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1 "Doacer data; Pud frsrribused" Question thats the sample 175 Inconec 3 approximate confidence 3 U runners 1 3 Intenlestmates the samp confidence { edev...

Question

1 "Doacer data; Pud frsrribused" Question thats the sample 175 Inconec 3 approximate confidence 3 U runners 1 3 Intenlestmates the samp confidence { edevationte 1 Is the race Interval 7.5 imc U 5 Enter your seconds the population mean 1 FFEDBACA W eace MEMANSTER distribution of tlmes race times based on the following 1 format (lower,upper) where SuBMI W sample8 UnG Ol8

1 "Doacer data; Pud frsrribused" Question thats the sample 175 Inconec 3 approximate confidence 3 U runners 1 3 Intenlestmates the samp confidence { edevationte 1 Is the race Interval 7.5 imc U 5 Enter your seconds the population mean 1 FFEDBACA W eace MEMANSTER distribution of tlmes race times based on the following 1 format (lower,upper) where SuBMI W sample 8 UnG Ol 8



Answers

Construct the confidence interval for $p_{1}-p_{2}$ for the level of confidence and the data given. (The samples are sufficiently large.) a. $80 \%$ confidence, $$ \begin{array}{l} \mathbf{n}_{1}-300, \hat{p}_{1}-0.255 \\ \approx_{2}-400, \hat{p}_{2}-0.1 Q 3 \end{array} $$ b. $95 \%$ confidence, $$ \mathrm{w}_{1}-3500, \hat{p}_{1}-0.147 $$ $$ \mathrm{w}_{2}-3750, \hat{p}_{2}-0.131 $$

Mhm. Okay. This question were given the end 725 and X musical 275. It's so cute simply X summer. And Just to 75-85, Let's get this year 35 mm he said of moving to value. Mhm. For the 95 confidences Is 1.96. Get everything. Okay. Okay. And the 95% confidence interval about the population proportion of adults follow college football and then be given in this general over the people. That's what is? I don't have to discouraged. He persecute from the peak. Okay. Right. Which would give us Europe 3 5 Less than -1.96 spirit. You have been 35 times 655 over. And which is given to the 75? Yeah, That's 0.317. What's your .383? It's a buster miners.

The following is a solution to number three and we're asked to find the 99.9% confidence interval for the difference of two, population means given the following data here, and we're gonna use the two sample t interval, because one of these sample size is not at least 30. So in order to use the Z interval, we either need to know the population standard deviations, which is not usually very typical or at least one of the sample size is less than 30. And that's what happens here. So, I'm gonna use the T. I 84 here and if you just go to stat and then tests and then we're gonna scroll all the way down to the zero option where it says to samp T and that stands for two sample T interval, click enter and make sure stats is highlighted, and then you're just gonna pop in your data there. So there's the main standard deviation sample size for the first sample mean standard deviation sample size for the second sample And the confidence level is .999, that stands for 99.9%. And then under pulled we're gonna keep that as a yes, because it says that we're assuming that the standard deviations are the same. So whenever that happens then we're just gonna assume that it's a pooled um appalled uh huh uh what do you call it? Topic or experiment? And when we calculate, we have .133 and .467. So that's our confidence in the rule. So we're 99.9% sure that the difference of the two means between 133 And .467. Okay, so that's our confidence interval there. And then the second Part of this is a 99% confidence interval. Same thing. We're going to the t interval because that sample sizes less than 30 at least one of them is so we go to stat and then tests and it's the zero option And so we need to actually change the stuff. So 77.3 is the mean 1.2 is the first standard deviation and that sample size was 1875 was the second, I mean 1.6 was the standard deviation and then 32 was that sample size and we want to be .9999 Confident there. And again we're gonna keep it as a yes pulled and we calculate so that's 1.1377-3.46-3. Okay, so one point 1377 234 6 to 3. So that's our 99% confidence interval for the difference of two, population means

The following is a solution for number two and we're asked to find a 90% confidence interval for the difference of two population means given this data now, since the two sample sizes are less than 30 or at least one of them is less than 30 we have to use the two sample t interval instead of the z interval. So I'm gonna use a graphing calculator here. If we go to stat and then test and we are all the way down to the zero option where it says to samp T and that stands for two sample T interval and then we click enter and then just make sure stats is highlighted and we punch in our data here, so X one, bar, s one in one in the next two bar S two and into so that's all the data that was there and the confidence levels nine for 90%. Then you get to this pulled and just make sure it's yes, because it says that that assume that the two standard deviations are the same. So whenever that's the case, then you can go ahead and pull them and then we calculate, and we get this 11.371 to 16.6 to nine, It's just gonna write that down. So 11 .371 To 16, 6- nine. Yes, that's the 90% confidence interval. And then similarly we're gonna do a 99% confidence interval, still using the t interval since they're both Or at least one of them is less than 30 with the sample size. And so if we go to stat and then tests and then just go to the zero option And we need to change this data here. So 68 was Rx one, bar eight was Rs one and then 14 was our first sample size and then uh 43 was our second sample mean three was our standard deviation and 20 was that sample size? And we want to be 99% confidence. And again, we're gonna be pooled. So we say calculate and we get 19.657 to 30.343. Okay, so 19.6 57 2, 4 3. So we're 99% confident that the difference of the two means Given the sample data is between these two numbers.

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


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