 Hi, this is Dr. Don. I have a problem out of Chapter 6 on confidence intervals and in this problem we're asked to find the critical value of t, not z, for the confidence level c equal 0.95 or given the sample size and equal 14. If you remember from the last video, when we're doing critical values of z, the only things we need to determine the critical value or the confidence level and that's it, just the confidence level. But when we're doing the t distribution, we need to also know the sample size. So that makes it a little more complicated to find the critical value. If you remember when we're looking at critical values for confidence intervals, we need to think about the confidence level c being centered around the mean and we need to find the critical values associated with these areas in the tails, which is 1 minus c divided by 2. Half of this area that's not blue is located in each tail and so we end up with two critical values, a lower critical value or a minus critical value and a plus critical value. So I'm going to show you how to do this using Excel, but first let's go back to our problem and you can see they give you the t distribution table and on this particular problem, the t table is not that bad. I want to click on that and it opens up and it gives you across the top this particular version of the t table, confidence levels of 0.8, 0.9, 0.95, 0.98 and 0.99 and the degrees of freedom and all you need to do is just find the intersection of the degrees of freedom which for t distribution is just the sample size minus 1 and in this one it would be 14 minus 1 would be 13th the degrees of freedom. We read across and we look down in the column for 0.95 and we get 2.160 which is the value they want there. That's not too bad, but what do you do if you've got a request for a confidence level of 0.83 or 0.96? Hmm, a little more problematic. That's why I recommend using StatCrunch or Excel in case you run into one where you've got to find something that's not in a table. So I'm going to close that out of the way and we're going to open up Excel. Okay, I've got Excel opened and as usual I'd like to label my cells and also use some color coding to help you remember blue is places I enter data, yellow are cells that I have formulas. We're given the confidence level and the sample size and the problem. I'm going to find the area in the tails first of all by equal 1 minus that confidence level C to get started then I want half of that so equal I'll take that value and divide by 2 hit enter. So now I've got the area in the tail and as I said when we're doing the t distribution for single samples it gets much more complicated when you have more than one sample but in this case we're dealing with a single sample confidence level we just need the degrees of freedom which is equal to the n minus 1 and that gives us our degrees of freedom. To find the critical values we've got two ways in Excel I want to start in that cell click equal t to get t distribution options up there we're going to use an inverse because we've got a area and we want to find the t so I'm going to click on that t inverse to insert that and it asks for the probability which is our 1 minus c over 2 comma and our number of degrees of freedom which is that cell and hit enter and I get minus 2.160 and you recall that when we're dealing with the standard table or the standard functions in excel we get the area under the curve from left infinity to our point so we need to get the absolute value of this and I'm just going to insert my cursor up there in the formula bar a b s to call up the absolute value function put a closing parentheses and hit enter and so I've got my value there the plus one we want 2.160 which is the answer they have over here now the other way of getting this in excel you hit equal and I'm going to go back to the t distribution if you notice down there we've got a t inverse two tail and that recognizes the fact that for confidence intervals we're always using a two tail and this particular function I'm going to click that we want the probability but here we don't want the probability half of that value we want the whole probability the two tail probability so I'm going to select the 1 minus c comma and my degrees freedom and hit enter and there we get our positive value 2.160 and again remember you use the equal formula text click on that to get that function I'm going to select that cell get the formula in these cells I'm just going to click on that formula get my little plus cross hair and drag down and now I've got the formulas for all of those so you've got two ways with excel to get your critical value and again one of the beauties of building your model in excel and formatting and labeling it is that you can reuse it let's go back over here in this problem and I'm going to reload to get a different value of the confidence level and the sample size and now we've got a confidence level of 0.98 and a sample size of n equal 12 so we go over here to our excel I'm going to change that to 0.98 hit enter and hit my sample size to 12 and hit enter and it recalculates and we can see that our critical value of t is 2.718 which is the answer one over here so another benefit of using excel I hope this helps