 Okay here's our problem again from chapter 8 on the confidence interval for a difference in mean and reminding you that we're given the summary data for the samples. We are not given the sigma for the populations either first population or second population. So that tells us we have to use the t distribution as does the fact that we've got less than 30 for our sample size. So we're going to use pH stat in Excel to solve this rather than crunch all the numbers and build these equations and crunch the numbers. So the first thing we're going to do is go to add ends pH stat and you might be tempted to use the confidence interval table there or the dialog box. But if you look we've got mean mean population variance, population variance, population total, total difference. That's not the mean difference. That's not going to help us. So let's go to two sample tests. We've got summarize data and then we have a choice here of three different t-test and f-test, z-test, and so forth. We want to use the t-test for equal variances. Remember it told us that the variance were equal. In pH stat parlance that's pool variance and in many stat books it's called pool variance. So let's just click on pool variance and we'll bring up this dialog box. Let me move it out of the way here so we can see our data. The hypothesis size difference is always zero for mean difference. Our level of significance alpha is one minus or confidence levels so that would be point one zero. Our first sample size is nine and our second sample size is nine. Our first sample size is four four eight. Our second sample I'm sorry sample mean is four zero one and our first sample standard deviation is five point eight and our second sample deviation is eight point one. We always use a two-tail test for a confidence interval that puts alpha divided by two in each end. On the equal variance option or they call it the pool variance t-test you can click confidence interval. Make sure you put the right confidence interval in there sometimes forget that but it's 90% confidence interval which goes along with our alpha of ten. So we can click okay and we get the screen come up and it has all our input data which is in blue and there's the confidence level it's also input data. Once you generate one of these if you want to go around and just play what if you can change some of the data and it will output new information here. Down in the very bottom we have our upper and lower limits for our confidence level that rounds to 41 for the lower and 53 for the upper and if we go back to our problem those indeed are the answers that they asked for. So that's really how quick you can solve it just as a reminder if you wanted to check these upper and lower levels the output here gives us the difference in the actual sample means 47 and it gives us a standard error to find the margin of error that you add into track from the sample difference you just multiply the standard error times the upper and lower level let's just do that real quick lower level lower limit upper limit and I'm going to use equal my difference in two means plus I'm going to put it in parentheses my standard error multiplied by my lower critical value close I did it again that standard error in there I forgot to click it hard enough and that gets my lower level which is same value there upper level equal difference plus parentheses standard error times upper critical value of t and so that's I keep messing up there got to add in there we go Excel's messing up tonight 52.79 same answers that we get there so just to show you that you can do that and the reason I show you that if you're solving for the unequal variances in ph stat it does not give you directly a checkbox to get the confidence interval for some reason but it gives you again the standard error and the difference in the means and the critical values and you can solve for the upper and lower limits on the unequal variances the same way let me just show you that here is the same problem I worked using the unequal variances and as I said it didn't give us the upper and lower limits but I calculated the lower limits the same way the difference plus the standard error multiplied times the lower limit gives you those values so it's a very useful tool