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This exercise is tedious but, if you want a more concrete and tangible understanding of sampling distributions and the two theorems presented in this chapter, then it may have a significant payoff. At the end of this problem are listed the ages of a population of college students $(N=50) .$ By a random method (such as a table of random numbers), draw at least 50 samples of size 2 (that is, 50 pairs of cases), compute a mean for each sample, and plot the means on a frequency polygon. (Incidentally, this exercise will work better if you draw 100 or 200 samples and/or use larger samples than $N=2 .$.)a. The curve you've just produced is a sampling distribution. Observe its shape; after 50 samples, it should be approaching normality. What is your estimate of the population mean $(\mu)$ based on the shape of the curve?b. Calculate the mean of the sampling distribution $\left(\mu_{\bar{X}}\right) .$ Be careful to do this by summing the sample means (not the scores) and dividing by the number of samples you've drawn. Now compute the population mean ( $\mu$ ). These two means should be veryclose in value because $\mu_{\bar{X}}=\mu$ by the Central Limit Theorem.c. Calculate the standard deviation of the sampling distribution (use the means as scores) and the standard deviation of the population. Compare these two values. You should find that $\sigma_{\bar{X}}=\sigma / \sqrt{N}$d. If none of the preceding exercises turned out as they should have, it is for one or more of the following reasons:1. You didn't take enough samples. You may need as many as 100 or 200 (or more) samples to see the curve begin to look "normal."2. Sample size (2) is too small. An $N$ of 5 or 10 would work much better.

Intro Stats / AP Statistics

Chapter 6

Introduction to Inferential Statistics: Sampling and the Sampling Distribution

Sampling and Data

University of North Carolina at Chapel Hill

Oregon State University

Boston College

Lectures

05:14

How important is the assum…

24:15

To complete this exercise …

21:57

The data set mentioned in …

17:37

Please provide the followi…

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NAEP scores Young people h…

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Use the information below.…

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Several statistics are com…

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You can construct a confid…

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According to an article in…

01:18

Find the sample size requi…

01:45

For Problems $7-18$, pleas…

12:40

Independent observations $…

05:05

03:00

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01:44

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The sample size needed to…

Hi. This question. We need to use many tab, so I'm gonna show you how to do most of the steps. So, first of all that you have to go on many tap. I use many top 17. So you go to college, then just goto Rhonda Data on Click Normal. You're gonna get something like that. Okay, then just put number of frogs 2000 as, ah, pacified. And then the question and just put them and see one, which is the first column. Um, we're gonna use the standard normal distribution, which is, um, a normal distribution off me and zero and standard deviation one, then head. Okay, then you're gonna see something with ah, uh, the The date is gonna be generated in and see one, so go back toe graph. Ah, you're gonna see ah, Choice called instagram. Then click on that with fit. Don't choose the simple one. Just go ahead and click with fit and and choose. The data said, that's we already generated, which is on C one. I happen toe called 1 51 for the question. So and as you can see here, it's absolutely normal because we generate from normal distribution and we get the the mean very close to zero and standard deviation off one. And the sample size was 2000. After you finish this one, you have to generate now at least samples from whatever we generated. So we are not generated from from a distribution that so But from the from the column that we just drink. So you have to go to Calcutta clearer random data and go Ah, to this option sample from columns. And after that, you're gonna generate Ah, turn off them. So see one tool. See, Tim, After you finish this one, you have to go to Stat Rose to the sticks here, and you're gonna be navigated to this one. So you go ahead and choose standard deviation here and choose all the columns. As you can see here from t one, I just rename it. Do you want to teach in or basically from sea to to see 11. So the 1st 1 was generated from normal distribution on from C two to C 11 is generated from the first column. And just click on this one center deviation and just choose them variables that we were just generated from the sample on store the the values off standard deviation and in any count that you would like, but usually but it here. So I haven't to To put it and sit well on, I rename it to standard deviation, then Hecht. Okay, After that, you have to do a comparison between the two values. Something like that. Um so let me show one and you're gonna continue. So here's the number biz. It's 12 and so on on, then you're gonna get something like that. The probability off it, Andi any of it, The area to the left. So for this probability, you can we know that we have 200 samples, so that will be won over 200. This one is going to over 200 and so on. So, basically, whatever ends in over so, honey and hear from the defense that we were gonna fund that as going Oh, the 93 on you gonna find this one is 1.1 all three and so on. So I'm gonna give you justice numbers for 10. It is 18.3. So after you calculate this one, you gonna find that Onley probability and in one is matching. But the other one actually are higher than calculated. Hopefully that Wasim full anti

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