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IH An W 07 9 Investigator I Interested In ALT+F10 (PC) 1 H or ALT+FN+F1O (Mac) V standard the the population mean 1 1 welght of Aish was L.2 H 4 4 W 'ithin Wha...

Question

IH An W 07 9 Investigator I Interested In ALT+F10 (PC) 1 H or ALT+FN+F1O (Mac) V standard the the population mean 1 1 welght of Aish was L.2 H 4 4 W 'ithin What

IH An W 07 9 Investigator I Interested In ALT+F10 (PC) 1 H or ALT+FN+F1O (Mac) V standard the the population mean 1 1 welght of Aish was L.2 H 4 4 W 'ithin What



Answers

Using the computer output and information in Exercise $8.153,$ determine the value of the following: a. Hypothesized value of population mean b. Sample mean c.
Population standard deviation d. Test statistic

I really learned So today we've been given this computer output on what's gonna identify some of the values on here. So there's four questions basic afternoons to identify four different parts that are given in here to the first past. Asking about the hypothesized by the population mean that is given to us right here. So we're looking at thes hypothesis. The test of mu equals 6.250 versus mu is not 6 25 0 so that's the population mean that we're hypothesizing. So that is part a there, Similarly, the sample mean is here. Now I know these are both means, but it's important to recognize which one's which on this here is the ones calculated using the sample rather than one that we use in the hypotheses. Thirdly, rest about the population standard deviation, and that is hidden right here. It's not this value here. That's the sample standard deviation. And we usually don't need that for hypothesis testing. Unless not least, we've asked for the test statistic, which is this value here? We've been calling it said star book A century. That is our cast statistic. Right there

In this problem, we have been asked to determine the population mean or the sample mean? And this problem, population is given the data points are 1, 19, 25 15, 12, 16, 28 13 and six. No sense of population is given. We will need to determine the population meat. And in this population we can see that the number of data points is not. Does the population mean? You Will be equal to the sum of the data points? So that is 1-plus 19. just 25 plus 15 plus 12 plus 16, 28 plus 13 plus six. This sum divided by the number of data points, which is equal tonight. So the some in the numerator is equal to 135. We divide this by nine In order to get 50, Hence the required population mean is 15. Yeah.

Hello Syringe here in this question we have given a data which is 598 12 7 13, 10 and 14. Okay. For this data we need to find the means of the Cuban if you do. And Q three. Okay. Q 1 to 2 to three. Rd quarter into the first quarter. Second quarter and a third quarter. So for finding Cuban to 23. 1st of all, we need to arrange their data in ascending order. Okay? So if we arrange the data in ascending order then it comes out to be 57 89 then 1213 and 14. So this is our data. So first of all we'll find the value of cuba. Okay, Cuban is a lower court. Lower quartile is given by And Plus one x 4 Tom. Okay. And plus one by fourth tom is all lower quality. Okay. So if we see the value of end for this data is eight. Right? There are eight. A number of data's Okay, so the value of N is eight. So if we put here then Q one comes out to be two point tools down. Okay, so this is a fractional town, how we'll find it. What we'll do is We'll take 2nd town as it is. Okay. And plus will multiply it by zero point to fight. That is the remaining part with the third. 3rd Data -2 Data. This is the formula for finding the fractional to barter. It's okay. So the second term is seven plus 0.25 times of the third time, which is eight minus the second damages seven. So quartile one that is lower. Quartile comes out to be 7.25 Okay. Now for the second quarter will just do the same procedure. Okay? Second quarter is also called the meeting of the data but we'll find a better formula of quarter. It's okay. So quartile. Second quarter is given by and plus one by four, multiplied by two. Okay, for one will multiply by one. For second quarter will multiply by two ft are quite I will multiply by three. Okay, so this town will give us the second quarter, so if we put the value of and it comes out to be 4.5, okay, four points of trump believes as the quartile too, so it is also the fictional town. So what we will do is fourth trump Plus 0.5 multiplied by 5th -4 Jump. Okay, this is the formula. So if we look at the data, fourth thomas, 4th time is nine Okay, and the system is 10 So forth, Thomas nine Plus 0.5 Times off. First time is 10 and fourth time is nine. Okay, so it comes out to be 9.5 so cartel to comes out of the 9.5. Okay, now the last part remaining. A Squat L three. Okay. Support squad L three for quartile three. What will be the formula and plus one by four. Multiply by three at this time. Well, diversity quite entry. Now putting the value of and it comes out to be 27 by four. Okay, this time that means it is 6.72. Okay. Now you can easily uh Tell what will be the 6.75 jump. It will be the sixth time plus 0.75 times off. Seventh trump minus the sixth time. Right? This will the formula for 6.7 at the time. So putting the value the sixth time is 12 plus seventh. Tom is 13 and six time is 12. The difference comes out of the one might have a 0.753 by four. So it comes out of the 12.700. Okay, so quartile three is 12.75 Now we need to find the mean of all these quarterbacks. Okay. So I mean of all the squad tiles will be Cuban plus kill. Do plus Q three Divided by three paid. So Cuban was 7.25. Right? And Kyoto was 12.75 and Q three uh, was 9.5. Okay. Sorry. Koda was 9.5 inch of this. 12.75 Okay, divided by three. Now it comes out to be 29.5. If you calculated 29.5, that means me Comes out to be nine point it. Okay, so this is the answer. Thank you.

Recommend that the U. S. Population and millions can be approximated by this equation here Where T. is a number of years since 1790. So now this question is asking us to find the average population between 1900 and 1950. So to find average, got it up here, you need to first find the total, so that's going to be the integral of the population. Um And then we had to divide it by a number of years. Okay, so in our case Um because it's from 1900 to 1950, R. T. Would actually be from 110 And 106 Because he is a number of years since 1790. Okay, so let's go ahead and find this interval for So the integral that we're looking for is the integral from 1 10 to 1 60. um And it will be the situation here. So that would be 1 90 over one plus 48 times into negative 0.31 17. Mhm And how to evaluate this? We will have to do um a substitution. So we are going to let you and you might do this a little bit differently. There are multiple different ways of doing this. But I'm going to let you be the entire denominator. That's one plus 48 pete and negative 0.31 70. Case of this means to you is going to be 48 times -0.03170 Times E. -0.03170. Okay. Mm So actually from here you we can actually reorganize this. We organize this and isolate E to negative 0.31 17. So this would be U -1/48. It's equal to e to make it a 0 20031 70. But the reason I want to do this because now we can actually substitute this back in here so we no longer have anything in terms of teeth. So D. You is going to be let's actually multiply that through so we don't need to keep writing that. So 48 times negative .037. Okay so this is equal to negative one point 5216. And then this E. The power. Well that is just U minus one over 48. Okay. And then finally we can isolate the T. So D. T. Is equal to negative 48 over 1.5- 1 6. Mind You -1. Thank you. Okay so now we're ready to put this all back in. Um And the last thing that we need to do is change our limits of integration. So if you was starting at sorry if she was starting at one time they need to put this one time into. Yeah and if a girl what are you limits integration. So once you do that you should get your new limits of integration. Are putting in one time will give 2.47 And then putting on 60 would give one point three. So I've rounded them off best if you store them in your calculator because um you don't want to end up with around here And then this becomes this is 192 over and the entire economic matters now you and then DT is negative 48 over 1.5- 1 6 times U -1. Oh so let's clean this up a bit. We're going to pull all of the constants different And then multiply them together so that's 192 times negative 48 Divided by 1.5- 1 6. Okay so the number of it should be negative 6000 56.78 again, make sure you store the entire number and don't round off And then we have one over a few times U -1. We can actually split that up into two fractions because that is just why over u minus one -1 Over You. You can check that yourself. If you put it overcome the denominator you you'll see that you end up with this. So the reason we want to do this is now we can integrate this because this is just one of U -1 -1 of you. That's negative. 605 6.78. And then that becomes one Hugh -1 minus one. You And then we're evaluating that around 2.47-1.3. Okay, so now it's just putting those numbers in. Okay, So once you put all of those in, you should get this is roughly 5000 700 20 point seven. So this is the total population over the 50 year period. So which means the last thing you need to do, which is find the average Is going to be that number 5720.7 Over the number of years, which is 50. So therefore the average is 114.41 million.


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