 Hi folks, this is Don and I thought I might take a few minutes to answer a question that one of you posted in the preparation for the midterm exam and it has to do with constructing confidence interval for the population of mean mu. You're given the confidence level of 0.95, the sample mean x bar of 5.7, the population standard deviation sigma of 0.8 and an n of 41. Now Anthony, excuse me, Ernesto went through and worked the problem and he did it using the formulas that are given and Larson and other textbooks in which you go ahead and find your critical value of z, you convert your sigma to the s, the standard deviation of the sample by dividing of the square root of n which is 41, and you crunch those numbers down and you end up with a margin of error or really an interval with to be more precise that you add and subtract to the sample mean. Now Ernesto says rounded to 0.2 and depending upon what my stat lab asks or what your problem is, that's okay. Generally what I like to do is keep it out to 3 or 4 decimal places until the very end and then round and I did notice a little minor thing here. In his explanation he shows the x minus the interval less than x plus the interval which is correct and then he shows that same thing with the numbers inserted which is correct but on the final step he reverses it. Generally you would have the lower limit than the upper limit but the values are okay. But let's do it using first stat crunch and I'm going to bring up stat crunch. You can if you're interested find the critical values of z using the normal calculator in stat crunch because we've got a confidence interval that means we've got rejection or excuse me critical values both on the lower and the upper and we have to divide the alpha by 2 so that would be 0.025 I think. Click compute and we get a negative 1.96 for the lower end and by symmetry we know that on the upper end we have a positive 1.96 for our two critical values so that's useful. Let me get ready to actually calculate the confidence interval. One thing I wanted to point out if you remember whatever we're doing hypothesis test and then the confidence intervals around those you have to make a decision whether to use a z test or t test and there are two things that you need to look for if you're given the population standard deviation sigma then generally you use the z test and that is what we have in this case if you're not given the population standard deviation if you're given the sample standard deviation then generally you have to use the t test but here we have this population standard deviation and here's where I see a lot of students getting confused. We have our sample mean and let me pull this down again so we can see that of x bar 5.7 our standard deviation now here it gets confusing notice confusing it notice it doesn't say sample standard deviation it says standard deviation which implies sigma so we just put .8 in there we don't have to convert it to s our sample size is 41 we go down here and we click on confidence interval for our level make sure that's equal to our level .95 and we click on compute and we get our answer we get a lower limit of 5.455 or 5.46 and an upper limit of 5.94 let's see if that's what yeah that's what Ernesto got he rounded it to 5.5 which you you ran that all the way up you get 5.5 and round that oh that'll be close because if you you um round 48 to be .5 then 5 to .95 so that that would be close to 6.0 depends on on how you go about doing your rounding so that's how you do it using stat crunch it's really pretty straightforward and the only tricky thing is to remember when you're looking at this dialogue box that that is the population standard deviation not the sample standard deviation so you don't want to divide by the square root of n okay let me show you another way of doing this and this is using a add in that you can get uh called ph stat it's an excel add in those of you who are going to go on and do business for 30 you will need to get the ph stat add in generally if you have a Pearson account and I think it works even if you have a my stat lab account you can can navigate over to the Pearson site and download either a free copy of ph stat or you for 10 bucks can buy a copy and it's a bargain uh you're buying a copy you're not buying a license so once you get it you can continue to use it from then on and it's a good tool this is the output but let me show you how it works click on ph stat and we've got confidence intervals and here we have a choice we've got estimate for the mean sigma known which we do know sigma or you've got estimate for the mean sigma unknown and what that does is does the calculation that Ernesto showed you but let's just click on sigma known we bring up this dialog box our population standard deviation is 0.8 our confidence level is 95 our sample size is 41 our sample mean 5.7 uh if we had the raw data we could click here and input the range we don't need the title and we're not going to be concerned with the five not finite population correction but the there are questions in my stat lab that have to do with that uh ph stat will solve that for you so we just click okay and can't really tell because it just duplicated again it brought up our answer the 5.46 and the 5.94 which is what Ernesto got it gives you the critical value of z of minus 1.96 and from the standard error which is nothing more than the population standard deviation divided by the square root of 41 that's at 0.1249 you multiply those and you get the the interval half width and then you add and subtract that to the sample mean to get these so the ph stat is a pretty quick way of doing that and it's got a lot of um let me go back to it of neat statistical tools there's our descriptives and it gives us all kind of plots our histogram which you'll see a lot of stem and leaf scatter plots and the box plot which is very very useful and a dot plot is too if we're doing decision making which you use in business 430 you've got a number of things that are useful population distributions we have a lot of questions about that and and business 233 and there are the various distributions that we use sampling we can generate random sampling confidence intervals we've gone over sample sides that's a question on a lot of the quizzes um and then our hypothesis tests one sample test both the z t chi square and z test for proportion two sample for our raw data and that gives our pool variants and we'll talk about that two sample multi sample which is the ANOVA's that we generally do in the chi square and regression simple multiple and some more advanced versions of that so ph stat I would encourage you to look at um I wish I had mentioned it at the first part of the class for ten dollars it's uh it's a very useful tool it's bills right into excel and what it's doing if you look at these um equations are these areas blue is input yellow is the final output white is the intermediates you can see it's using the excel formulas to calculate these values same thing for the z value and the standard error and um you once you develop these spreadsheets if you relabel them you can just go back and put in uh new data i'm going to put in one and everything recalculate so you can reuse that it's a quick way to build a a workbook that has a lot of built in template for you and I have no stock and ph stat