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Which of the following calculations is NOT derived from the confidence interval?Choose the correct answer below:0 A Difference between the limits , 2E = (upper conf...

Question

Which of the following calculations is NOT derived from the confidence interval?Choose the correct answer below:0 A Difference between the limits , 2E = (upper confidence limit) (lower confidence Iimit) (upper confidence limit) _ (lower confidence limit) The margin of error; E =The population mean p = (upper confidence limit) (lower confidence limit) (upper confidence limit) (lower confidence limit) The " point estimate of p, X =

Which of the following calculations is NOT derived from the confidence interval? Choose the correct answer below: 0 A Difference between the limits , 2E = (upper confidence limit) (lower confidence Iimit) (upper confidence limit) _ (lower confidence limit) The margin of error; E = The population mean p = (upper confidence limit) (lower confidence limit) (upper confidence limit) (lower confidence limit) The " point estimate of p, X =



Answers

Estimate the minimum sample size needed to form a confidence interval for the proportion of a population that has a particular characteristic, meeting the criteria given. a. $p=0.81,95 \%$ confidence, $E=0.02$ b. $\quad p=0.81,99 \%$ confidence, $E=0.02$ c. $\quad p=0.81,95 \%$ confidence, $E=0.01$

So for all kinds parts of the problem, we are going to use the formula, those Z squared, I used this, Yeah, tv standard deviation squared divided by e squared. Yeah, So starting with answer a we have a 95% competence Of a standard deviation of 30 and e value equals to 10. So first we want to get the confidence interval into is a score. So we would take put it a small and subtracted from one. So you would get points There are five and then you would Divide that by two, that equals .025 and then you would look on your table and see what that equals and you'll find about you 1.96. So now we can put it back in our formula would be 1.96 squared I'm already which was the standard deviation and you divide that by e squared which was 10 and you get an answer of 34 557 and a decimal is the best around up. So the minimum for this one would be 35 I'll do the same thing for B and C. So we had a 99% confidence interval, The standard deviation is 30 and e equals 10. So we're gonna start with the confidence interval, 88.01 and when you divide that by two you would get .005. And if you look that up on a busy table value is 2.58. So now we can plug it into our formula, So maybe 2.58 square types 30 squared Divided by 10 squared. And you get 59 ft nine. So your minimum value Would be 60 participants. Then finally, 1st Steve we have again The information 30 and 95% confidence in a real But our E has changed a five. So you look different. So since we're already doing the 95 in the per A we'll just use that number. So one point not six squared times 30 squared. Bye Bye. five square this time. And you get 138.3, and you would Round up to 1 39 minimum participants, right?

Oh so to do this problem. The formula we need is the square types of P value Times one -P divided by he squared. Yeah. So so we know we started with per day So RP value is 037. There is An east score of .05 and we have 80 confident center pill. So the first thing is what's going to want to take the confidence interval and change it to a Z score. How we do that is we subtract it from one. So we can point to, we divide that by two because half of it, That would be .1. And when you look at up on disease table, I know that the score will be .54 and now I can plug it into our formula. So it would be put by poor square Times .37 times 1 -3.7 Divided by .05 Squared. Yeah. In when you put that into the calculator right now it's 27.1 night but we need a whole number because sample size one person in the sample just can't be a fraction as a whole. So we would have to Round up and up the 28. Yeah, no do part B. The P value was .37 You have a 90% confidence center rule ENRE value is .05. So listen, we would have to change the competence thinner will do these four will do the same thing. Yeah .05. And we looks set up on it and see table. Find out if the score is equal to 1.64. Now we can put that into our formula. So maybe 1.64 squared times .37 times my 1 -3.7 invited by .05 Squared. And we get 250.78. 50.78. And Like he said, we would have to round up to get the minimum sample size that for 251 now for C. P values, it's the same as a 80% confidence interval. The E score has changed this time. So, so because we did the 80% confidence and everyone party, hey we can just use that score because it would be the same. Good .54 sq Types. .37 times one was .37 Divided by .01 Squared. And then calculator unit 679.72. And we kept round up to 680

So for this question we will be using the formula for all three parts is c squared standard deviation squared quite a by the evil he squared. So for a we have a standard deviation of four, We have a 95 confidence interval. Mhm And E equals one. So first made after you switch the confidence interval into a Z score, So you would change it to a distance of traffic from one And then take that divided by two. And for this one you get .025, you look that up on what that score would be on AC table Andrew Value is 1.96. So that's what you'll be using the formula. There we go. 1.96 squared times four square divided by one square, which would just be one of course. And when you put this in the calculator, you get 61.5, but you would need to round up Because you can't really have a half a person, so it would be 62, the property well, I do something pretty much just saying, be just different value. So you have the standard deviation up for 90 99% confidence interval, Your E is equal to one. So switch the comments and a rule to a Z score again. Oh right, to and you get points here is your efi and when you look that up on easy table, The value is 2.58, So now we can plug that into the formula To be 2.58 squared Times four square divided by one squared again, This one you hit when I was 6.5, but we would need to round up For this case, so the minimum participants would be 107. And then finally, for C you have a standard deviation for 895% confidence interval, what he is able to 8950.5 and because we already did the confidence interval to disease from apartment, we can just use that number. I was walking Point or 1.96, I was four squared divided by a half squared and you get 235.9. But again, we have to round up, so that would be A minimum of 246 participants. Okay?

All right. And this question we are looking at finding the minimum sample size needed for um achieving a given margin of error. And on this one we're using the same formula as before. So first thing we have to do is figure out our alpha, which if it's a 95% confidence, that's gonna be a 5% alpha. We split that in half to figure out our Z score based off of the appendix table in the back. So I'm gonna go to tea with a tail probability of .025. I'm going to scroll all the way down and I get 1.96 which is always the Z score for a 95% confidence interval, which is the most common one used. So then I'm going to plug in to my formula 1.96 squared times 0.5 Tom's .5 divided by my given margin of error squared. And we can enter that into our calculator and copy and paste will be your friend on these And we get 2401 for part B. Were changing too. A Um 99% confidence in it. Well, it's the only thing changing. So going back to our table or tail probability is half of a percent um which is to .576 2.576 Squared times 0.5 thomas 0.5. Remember we're using our most conservative estimate for P. Hat, which is .5 because it's not given otherwise. And then our margin of error I believe is still oh two Squared. Yes it is. And we can get our sample size clearly goes up rather significantly. We always round up one because we're talking about people here, we round down our margin of error is going to shift down a little bit and we don't want that. And then part C. again a 95% confidence, So 5% alpha, which is the most standard we use, Um which is the 1.96 plugging into our formula and our margin of error is smaller, so it is going to go down and we can copy and paste that into our calculator, like what we had on um part A and just change the point to To be much smaller at .1 and we get 9604 would be are needed sample size for that one.


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