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You may need to use the appropriate appendix table or technology to answer this question_ In a survey, the planning value for the population proportion Is p* 0.28_ ...

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You may need to use the appropriate appendix table or technology to answer this question_ In a survey, the planning value for the population proportion Is p* 0.28_ How large a sample should be taken to provide 95% confidence interval with margin of error of 0.05? (Round your answer up to nearest whole number:)

You may need to use the appropriate appendix table or technology to answer this question_ In a survey, the planning value for the population proportion Is p* 0.28_ How large a sample should be taken to provide 95% confidence interval with margin of error of 0.05? (Round your answer up to nearest whole number:)



Answers

In a survey, the planning value for the population proportion is $p^{*}=.35 .$ How large a sample should be taken to provide a 95$\%$ confidence interval with a margin of error of .05$?$

In question 19. We're going to be finding the 95% confidence interval for row and were given four cases. And in these four cases we have the sample sizes and the sample correlation, and we're going to use this devil off confidence belts to determine the nature vipers and confidence interval. So we need to have vertical lines and horizontal lines. And for those practical result, your lines are going to be using these red lines here. If you're going to use your book, you could use a ruler to draw the magical Ninth. So let's start with the first case. In the first case, we have r equals 0.6, so we should move to r equals 0.6. So I would move my leg two r equals 016 that we have. Guess then, after that, a move my horizontal line so that it's much is a sample size of 50. We have two fifties. We have a 50 here that talk, and we also have a 50 here. The bottom Celeste us from the top and you go to the bottom. So I'm going to move my lane up until I get to 50 50 eso. As you can see, we have 50 here and goes up until it meets. Yeah, well, we have a 50. Here it goes until it means the vertical line at this point. So let me just suckle that point for you to see that this is where the line the 50 line for 50 meets with with the vertical life. Place me to move. It's likely up. Yes. So that's the point. Where the two queen site. Okay, so that's the fast 50. The second fifties, at the bottom. You can see the second fifties here, and I have to see where two lines meet and find it somewhere here so they know how to move my line up. So now we have it. Thank you to that point. Good. So now we have our to limits s so we can see clearly that of the 95 confidence interval is from 0.4 on the bottom two 0.7, this is 0.7 and this is your 0.8 and 0.75 So we could approximately to be 0.74 No, that's how fast confidence interval. So it's 0.420174 Then the second confidence interval this when the sample size is 12 and are easier. Negative Europe for five. So I want to do that and we're going to see how that goes. Three. Move this fast. Then we move. Must to article negative 0.45 Remember, we had a rule that this would be much easier and faster. So 0.45 this year and then we go to 12. Sample signs off 12. This is where the sample size of trophies. So the top line me. Move this lying down. Yeah. So the top line is here? Yes, there we have it. Onda, Uh, the bottom line is here. We should look for 12. Case 12 is here to this point. Yes. Okay, so now our 95% confidence interval stance from negative 0.8, slightly above negative 0.8, we could say negative. 0.81 It's going to be from negative 0.81 to Ah, the took back slightly above positive one. Good. This is one. And this is 1.5. So this is 0.1. Yet because 0.1. Then this would be 0.15 tweets from negative 0.812 Positive. 0.15 Okay, let's go to the next one. So we have an R equals 0.8 toe. Have to move my vertical line to the side. Believe it's easier to move from here. Okay, so going all the way to 0.8. Good. And after that, we go to a sample size off six. So we need to commit Mickey concert with the sample size of six. Okay. On where they meet, the me tell my head top curing. Then we now go to the other line and look for some process of six as well. We need to move the hours under line and wicked coincide. Yeah, I got it the length. All right. So go up until where the line coincide. So six coincides at that point somewhere, the center good. So now we are able to tell how where the two points are. So as you can see, the fast point is just above zero. And that's going to be yeah, slightly above zero and equal six. And that's going to be at zero point five, just above 0.5, because his 0.6 0.6 actually yes. 0.6 to the top part Here is 0.95 case of one more to go. We start with our negative 0.56 We have to move now. You are vertical nine. Remove it to negative zero from 560 This is negative floor. This is Nicotine Five, this is negative. Zero point 55 slightly to the left. So I assume that's approximately negative. 0.56 Now we're looking for sample size of 200. Okay. Very close to each other. Going to start here. The rights of 200 the 1st 200 year and the 2nd 1 200 is these points. We're going to move this land until gets down. Yeah, I have it. Okay, so this is where 200 ease death case. So you see that they're very close to each other now. Unless that and see the the law won its negatives. Negative. 0.6 five. But someone is negative. 0.65 to que that's faster in the 2nd 1 It's negative. 0.4 five. Good. And now we have all the confidence intervals for the four cases. And now you know how to read from the confidence bells.

In question 18 We're going to be determining the 95% confidence interval for the true population linear correlation coefficient and were given four kisses. And in these four cases, we know the sample sciences and and we also know the sample correlations are and to determine the 95% confidence interval for road the population correlation, we will be using the confidence belts for the correlation coefficient. The's confidence belts are such that on the Y axis will have this skill off rule here and on the X axis will have the skill off art, which is a sample correlation. Now every belt is corresponds to a given sample. Thanks to all these belts are for different sample sizes. So this is the sample size off 345 and so on. So we're going to start off with the fast case. In the first case, we have a sample size off eight still market then. So we have eight appearing twice so that we get the to enter the two limits for the confidence interval. Now you also have AJ 0.2. So we're going to start here us that 0.2 and from there. We're going to draw a vertical line. I'm going to try and draw a straight vertical nine. No, it's not possible to do this free hand because I'm using My mouth's going up. But when you're doing this, he should use areola the pencil in case you want to. I guess you make a mistake and you want to do it again. So Drew a straight line van Tickle nine going up. And once you're done, look it The points where the belts marked for the correct sample size. Cross the vertical lying. And these are the bells the fast built is here. Eat the bottom here. So we're going to find where the belt for eight crosses the vertical line, and I can see that point there also at the top. I see that the belt with sample sizes and eat. I see that the belt crosses. It's here. Okay, so once I have those two points off intersection, I should drew our results online, both cases to be able to get the skill off peak. So let's draw fast particle fast horizontal line and fast horizontal line is here, which will use a ruler for this to be much easier. So that's where the line crosses the y axis there y and then we go to the second horizontal line. You may my legs also straight so I can do this. When you do this, you have to use a ruler to make sure you get the accurate reading. Okay, so our confidence interval is going to range from point A to point B on the Y axis. So in point A, we need to read the value we need to read the value that on the Y axis that corresponds to the point where the line crosses the Y axis and as you concede somewhere just because of center here, zero negative 0.5 and this is negative 0.6. So you'll notice that it's somewhere in between. Negative 0.5 and negative 0.6, and Green will see that it's actually between negative 0.5 and negative 0.55 So we'll say that the fast limit is negative. Zero points 5 to 5. Okay, because it's an interval, you have to say that drenches from negative zero point 5 to 5 to a second value, which is obtained at the top here for B and ah. As you can see, that value is between 0.6 and 0.8 more presently between 0.7 and 0.8. So somewhere in between that's going to be 0.75 Okay, So the 95% confidence interval for the fast case where the sample size and is eight on where the sample correlation R is 0.20 will be from negative 0.525 to 0.75 So you follow the same steps for the other cases where N is 100 on where r is negative, zero points for the roof and you will get the 95% confidence interval. And we do that for case be, it will be zero point negative zero point 55 to negative zero point. Sorry. Yeah, negative zero point 25 As for the second case on for that case, where any is 25 R is 0.65 somewhere here you will find that the 95% confidence interval ranges run 0.35 to 0.85 and lastly, when the example size and he's 15 and the sample correlation is negative. 0.23 You find that the interval is from negative zero plane 6 to 5 to zero 0.30 So those other results for four given kisses.

So for this question will be using formula who's he squared times P. That modifying one minus P. And divide all that by E squared. So I started with per a. The P value is .81. It is a 95% confidence interval And the e. value is .02. So before we put all the numbers of formula we need to get Z. And we need to see by changing the confidence in our whole Into a Z score. So first you would change to destinations attracted from one and then get the difference to buy the difference way too. And then that's the number you look up on the sea table and you find out it's 1.96 around it. Yes. Now we can put it in the formula so will be 1.96 squared Times .81 times one minus .1. Then you would divide that all by .02 And you would find out that answer is 1004 out of 78 points six. But because that's like You can have one fraction of this person and a sample size you need to round it up to the nearest whole number and you get 1000 479 for this answer. Yeah. Yeah part beef we use the same formula. So p value it's .81 Lives up to 99% confidence interval. E. is .02. So first again we'll need to change considerable into a Z score. Going to find it carried it .005. And then when you look it up to see table is 2.5 gates. I would put it in our formula. Uh huh. You just do the same um interesting process. There's a switch a number And you get 2,561.5. Again we have to round it up to 2562. Yeah. Then for C. r. standard deviation is eight. Very sorry, P value, P value. It's 21. We have a 95% confidence interval. E. Is too. And because we did this in part a for the 95% confidence in the book, It would be the same number which was 1.96. So then it would be 1.96 squared Tires, Tires, 1 -11 Divided by point there one sq and unit 5012.22. He had to round it up for the minimum it would be 5009 hired 8:13 Yeah.

The following is a solution in # nine, and this says that we have a random sample of 40. Now, it doesn't say the population distribution, but it doesn't matter because that sample size is big enough to assume normality and assume the central limit theorem. So, had this been a Sample of like size 20 or 25, Then we would actually have to say, but it comes from a normal population, but since that sample sizes 40, it doesn't matter how skewed or or whatever the population is, 40 is big enough. And the means of that sample is 120.5, and the standard deviation of that sample is 12.9, and were asked to find the 99% confidence interval for the population mean, μ So first off, let's decide what method to use. We're gonna use the tea interval here. So the T interval. The reason why we use the tea interval is because we're estimating the population mean, So it's either going to be the Z. Or the tea interval. And the reason why we can't use the Z. Interval is because we don't know what sigma is, we don't know that population standard deviation. We only know the sample standard deviation S. So whenever you don't know that sigma, you don't know that population standard deviation, you have to use the T and a rule. So you can use the tea interval formula or you can just use technology, I'm going to use the calculator. The T. IATA four calculate because it works out pretty nice. So if you go to stat and then tests it's his eighth option down here at the T interval, so click eight and then summary stats should be highlighted there and then we can start punching in our numbers, so X. Bar for number nine was 1 20.5, and then the sample standard deviation was 12 9, And then the sample size was 40. And again we were asked to find the 99% confidence and it was a .99 would be our confidence level and then we calculate, and then this top band here, that's going to be Our confidence interval. So 1 14.98-1 26.02. So let's go and write that down. So 1 14 9, 8 To 1 26.02. Okay, so it doesn't say to interpret this, but if you were to interpret even though there's no context to this problem, we would just say we are 99% confident that the true population mean is between 1 14.98 and 1 26.2


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