 Hi, this is Dr. Don. I have another problem out of Chapter 6 on confidence intervals. Here we're given some summary data from a sample and we're asked to construct the 98% and 95% confidence intervals for the population mean and then interpret the results and compare the WIS and if convenient use technology, which I hope you use stat crunch. Let's take a look at this. We're given a random sample of 55, so our N is greater than 30. That would make me a little more comfortable using the Z distribution, but let's look. We have the sample mean of $113, but we're given the population standard deviation sigma of 1750. So since we have the population sigma we need and the N is greater than 30, we should use the Z distribution for this set of confidence intervals. I'm going to jump over this for a second and go down to the last part of the question. I want us to interpret the results and the thing I want to point out to you here is that the difference between the first two statements and the last, this one says it can be said that the population mean lives in the interval. Down here it says it can be said that the sample mean lives in the interval. Remember when we're doing sampling, we're trying to get data and make an inference about the population. We know what the sample mean is, but we're trying to infer what the population mean is, so therefore the quick answer would be the population mean lives in the interval. Now remember up here in question help, you can click on that and you should be able to open up stat crunch. So let's get stat crunch up here. As we usually do for many problems, we start with stat and this is a Z stat, one sample with summary. And we bring up our dialogue box there. We type in the sample mean of 113, the population standard deviation 1750 and the sample size of 55. Go down here and click on confidence interval of the mean and let's get to the 95% first because it defaulted to that. I just click compute and I'm going to bring that up and we have our lower limit. They want two decimal places, so 108.37 and the upper limit is 117.62 and that's the answers they have there. Now we need to get the 90% and the quickest way to do that is just click options edit, bring this back up and we change the confidence level to 90% and we click compute. And here we have the lower limit of 109.12 rounding up and this is 116.88 rounding down and that was the answers there. Let me do one final thing. I just repeated the operation to calculate the confidence interval again so we could compare the 90% confidence upper limit and lower limit and the 95%. You can see that the 95% is wider. The lower limit is 108.37. Here's 109 so it's lower than that. The upper limit is 117.6 so it's to the right of that. So the more confidence you want to be means the net has to be bigger. The interval must be wider so I hope this helps.