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Online Assignment #2Okay, now we’re at the inferential statistics part of the course, where we use statistics (numbers that describe samples) to make inferences – guesses – about parameters (numbers that describe populations).We do this guessing in two ways: estimation, and testing claims.This time we’ll do estimation.Let’s say we want to guess the average height of Mendocino College students. (I hope you have the CDBS20 program on your calculator. If you do, run it.) You’ll see that to the nearest thousandth the mean height of our data base is 66.975 inches. This is an x, because it’s a sample mean.So if we want to make an inference (a guess) about the population mean, ? (pronounced mu, like mew ), our best guess is what we got for the sample, 66.975 inches. We call this a point estimate. “Point” refers to a single number.So x is the point estimate for ?.But I’m sure you can see that if we had a different sample of 81 students, it’s very unlikely that their average height would be 66.975 inches, so what we do is form a confidence interval, where we go down from x a certain amount, and go up from x the same amount, which we call E, the margin of error. The resulting statement looks like this:x-E< μ<x+EI hope you can see that the bigger E is, the surer (more confident) we can be that we actually captured the population mean between x-E and x+E. What if E is 10 inches? Then x-E< μ<x+E becomes66.975-10 in. <?<66.975+10 in. or56.975 in.<μ<76.975 in.That seems to me to be a pretty sure bet: the average height of Mendocino College students is between 4 ft. 8 in. and 6 ft. 4 in. – a no-brainer, but also not terribly useful for, say, deciding how long graduation robes that the college orders should be.Anyway, we’re not going to go into how E is determined. Your calculator will do it for you. Here’s what you do. Go to the Tests tab under Stat:Pick TInterval:Your screen will look like this:At the top, you see there are two ways to input (inpt) the data. Since all our numbers are in a list, we use Data. Then we tell the calculator what list to look at (L3). “Freq: 1” just means that each number in list stands for itself; leave it as it is. “C-Level: 0.99” means that we want to be 99% confident that we’ve captured the mean. It’s called the confidence level. We’re going to use only the three most popular confidence levels, 99%, 95%, and 90%.When you get to Calculate, press enter, and you should see this (assuming you ran your CDBS20 program:Notice that the calculator gives the interval in traditional algebraic interval notation – left parenthesis, smaller number, comma, larger number, right parenthesis – but I want you to write it as, to the nearest tenth, 65.9 in. < μ<68.1 in.pronounced, “Mu is between 65.9 inches and 68.1 inches.”Notice that the calculator also gives you the mean and standard deviation of the heights in the class data base.What if you don’t have the data set in a list, but you do know the mean, standard deviation, and sample size? Then you opt for Stats in the Inpt line:Notice that when you pick Stats, whatever your last 1-Var Stats was, those numbers will appear, because they were stored to your calculator. So you just replace them by the current statistics:Notice that I put the statistics in to the nearest thousandth, for better accuracy. Pressing Calculate yields this screen:So the 99% confidence interval, with limits rounded to the nearest tenth, is:65.9 in. < μ<68.1 in.just what we got when we used Data. Use Stats only when you don’t have the data set in a list.So here’s the assignment:1) Do Worksheet #19 on p. 129. You don’t need to submit it, but if you have questions, let me know.2) Find and write the 99%, the 95%, the 90%confidence interval for these categories in the Class Data Base: Shoe size Age Number of petsRound your answers to the nearest tenth.3) When you use TInterval, the calculator gives you the limits of the interval but not the margin of error. So it displays, say 2.5, 4.5 instead of 3.5±1.0. 3.5 is x, and 1.0 is E. If you have the limits, you can find E by subtracting the lower limit from the upper, and then dividing by 2: 4.5-2.52=1.0. This works because if you add 2E to x-E, you get x+E. 2E is called the width of the interval.Use the information in the paragraph above to find, to the nearest tenth, the margins of error and the widths of the nine intervals you found in Problem #pare the widths of confidence intervals at different confidence levels. What do you notice as the level of confidence decreases?4) Find the 99%, 95%, and 90% confidence interval to the nearest tenth for the number of pages and the thicknesses of books in your project. Be sure to send your lists also. ................
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