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7I0 Dcints DevorestareDetearminecritical value for _ huo-sider Con-ideng intanaeach of the following situations (Rounc Your answerethra? Cecima places )Confidence95...

Question

7I0 Dcints DevorestareDetearminecritical value for _ huo-sider Con-ideng intanaeach of the following situations (Rounc Your answerethra? Cecima places )Confidence9596, df =Confidence9590, df = 15Confidence level 9900, df = 15Confoence9900,Confidence evel 9896, dfConfidence9900,

7I0 Dcints Devorestare Detearmine critical value for _ huo-sider Con-ideng intana each of the following situations (Rounc Your answere thra? Cecima places ) Confidence 9596, df = Confidence 9590, df = 15 Confidence level 9900, df = 15 Confoence 9900, Confidence evel 9896, df Confidence 9900,



Answers

Determine the $t$ critical value for a one-sample $t$ confidence interval in each of the following
situations.
(a) Confidence level $=95 \%, \mathrm{df}=10$
(b) Confidence level $=95 \%, \mathrm{df}=15$
(c) Confidence level $=99 \%, \mathrm{df}=15$
$\begin{array}{ll}{\text { (d) }} & {\text { Confidence level }=99 \%, n=5} \\ {\text { (e) }} & {\text { Confidence level }=98 \%, \text { df }=24} \\ {\text { (f) }} & {\text { Confidence level }=99 \%, n=38}\end{array}$

The following is a solution for # three. And we're asked to find a 980% confidence interval given this this data here. So we're gonna use the formula that I have up in red here, it's p one minus p two hats. In this case it's 20.255 -0.193 plus or minus Now the Z score here. If you don't have it memorized, that's fine. In fact, I can show you how to get it real quick because this one isn't as typical. So 1995-99 are usually the most typical ones. But if we go to distribution here and inverse norm And we type in .8 And then the center will be center is always for confidence intervals and then we paste, we get positive negative 1.282. So that's what we're gonna use for our z value. So positive, negative 1.282 times the square root of 0255 Times 1 -255. Which is 0.745 Divided by that sample size of 300 Plus 019, three Times 1- that. Which is 0807. And that's divided by the other sample size of 400 and you should get 0.062 plus or -0.041. So you can leave it like that. Or you can actually expand it out Where you subtract and you add you should get 0.021. Oops, Okay. All the way up to 0.103. Okay, so either answer is acceptable. Now we find a 95% confidence interval Given this following data. So we started out the same way now 95% confidence that we should know that Z value that's 196. But let's go and start this .1 47 which is the P one hat minus 10.131 Plus or -1.96 which is the critical value for 95 times the square root of .147 Times 1 -147 which is 853. And then divide that by the sample size of 3500 And then plus .131 Times 1 -131, which is 869. And divide that by the sample size of 37 50. So whenever you do that you should get .016 plus or minus .0159. So you can leave it like this certainly. Or you can expand it out groups Where you get essentially zero, also point 0001 All the way up to 0.0319. Okay, so those are two representations of the 95% confidence interval. Given this data

The following is a solution to number four and we're asked to find the 99.5% confidence interval for the difference of two population means given the following data here, and we're gonna use a two sample T interval. The reason why we have to use a T intervals because the sample size isn't greater than 30. So if at least one of these is not Uh at least one of these sample sizes less than 30, then we've got to use the tea interval instead of the z interval. So I'm gonna use a tt for here. If you got a stat, There are over two tests and it's gonna be option zero. So that's all the way down here where it says to samp t ent press center and just make sure data, I'm sorry, stats is highlighted and you can just punch in your data there. The confidence level is 00.995 stands for 99 99.5%. And then under pooled, you're just gonna want to keep that is Yes. The reason being, is that the two standard deviations are the same. Whenever that happens, then we have to have a pulled experiment And then we calculate in this top band here is our confidence intervals, so 10 4-9 and 14571. Okay, so we're 99.5% confident that the true population mean difference is between 10 4-9 and 14 .571. Okay. Mhm. And part B. It's very similar. We just want to be a little more confidence in 99.9% confident for the difference to population means again we're gonna use the tea interval because this 25 that's not greater than 30. So if we go to again stat and then tests and then the zero option. Now I actually have changed these because it's different data obviously. So 215 is the X one, bar seven is the standard deviation and 25 is that sample size? And then 1 85 is that I mean 12, is that standard deviation? And then 35 was the second sample size and we want to be .999. So 99.9% confident pull this still yes. And then we calculate and we get between 20.713 and 39.287. Okay, So let's go and write that down. 27 13 all the way up to 39 0.28 7. 99.9% confident that the true difference of the population means is between these two numbers. Mhm

Problem. Number four degrees of freedom is equal to end minus one, which is equal to 15 minus one so is equal to 14. So giving a is equal to one minus. Opened 99 34 to operate or one and the value of X are square with opened 995 and agree to Freedom 14 is equal to 31.319 for the critical value. Uh oh X squared with or point or four or five and degrees of freedom equal toe 14 The critical value ableto four points or 75

Problem. Number four degrees of freedom is equal to end minus one, which is equal to 15 minus one so is equal to 14. So giving a is equal to one minus. Opened 99 34 to operate or one and the value of X are square with opened 995 and agree to Freedom 14 is equal to 31.319 for the critical value. Uh oh X squared with or point or four or five and degrees of freedom equal toe 14 The critical value ableto four points or 75


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