not reject the null hypothesis. So, if we go back, what does that tell us? Okay, let's summarize. Here's what we got from PHTAT. The test statistic was not in the rejection area, and the p-value was not less than the alpha value of 0.05. Thus, we do not reject the null hypothesis. What can we conclude? Our conclusion is we do not have sufficient evidence to reject the claim. Remember that the null hypothesis was the claim, and since we cannot reject the null hypothesis, we cannot reject the claim. That the mean profit was at least $4,500. Let's look at the second part of the problem, and I'm going to let you do the PHTAT part yourself. But let's define what the problem says. The company believes the average profit exceeds $4,500, and we're asked to test a hypothesis to determine if there's evidence to support this. Okay, the critical phrasing again is that the company believes the average profit exceeds. So I'm going to highlight that. This time in a green. Exceeds. Exceeds implies a greater-than operator. So if we go down and set up the hypothesis, the claim is that the mean profit is greater than $4,500. Again, that exceeds. And because it includes a greater-than operator as a form of inequality, it has to be the alternative. The claim is the alternative. The null has to be the complement of the claim, or the complement of the alternative in this case. So it has to be everything except greater than $4,500, which is a form of equality less than or equal $4,500. Okay, with that information, you should be able to go to PHTAT and set this up and run the T test for the single sample mean with Sigma unknown again on your own. Good luck.