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LaaiiiThis Question: 13 ptsTme Remalning: 01:15.39 Subr | Tosi20 of 24 (19 completc)Thls Test: 115 pts possibleTwa independent random samples have been selected; 10...

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LaaiiiThis Question: 13 ptsTme Remalning: 01:15.39 Subr | Tosi20 of 24 (19 completc)Thls Test: 115 pts possibleTwa independent random samples have been selected; 100 ohsorvations fromn popu lation D0 fromn populalion 2 Populations Sarnole krown that Ihe variances are G2 Meal and 02 49 Complele parts Uhrough ugiot Click the Icon vic Ihe iable norial curve arcas69 andWefe hblained From timmii expemente W IrageFind 0/x1olxt X2) =(Round Ioui decima piJCe 5ncuded )Skeich Ihe approximate sampling dis

Laaiii This Question: 13 pts Tme Remalning: 01:15.39 Subr | Tosi 20 of 24 (19 completc) Thls Test: 115 pts possible Twa independent random samples have been selected; 100 ohsorvations fromn popu lation D0 fromn populalion 2 Populations Sarnole krown that Ihe variances are G2 Meal and 02 49 Complele parts Uhrough ugiot Click the Icon vic Ihe iable norial curve arcas 69 and Wefe hblained From timmii expemente W Irage Find 0/x1 olxt X2) = (Round Ioui decima piJCe 5 ncuded ) Skeich Ihe approximate sampling distnhution (X1 assuring Ihat Cllick select your answet(s}-



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Given the sample data $\begin{array}{cccccccc}x: & 23 & 17 & 15 & 30 & 25\end{array}$ (a) Find the range. (b) Verify that $\Sigma x=110$ and $\Sigma x^{2}=2568$ (c) Use the results of part (b) and appropriate computation formulas to compute the sample variance $s^{2}$ and sample standard deviation $s$ (d) Use the defining formulas to compute the sample variance $s^{2}$ and sample standard deviation $s$ (e) Suppose the given data comprise the entire population of all $x$ values. Compute the population variance $\sigma^{2}$ and population standard deviation $\sigma .$

This question wants us to examine the normal contour plots were giving. And it was supposed to tell me whether the sample size sample data has a population with a normal distribution. And we can tell that in normal Quintal plots for the dunking donuts. Um, it shows us cautious chorus for data for simple data that did not come along the street. My concern. The graph from the graph. We can tell that the points don't have a straight line. So the point show a career where Patton the point under graph our nods Strayed's on. They show they show a covalin AEA. They show it Covalin AEA pattern. So therefore we can conclude that the data doesn't have a normal population. So so the data dozen have in normal population mhm.

All right, and it's moved to question 1 84 Um, so in this question, our sample size can is equal to 80. The now hypothesis ISS, the population mean is equal Teoh 200. And if we use me to represent the population mean it ISS equipment and to say our no hypothesis is is mu equaled Teoh 200. All right, part be the alternative hypothesis ISS population mean is different from 200. Or we can just employees say our mute is now equal to 200. All right, um parte see, what's the value for Alfa? You hear our alphas? He co two Thera playing there a one because we're interested in on Thea Aeroplane there a one level of significance. All right, parte de, what's the is that value for Alfa divided by two? So here it is, the critical value off Seth for the to tout situation as we desired. So we can go Teoh table for four b and find the corresponding Call him for the, um, Alfa Value. Which is there a point there? What? And we will have the critical value equaled Teoh 2.58 Okay, in part B What is the value from you May sound the null hypothesis is so, as we said in part a, our mu is 200. All right, on, then. What is a value for ex parte here? Export is how a simple mean And according to the question, our simple mean is equal to 205. All right, and, uh uh, this standard deviation, which is sick a lot. Yes, he called to 15. It is given in a question and, uh, cart age ciccolo off export. Or so it is a standard arrow off the mean and it is equal to speak a lot of item by square root off school which is 15 divided by a squared off 80 and IHS, he could chew one point 68 All right. And we need to calculate the past a statistic that star. So according to the formula that star is, you go to your ex four minus the hypothesized value for you over sick. A lot divided by square enough. And and here the denominator is also he quote Teoh seeking law export, which is the center arrow for the mean all right way won't just plug in the numbers, Um, using the original formula. So the simple me is to go five minus 200. Go far 15 divided by a squared. Rode off Katie. And what we have, IHS two point 98 So this is ours. Test a statistic. Oh, here, we need Teoh. Make the decision. Can We've already have the value for the Zet off Gulf over to it as you go to 2.58 And we also have our test, a statistic that star is equal to 2.98 So to make the comparison between though and we found power is that star is greater than the that alfa over to you. Which means Oh, where is that star falls into the critical region. So we're going Teoh reject. Well, no hypothesis. All right. And if we draw a curve, Um imagine the critical value. Sad elf over two is here. And then as he go to 2.58 here we have the negative one negative 2.58 And the area for this How in this towel they ended up together is equal Teoh health, which is their applying? There are one, but our test of statistics that star and somewhere here and as 2.98 So obviously, um, can't falls into the critical ranging. So we're going Teoh reject the null hypothesis.

All right, That's the question. 1 83 So in this question, our simple size and IHS 50 are a We moved to the question part So part A what is a no hypothesis? So here the now hypothesis iss the population mean the population mean is 100. And if we use me to represent the population means so our no hypothesis is going to be your equivalent to say, um us Equal Teoh 100. All right, Part B, what is the alternative hypothesis? So here we can say the population means is not 100 or we just say mu does not equal to 100 note. Here it is a not be close eye. So when we considering the peat p value winning to consider two tails together, just keep in mind. All right, heart, see what's value for Alfa here in the question it is stating that using a airplane there a one level of significance. So that means our Alfa is going to be there a point there or what? All right, um, de what is a hypothesized, uh, value from you? So has wasted in the part a, um in the no hypothesis, our hypothesized highly valuable for me was going to be 100. Okay, part A what? Ihsaa value for ex parte um, export. Here it ISS represents the Sam Pony, and it is given in a question. On the better is 96. All right, heart f What is a standard deviation? They're here. Siegel eyes representing the standard deviation TV's. Okay. And, uh, and as equal to 12 partying siga off export. Here it is representing the standard arrow center era off. I mean and by the formula Friends, it is equal to speak on Monday, but Abay Square showed up in, so it's going to be 12 over square. Oh, no. 50. It is equal to 1.7 Terrible. All right. And we moved to h. We're interested in the testes. Statistic is that star. So we need to do some calculation here. According to the former learns that that start is equal to x bar minus the hypothesized value over mu over Segolela divided by square enough. And so we just plug in numbers. We have 96 minus 100 divided by 12 over Square Rudo 50 and it is equal. Teoh Negative 2.36 All right, what is the What is a P value here? The P value is going to be the probability off a random bearable that which absolute value is greater than or equal to the absolute value of ours that start Or, in another words, it issue. Go to the probability off a stunner. Normal, um, random bearable. That which ISS smaller than or equal to negative 2.36 So this is our of value for its that star. Plus the probability off is that greater than our equal? Teoh? Positive 2.36 All right, if we draw occur, representing the center normal distribution in here and it is going to be negative. Teoh calling 36 and symmetrical way Here it is. Positive 2.36 So our Peabody, who is going to be the summation off the area for this Tau and the sheriff of this tale as well? The ended up and equal Teoh the P value. So this, um, south is equal. Teoh Narrow point narrow 18 All right, Pant heart J wants a physician. So we were going to compare p value with our level of significance with the Alfa I recall Alfa is U Boat Teoh. There a point there. What? And hear? The P value is equal to their opined there. 018 And obviously our people I always greater than Alfa So here we are fell Teoh reject the null hypothesis.

Hello here. In this question, we out toe estimate to determine the sample size. Right? So it is given 99% confidence in tribalism. 99% confidence level is there on board within 10% off. Standard deviation. 10% days off. Standard deviation. So we just tried to use the table in the table. We have to see 99% conference in trouble mints. We know. Physical 19%. That means began, right? 0.99 Right. So, corresponding to 9.9, we know Alfa values will be one might see that is equal to 0.1 Welcome. So we know all this data we just to refer the table on. We see what is the number of sizes possible? So when we check the table, we get when C is equal to 99% Andi standard deviation is given 10% e values 10%. So in the terrible and we can see it is equal to $300. 36. So the required sample sites sample size is given by 336. So this will be the required answer. I hope this answer the question. Thank you.


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