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12. Write down the confidence interval formula for (Read page 379)...

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12. Write down the confidence interval formula for (Read page 379)

12. Write down the confidence interval formula for (Read page 379)



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Construct the appropriate confidence interval. A simple random sample of size $n=12$ is drawn from a population that is normally distributed. The sample mean is found to be $\bar{x}=45$ and the sample standard deviation is found to be $s=14 .$ Construct a $90 \%$ confidence interval about the population mean.

You were asked to use a computer calculator to construct a confidence interval of 98% with the sample data given to us, which is gonna be 67 12 mine. 10 8 59796 So how even do that is go to excel and enter are sample data there into a columns to make sure it's going downwards so you would enter in your cells. Let's say you're starting a A. One would be six. A two would be seven. A three would be 12 and so on and so forth. So once you have that column solidified, you're gonna go into your mini tab and then you would select stat, and then you would go to basic statistics. And then you would click with one sample T because we have just one set of data that we're looking at. So then you would in the samples in columns, you would select whatever you put your columns. And so let's say it was just a so a one. Make sure that it's clicked and then you would go to your options, and then you would put in your confidence interval for a confidence level of 98.0. And then you also just need to make sure that the alternative is set Teoh not equal. So I'll give you the correct output. So once you have all that, all your data is in there. You can click, OK? And you give you something that looks like this. So it should be one sample t and then whatever calling you wouldn't. So let's say a one you shoes day, it'll spit out the output that looks kind of like that. So at the top of the your variable your en your mean your standard deviation your sample mean in the 98% confidence interval so that it'll show what column used for her very most. How many which is calculating of 12 the mean, which is also calculated, the standard deviation which they calculated the sample standard of Asia. And then our confidence interval right here, which is what we want, shows us 6.73 to 9.4 27 So the answer for that is 98% of our data is gonna fall between the range of 6.73 and nine point for juice

All right, so far as to compute the 98% confidence interval using the chi squares. So in red, that's what it's going to be, Our degrees of freedom is given by one less than the sample size, so 15 minus one is going to be 14. I'm gonna go ahead and substitute those first few values and then find out those critical points there after. So 1.54 is our standard deviation and minus one is only 14, and then we're going to calculate the other parts. Yeah, that we have 14 up top here, so now we just need to find out what these guys are half a half and 19 south a half, So alpha is 2% so we'll split those two, so that means we have 1% on each end. So for the first one, we're gonna be looking at the 99% or e chi square at 0.99 with 14 degrees of freedom, yep, that's right, So scroll down the table seven here and then we have chi square 2.99 with 14 degrees of freedom gets us a value of 4.660 So it's gonna be this one right here. Yeah. And then for the other one that's gonna be chi square appoint on one at 14 degrees of freedom and we find 29 141 Yeah. Okay, calculating the south we get we got 1.7 to 2.67 for our 98% confidence interval.

Hello. Hi. Here In this question, we have been given a question from Atkins weight loss program. Right. The question is given like there is a weight loss program. Is there on the number of people use these 40 people has been used on after toll month. They're mean weight loss is found 2.1 l b. On question is asking whether this conference in trouble given in the question information, it will be effective for the date. That is the question. Okay, so basically, we need to find the confidence in trouble. Estimate for standard deviation. So to do that, we know how to find confidence. Interval estimate first and activation. Right. So we're going to find what are the points given here? First we know number off samples given it is 40 Onda. We can find the degrees of freedom for that we can use and my instrument. So we get 39 on when it check the table. We know there is no 39 in the chi square table, so we know 39 is greater than 30. So in the table, using the road 30. Okay. In order to get the value of K square and to find ice core value, we need to know, See value. See values Given in the question. 90% Asian 90% means that you can write a 0.9 on alpha value. We can find out one minus. C one minus t will be equal to one minus point night you get 0.10 Okay, now first guy square value that is left tail critical. Value will be given by Chi Square one minus sigma by two That is equal. Do Chi Square one minus Seema Baidu Alfa by Toby Help Founder That is equal to 0.1. So one minus signal by two you'll be getting one minus 10.5. You'll be getting 0.95 years. Europe lined 95 alphabet. Right? So from the table we get this values ical do 18 point 493 Similarly right tailed critical value Chi square Alfa by two that is equal Do chi square 0.5 From the table. We get that values equal to 43.773 So once you get guys core values next step we can determine the conference in trouble. Estimate right. We know the formula is given by wrote off and minus one by chi Square stigma by two times standard deviation less than Sigma Less than against Kyle Rudolph and minus one bye bye square one minus Alfa by two one minus Alfa by two times standard deviation. So we get we have to substitute all these values here we know and minus one is 39 so 39 bite 43.773 We found out into standard deviation value. We know that is equal toe 4.8 that is given in the question is the sequel to 4.8 less than Sigma Less than here also 39 by keister one minus alphabet to be found out 18.493 times standard deviation. So we just started toe Simplify this value standard deviation value we know which is 4.8 er So when you take a multiply here and simplify you get This value is equal to 4.53 08 less than Sigma and less than 6.9706 This big conference in trouble estimate four standard deviation we got. Now the question is asking us whether this confidence in trouble used the information about affect, you know, subject it will give affecting us out diet because the value we're getting is 4.53 to 6.9. Is there the required value? The given value is what? Standard divisions? 4.8. So this conference interval estimate is enough for affecting us off. That that will be the correct answer. I hope this answer your question. Thank you.

Confidence interval means is a range off value. We are fairly sure our truly value lies in. For example, we measure the heights off 40 randomly choosing in your strength students It could do 40. We get mean hide off. I mean, it could do 173 Sammy Standard deviation equal to 20. Sammy No, we have a formula for 90% confidence interest. I could do X X mean plus minus exact named Asselborn squired. And we know that export is the mean and exactly the choosen that very or for the table blue which is 95% confidence interval is one point 96 Oodle So x bar equal to 173 on and z article do 1.96 You know, standard deviation IQ will do 27 an equal do and is the number off observation and you can see that here the number of absolution is 40 Now the separate dude that value in this formula and we get 173 plus minus 1.960 time for Dundee born body Squire route squired 40. Now we've simplified this and we get 173 plus minus 6.2. Now you can see that 95% confidence interval is 173 plus 6.2. So now you get 181 point ready to and for the minus 173 minus 6.2, so it will be 168.8. So it means that when the measure their heights, then it will be like to be between 168.8 semi and 188.27 the 95 ports and says that 95 off experiment like we just did include the Truman, but 5% want so netted or final answer.


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