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How important is the assumption "the sampled population is normally distributed" for the use of the chi-square distributions? Use a computer and the two sets of MINITAB commands that can be found in the Student Solutions Manual to simulate drawing 200 samples of size 10 from each of two different types of population distributions. The first commands will generate 2000 data values and construct a histogram so that you can see what the population looks like. The next commands will generate 200 samples of size 10 from the same population; each row represents a sample. The following commands will calculate the standard deviation and $\chi^{2} \star$ for each of the 200 samples. The last commands will construct histograms of the 200 sample standard deviations and the $200 x^{2} \star$ -values. (Additional details can be found in the Student Solutions Manual.) For the samples from the normal population:a. Does the sampling distribution of sample standard deviations appear to be normal? Describe the distribution.b. Does the $\chi^{2}$ -distribution appear to have a chi-square distribution with df $=9 ?$ Find percentages for intervals (less than $2,$ less than $4, \ldots,$ more than $15,$ more than $20,$ etc. ), and compare them with the percentages expected as estimated using Table 8 in Appendix B.For the samples from the skewed population:c. Does the sampling distribution of sample standard deviations appear to be normal? Describe the distribution.d. Does the $\chi^{2}$ -distribution appear to have a chi-square distribution with df $=9 ?$ Find percentages for intervals (less than $2,$ less than $4, \ldots,$ more than $15,$ more than $20,$ etc. ), and compare them with the percentages expected as estimated using Table 8.In summary:e. Does the normality condition appear to be necessary in order for the calculated test statistic $\chi^{2} \star$ to have a $\chi^{2}$ -distribution? Explain.

Intro Stats / AP Statistics

Chapter 9

Inferences Involving One Population

Section 3

Inferences about the Variance and Standard Deviation

Confidence Intervals

University of North Carolina at Chapel Hill

Oregon State University

Boston College

Lectures

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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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