5

QUESTION 1Let Ho: p=0.8 for Xs12 H1: P>0.8 for X>12 Find 8 for given n = 50 when p=0.9. Use normal approximation0 050 10 None of these...

Question

QUESTION 1Let Ho: p=0.8 for Xs12 H1: P>0.8 for X>12 Find 8 for given n = 50 when p=0.9. Use normal approximation0 050 10 None of these

QUESTION 1 Let Ho: p=0.8 for Xs12 H1: P>0.8 for X>12 Find 8 for given n = 50 when p=0.9. Use normal approximation 0 05 0 1 0 None of these



Answers

If $n_{1}=40, p_{1}^{\prime}=0.9, n_{2}=50,$ and $p_{2}^{\prime}=0.9:$ a. Find the estimated values for both $n p$ 's and both $n q^{\prime} \mathrm{s}$ b. Would this situation satisfy the guidelines for approximately normal? Explain.

Okay. And this question, we're interested in the estimate off the standard Arab. Um, before we do the calculation, I just wanna, um, right down the formula we're going to use, which is a formula for the standard era. Um, so we write, like, secret mono p one prime minus p two prime, which is because too square root off heat one times cute 1/1 waas p two times. Cute, too. Our end to, um no. That here. The, uh P one Q one p to Q two. They're all unknown value. So, um, we can now move to the estimate off the standard Aargh and how we're going to do that. We just replace p. Want Q one p to Q two by P. One. Prying Q one crime P to crime and Q two prime. Okay, so so does Kat. Part A in partner. We have, um, one. He goes to 40. He won crying. You goes to Europe 0.8 and to iss 15 and to prime. Is there a point, Kate? Okay, we calculate the Q one prime its narrow point. You seem as a cue to prying, so we just plug in the numbers. You write like this single a hat because they got to, um, there a 0.8, which is p one prime times. You're a point to over 40. Plus, there a point. Pay times their point. Teoh over 50. And we got the number. Should be, uh, pointing their a for night. So this is a our estimate for the center arrow off the difference between this two proportions. Okay, we're part B. Um, heart be. We have one too Big Terry. Three. You want prime in there? A 0.6 and to ISS 36 and Pete to prying ISS point 65 All right. And we coagulate the acute one. Prime it point for Q two. Prime is 0.235 Again, we just plug in the numbers square. I know, Pete one crime, which is 10.6 times cute one prime, which is quite for over a one. So it's 33 plus, Pete your pride, which is 0.65 times, Q two prime there a 20.3 high over and to riches 36. And the final answer for this is buying 1166 They're 11 ones. Your sticks

We want to check if the requirements to use the normal approximation to the binomial are met for the binomial distribution described. And if so, calculate the probability we have binomial with M equals 50. Probably to success P equals point too. And we want to find p of exactly 12. If the requirements are met first, let's check the requirements requirements. RMP greater than five nQ or end times one minus p. Greater than 53 and 50 p 500.2 and 2.8. We have 10 greater than five and 40 greater than five. So we're able to use the normal approximation. Since we're able to use the normal, let's calculate the mean and standard deviation news. Mp 10 and sigma is rude and QP two route to next We want to express our probability with a correction for continuity. The probability of exactly 12 is the probability that exits between 11.5 and 12.5. Since we're making the transition from the discrete to continuous distribution Next, let's we express our bounds Z scores where Z is equal to x minus mu over sigma. This gives us probability Z between 0.53 and 0.88 and plugging into the area under a Z table are using the Z score calculator. We obtain p 0.53 lessons 11.8 point 1086

You're asked salt problem during 23 In fact, you are a rescue. Find the limits of any purchase and indeed of the sequence to and high one over and Stirling's approximation buying across the nation of in Victoria. So first we have balloons and approaches infinity to fight the one to win. Thanks the ex A natural law of extorting dysfunction cause of this is to But when it has any hope of saving a natural law to imply the one of the story. Do this because here we have independent maybe your hero and this becomes law rules. Natural law. You went high over to in Can we have it? Yes, it is a continuous function. So it's all those That team was function parent sequences. This is people The natural law, you imply over two A And here we have form are formed. Natural law intended over is the same. So by Loki calls rule this is equal to eat to me infinity the very top. The chiefs want to imply times pi or 25 over, divided by the Americans that the bomb was sent to cancelling out get this is eat to the mix as encourages infinity, uh, one over to win. And this is just is your, which is one additional linen is one now using sterling approximation. You have this in Factorial is approximately people too. Over the end finds the in front of two and five. So take in through both sides, Get and proven in factorial. Okay? No, Burt. And then it comes and swear, Uh, you wouldn't fly. I think so too. Doing time in the state. And we have Yeah, money and purpose. Infinity, Uh, factorial. Approximately two minutes. A affinity of an over eyes. The land square here is limit Purchase infinity wise limits of two and five in my part. And you have that this last moment, people to one. So all those that large enough And the Emperor event factorial approximate and over. And part me Braschi your crops. In nation, we have team using capital later. Starting at n equals 40 and elevating meets a 10 as far as the calculator world will allow and and the proper use. But part the those captain years Have you be interested, then factorial destroyed. Undefined. Yeah. Then lose greater than or equal to 100. But when calculating values, we see that in every is a fairly good approximation for the Emperor. It in Victoria

We will find a number and of serve intervals for by a the midpoint approximation and sub en uber p the Travis soil approximation TN any parties Simpson's rule approximation as n to ensure that the absolute error when approximating the integral in exercise one will be less than five times tend to negative four. In this exercise, we will use inequalities 12 13 and 14 off the euro bounds Yeah. Um, given on theory, Um 772 page 500 40 of the textbook to remember Exercise one. Yeah, In exercise one, the integral we were approximating waas integral from 0 to 3 off the square root off X plus one. So the function we got to consider here is square root of X plus one and dysfunction is defined on the interval 03 Yeah. Okay, Then to use the you were bounce on inequalities 12 13 and 14. We got to remember also the maximum values off he second derivative up in absolute value on the absolute value of the fourth three that we calculated in exercise seven. So in exercise seven, we found that k two which is the maximum value for X on 03 off the absolute value of the second derivative off these function F is equal, right? Come on is equal to 1/4 and K four, which is the maximum value for X on the interval. 03 of the absolute value of the fourth derivative of F is 15/16. So these values this constant are important in calculating now the numbers of intervals and in each case, so we start, we start with midpoint in part A. So Okay, we used the inequality, the bound here in inequality 12. So the absolute value of its of them, that is the absolute error for the midpoint method is less than or equal to B minus eight to the third over 24 square times k two. And we want to find end in such a way that these errors be less than 5.5 times 10 2084. Okay, Yeah. So to ensure that thes error here is less than five times the opportunity for sufficient to find answers, that thes bound here is less than five times 10 to 94. Because you use transitive ity being this bound less than five times tend to the negative four way will have automatically. That thes error is also less than these quantities. So that's the, uh, it's the ideology we're going to use. But before that, we're going to write a little bit what the's values are. And in this case, a and B are see Run three, respectively. So we get here three minus zero to the third over 24 in square times K to which we remember is equal to 1/4. Yeah, yeah, And so these are expression which is simplified to be equal to nine over 32 inch square. So now we can say that if he's found nine over 32 inch square is less than five times 10 2084 then we can ensure, okay, that the absolute value of the sort of ever. I want to say absolute error will be also less than this quantity when we less then five times 10 2084 because, well, plane that before, If this expression here it's less than our target bound thing we have using trans activity at the after error will be also less than that. Yeah, so we get solved thes inequality here for? In yeah, this inequality here, Gary Resell for an that is finance such a thing. What is true? Oh, and not for runs these inequality nine over 32 inch square less than five times 10 to 94. We can say that using the fact that all numbers here are positive, including square, is positive because it's the square of a real number, often into your number. Then we can say that in square is greater than so. We have thes five times 10 to 94 that goes to denominator. But then to negative four in the denominator received 10 to the fourth on the numerator. So we get nine times 10 to the fourth over, 32 times five. Uh huh. And then this is equal to 100 1125 over to. And so we can say, because here we have positive values. Also, you can say the that end get to be greater than square root of this fraction 1125 or two, which is then approximately legal. Using a calculator to 23 times a 230.7 17 oak, eight, 25245 and and on into the which is square than these values. 24 for example, The first one. So we get that value. Yeah, you can take because in the case of the midpoint method and equals 24. So it's par A. And this means that if we assess, divide the interval of integration 24 equal What equals of intervals? Yeah. Then we if we use the midpoint to approximate the integral from 0 to 3 of this corporate of exports one, we'll get an absolute error, which is less than five times 10 2034. So this is the way off. Knowing in advance, using this mound of the Ruhr. Absolute terror, knowing in advance how many serve intervals we gotta take in order to have certain Curiously. Yeah, well, now we got to party. That is Trappist soil approximation. And here we're going to use inequality 13. And since the absolute value of E. T. That is the absolute error in this case in the traps. A little approximation, you know, using inequality 13 the slave they sent or equal to P minus eight to the third from over 12 and square times, K two and here we put the values is three minus serial square where now is third. I meant no over 12 and square. And K two is as we saw above in per a 1/4 eso disease. Mhm. Yeah, right. Ah, nine over 16 and square. And we noticed, right, as we said in previous exercises, that he's bound is just two times about for the midpoint method. If we multiply, it is found here by two. We get just eastbound here, so we get a, uh, we can find the final expression just by multiple. Multiply this by twos. We will get this body here. Okay, so now we can say but that ive thes bound we found here is less than the a cure security we want. That is five times 10 to 94. Then, um, we can ensure that the absolute error in this case for Travis social approximation, we'll also be less than sorry less then thes curious and that using just trans activity of inequalities and now from the inequality in 9/16 and square less than five times stand to the 94. Uh, we have that taking into account it and square is positive and all the constant that appear here. Positive two we get that end square is greater than nine times 10 to the fourth over. 16 times five. Yeah, hope. And, uh, this expression is equal to one Sorry. 1125 and so and get to be created than square root of that, which is approximately equal to 33 point 541 See you. 19 66 Yeah. And the first into the positive into the that is greater than 33.554 is 34. So we can take and equals 34. And this means that dividing the interval of integration in 34 Mm, He serve intervals of equal length. Then we we'll have an absolute error less than five times 10 to 94 when we approximate the integral by the trumpets Odle Method nine part C. Yeah, we will talk about Simpson's rule, and here we use inequality 14 and the, uh this inequality says the following since absolutely of yes, that is as an error in Simpson's rule, his less unequal the standard nickel to B minus a to the fifth over 180 into the fourth K four and putting the values is equal to three minus zero to the fifth over 180 into the fourth times. And remember, K four is 15/16 and this expression is equal to 81 over 64 to the fourth. So now if if we have that that this bound 81/64 to the fourth is less than our accuracy, that is five times stand to the negative four. Then we can ensure that the absolute error in this method yeah, absolute error and approximating senses the integral bites in some through method will be also less than he's security now from this inequality 1 81/64 into the fourth, less than five times 10 to the fourth to the Native Force. Or we get that. Yeah, and to the fourth. He's greater than 81 time. Stand to the fourth over 64 times five, and this expression is equal to 10,000 125 over four, and so, and he's greater than he right. Fourth a wood off 10,125 over four and using a calculator it is approximately equal. Yeah, to 7.9 306 26 75. This is this'll value. And here we got to remark, remember something is that in census rule, thes number of serve intervals and get to be an even incident. So we get to be careful in this case too. Take an even into their in a So our solution. So in this case, we can take eight, which is the first into your fulfilling this inequality, but is also even so we can take that value so we can take okay, and it will eight cheese. Okay. And even into the that's required. Okay. Okay. By seems in school. Yeah. So we have found the numbers of intervals for each method based on inequalities 12 13 and 14. Yeah, and we have used the same security for all three methods. And we found that the method that requires, uh, less numbers of intervals to be or to have the curiously the giving accuracy is Simpson's rule was respected because is a more accurate, accurate method. So we need less calculations. Also intervals to find the same accuracy


Similar Solved Questions

5 answers
Beam of particles of charge mass m, and velocity v is emitted from point source, roughly parallel with magnetic field B (say along the axis) , but with small angular dispersion. Show that the effect of the field is to focus the beam to & point at & distance 2 = 2rmv/lalB from the source.
beam of particles of charge mass m, and velocity v is emitted from point source, roughly parallel with magnetic field B (say along the axis) , but with small angular dispersion. Show that the effect of the field is to focus the beam to & point at & distance 2 = 2rmv/lalB from the source....
5 answers
2_ Use Taylor series to verify that & e(z3) = 322 e(2') . dz
2_ Use Taylor series to verify that & e(z3) = 322 e(2') . dz...
5 answers
Lnx + C(1 point) Verify that every member of the family of functions y solution of the differential equation €"y' +xy = 1. Answer the following questions. Find solution of the differential equation that satisfies the initial condition y(3) 10. Answer: yFind solution of the differential equation that satisfies the initial condition y(10) = 3. Answer: y
lnx + C (1 point) Verify that every member of the family of functions y solution of the differential equation €"y' +xy = 1. Answer the following questions. Find solution of the differential equation that satisfies the initial condition y(3) 10. Answer: y Find solution of the differen...
5 answers
MEAN (RiCucincicnt 'VariationVARIANCFZc(0) (70 points) Complete this table and use the computed valucs find thc Standard pcviation thc Rive sample Cnti Show INTERMEDIATE CALCULATIONS TO RECEIVE POINTSSitdStepTime(b) (10 points) Compute the Coefficient of Variation for the sample data set in (3}.
MEAN (Ri Cucincicnt 'Variation VARIANCF Zc (0) (70 points) Complete this table and use the computed valucs find thc Standard pcviation thc Rive sample Cnti Show INTERMEDIATE CALCULATIONS TO RECEIVE POINTS Sitd Step Time (b) (10 points) Compute the Coefficient of Variation for the sample data se...
5 answers
Mr Larsen's third grade class has 22 students, 12 girls and 10 boys Two students must be selected at random to be in the fall play:What is the probability that no boys will be chosen? Order is not important1/62/75/66/11
Mr Larsen's third grade class has 22 students, 12 girls and 10 boys Two students must be selected at random to be in the fall play: What is the probability that no boys will be chosen? Order is not important 1/6 2/7 5/6 6/11...
5 answers
Reactivity order of halides for dehydrohalogenation is: (a) $R-mathrm{F}>R-mathrm{Cl}>R-mathrm{Br}>R-mathrm{I}$(b) $R-mathrm{I}>R-mathrm{Br}>R-mathrm{Cl}>R-mathrm{F}$(c) $R-I>R-mathrm{Cl}>R-mathrm{Br}>R-mathrm{F}$(d) $R-F>R-I>R-B r>R-C l$
Reactivity order of halides for dehydrohalogenation is: (a) $R-mathrm{F}>R-mathrm{Cl}>R-mathrm{Br}>R-mathrm{I}$ (b) $R-mathrm{I}>R-mathrm{Br}>R-mathrm{Cl}>R-mathrm{F}$ (c) $R-I>R-mathrm{Cl}>R-mathrm{Br}>R-mathrm{F}$ (d) $R-F>R-I>R-B r>R-C l$...
5 answers
Express Inx + Iny as simply as possible: In(x2y2 ) 0 A *+y x2y2 1 D. I(y E. InBeset Selection
Express Inx + Iny as simply as possible: In(x2y2 ) 0 A *+y x2y2 1 D. I(y E. In Beset Selection...
5 answers
Question 3 (1 point) Find the volume of the sphere. Use 3.14 for T.units?Blank
Question 3 (1 point) Find the volume of the sphere. Use 3.14 for T. units? Blank...
5 answers
Find the derivative of y with respect to x (Hint Before differentiating express in terms of exponentlals and simplify ) csch ( In x)
Find the derivative of y with respect to x (Hint Before differentiating express in terms of exponentlals and simplify ) csch ( In x)...
5 answers
A) If the free energy difference between the equatorial and axial conformations for thehydroxy group in cyclohexanol is L0Q kcal/moland the free energy difference for the methylgroup in methylcyclohexane is 1.82 kcal/mol, estimate the equilibrium constant and the percent distribution of the two conformations of 1-methylcyclohexanolat 25'€. (AG? =-RT In K,R= 1.987 x 10-3 kcal/mol K)CH361 CH3OHOH
a) If the free energy difference between the equatorial and axial conformations for thehydroxy group in cyclohexanol is L0Q kcal/moland the free energy difference for the methylgroup in methylcyclohexane is 1.82 kcal/mol, estimate the equilibrium constant and the percent distribution of the two conf...
1 answers
In Exercises $9-12,$ at the indicated point find (a) the slope of the curve, (b) an equation of the tangent, and (c) an equation of the tangent. (d) Then draw a graph of the curve, tangent line, and normal line in the same square viewing window. $$v=x^{2} \quad$ at $\quad x=-2$$
In Exercises $9-12,$ at the indicated point find (a) the slope of the curve, (b) an equation of the tangent, and (c) an equation of the tangent. (d) Then draw a graph of the curve, tangent line, and normal line in the same square viewing window. $$v=x^{2} \quad$ at $\quad x=-2$$...
5 answers
12 + y2 = 1 cemberinin birinci bolgedeki egrisi iizerinde. mnesafede olan noktasmn koordinatlari bulunuz (20 Puan)noktasmayaki
12 + y2 = 1 cemberinin birinci bolgedeki egrisi iizerinde. mnesafede olan noktasmn koordinatlari bulunuz (20 Puan) noktasma yaki...
5 answers
CH;CHjHiC_IneetuabelsStrain enetgySubmlt AnawotRetry Entlre Groupmor 4roun attompts reMaininoCH3
CH; CHj HiC_ Inee tuabels Strain enetgy Submlt Anawot Retry Entlre Group mor 4roun attompts reMainino CH3...
5 answers
Points) Let Yi, Yz;Ya be random sample of size [rom the pdf(287) y-e-y/e , " > otherwisef(ylo)Find the rejection region for the most powerlul test of Ho 0 = Oo against Hi 0 = 01 assuming that 01 [Hint: Make use of the A2 distribution:]Is the test given in part (a) uniformly most powerlul for the alternative 0 > Oo?
points) Let Yi, Yz; Ya be random sample of size [rom the pdf (287) y-e-y/e , " > otherwise f(ylo) Find the rejection region for the most powerlul test of Ho 0 = Oo against Hi 0 = 01 assuming that 01 [Hint: Make use of the A2 distribution:] Is the test given in part (a) uniformly most power...
5 answers
63 09l04 ' nuclear equations for each of the following artificial nuclear 3. Please write balanced. reactions: is hit with a Hydrogen-2 projectile; producing sodium-24 and Magnesium-26 an alpha particle. Na + 14 SH Atotal ` 53 Zotal 24 1609 42 + 63 is bombarded with an alpha particle: producing & neutron and Ga- b. Copper 66. 63 Atoral ZLtotal ASC Magnesium-24 is struck with & particle; producing Silicon-27 and a neutronZtotalAtotol
63 09l 04 ' nuclear equations for each of the following artificial nuclear 3. Please write balanced. reactions: is hit with a Hydrogen-2 projectile; producing sodium-24 and Magnesium-26 an alpha particle. Na + 14 SH Atotal ` 53 Zotal 24 1609 42 + 63 is bombarded with an alpha particle: producin...

-- 0.019708--