2

An experiment was performed t0 compare the fracture toughness of high purity 18 Ni maraging steel with commercial-purity stell of the same type: For m = 32 specimen...

Question

An experiment was performed t0 compare the fracture toughness of high purity 18 Ni maraging steel with commercial-purity stell of the same type: For m = 32 specimens; the sampe average toughness was X == 65.6 for the high-purity steel, whereas for n = 38 specimans of commerical steel the average toughness was Y = 59.8 Because high-purity steel is more expensive; its use for certain application can be justifed if its fracture thoughness exceeds that of commercial-purity steel by more than 5.Assum

An experiment was performed t0 compare the fracture toughness of high purity 18 Ni maraging steel with commercial-purity stell of the same type: For m = 32 specimens; the sampe average toughness was X == 65.6 for the high-purity steel, whereas for n = 38 specimans of commerical steel the average toughness was Y = 59.8 Because high-purity steel is more expensive; its use for certain application can be justifed if its fracture thoughness exceeds that of commercial-purity steel by more than 5. Assume that O = 1.2 and Oy = 1.1 test the relevant hypothesis using alpha = 0.001 Compute 8 for the test conducted in Problem when /1 Hz = 6



Answers

The sample average unrestrained compressive strength for 45 specimens of a particular type of
brick was computed to be 3107 psi, and the sample standard deviation was $188 .$ The distribution
of unrestrained compressive strength may be somewhat skewed. Does the data strongly indicate
that the true average unrestrained compressive strength is less than the design value of 3200$?$
Test using $\alpha=.001 .$

I'll continue problem this time. We're dealing with aggression analogies. We're dealing with regression analysis, and when you think about regression, you have what you call the independent variable in. In this context, we always healthy explanatory variable, which is being dependent variable. And then you also have the dependent variable, which is our response variable. We define the response variable of y on the independent variable as X. Both X and Y are typically quantitative, uh, variables. And your goal is to find relationships our relationship between the X and the Y value and just midwifed by the slope produced by the relationship. So we called this slope coefficient, and in the context, off populations, the slope coefficient is usually a data if you only have one flop. So if you have one flop, you're going to college beta and then our other interests, or you can call it data one hour. Other interest is the, um, the intercept, which we call. I don't want I'm I'm using the ITT's Actually, Beta beta. Not so. This is the Intersect. And this is the point where you're saying if you're independent, variable zero uh, your dependence I's gonna be a position. Why? So, given a problem, given a typical problem, we have, ah, study. And our goal is to study linear relationship. Linear relationships where the, uh, why value is the breaking strength, the breaking strength. That's the white value on these air beans, these air wooden beams that wouldn't would remember. If you place a force on the beam on, it goes beyond it, uh, strength level or its Taliban, there's a likelihood that the beam can stress out and collapsed. And then also we have our X, which is the independent, and this is the, uh, specific gravity, a specific gravity off off the wood. That's the specific gravity off the wood. And we have, uh, 10 beans selected on. They have the equivalent. There are equivalents, cross sectional area, you know. And when you think about the confessional area of a beam, that's just having a demon and slicing it across. And so if you look at the front of you, it doesn't look like that, um, being breaking strength so way have a table on the table. Have numbers that we're gonna use eso this experimental. Uh, this is experimental data, and we have two columns the X Column and the White column. Three X column Represent the statistic. Gravity and the White column represents the strength. So we have those two items, uh, 0.499 0.558 0.604 0.441 of 0.550 So these are the units off the breaking strength at different positions. 0.5 28 0.418 0.480 a 0.406 0.467 on then we have 11.1 full, 12.74 13 points 13. 11.51 12.38 12 point 60 11 point 13, 11.70 11.2 and 11.41 I was gonna say 04 Now I don't know if 11.41 So these are the numbers were given, and we have three parts to this problem. The first part is figure out how this data can feed into the model whenever you have a model. If it's the perfect feet, then you're not gonna have any errors. But if it's not a perfect feet. You're gonna have errors or sometimes residuals if you're dealing with samples. So we want you to build a model to feed into that. The second part is we want to test the hypothesis. So this is hypothesis testing? Hmm. Uh, hypothesis testing, uh, to measure the significant significant off the model. And by significance of the model, it means, uh, slopes significance. This is the slope significance, which is significant off the model. So the now is a beta one is zero. That means there's no relationship, no relationship between the X value, which you can recall. We define that of the specific gravity on the Y value, which is the, uh, strength. So we have specific gravity on the strength. So if there is no relationship, but now the slope is gonna be zero. But if the relationship, then the float is not gonna be zero, and I think we don't know the direction off the relationship. We have a two tailed tests, two tailed tests since theme the relationship, uh, direction is arbitrary. So it's our Detroit. We have a relationship direction on. Then input fee was saying determined, becoming the beam strength being streamed when X, which is a specific gravity, is 7.50 point 590 Uh, baby, defend confidence level. So I mean, you know, you have to be, uh, confident. You have to be confident. That is an interval where, uh, this prediction falls, and that's what we're saying in this problem. So we're gonna go ahead and q of the steps for resolving this problem. So in part, A for building a model. And you have to use excel. So input the X and my value Still, eggs l spreadsheet, uh, on a side to side column on the side to side economy. So you know the way we have a place we x and while biden, uh, on the side to side column, that's fast things. And then the second thing. Hmm. Next work. Make sure you have the data analysis to to block download it. And, you know, usually this one is, but we're saying is downloaded. Sometimes they offer the package with the software so you don't have to download, but just make sure you have it right there on then, on the tool, bub on the toolbar connect collect, uh, data. You want to collect data on the tuba. Uh, in this war, display a main. So the data is gonna be like a drop down menu connected to that and then select the data analysis in the menu provided by the, uh, tuba. Then after that, a dialogue dialogue box popped up. Dialogue, books, folks, stop. And then you wanted to elect regression from the ballot box from the dialog box. And, uh, inputs range. Uh huh. Or rather input wide range in the dialog box firings. Um, and put wire range. Select the legs being, uh, dependent Variable from your data. And our dependent variable is if you go back to the table, the exult table or the table that you get from their question, uh, statement the district. It's gonna be the same of strength. So that's where you collected on then? Of course. Uh huh. Click the inputs X range and connect the independence variable. Mm hmm. In this case, you know, it talked about the independent variable. That's one of the this one. The specific gravity off the course section, um, on select, independent, viable, uh, the specific graphic. That's what you're looking at. This problem and then finally, this is the final putt. Click. Okay. Mm. And you're your output results would explain your output resolve. Full This way. Hmm. Including a column below of the regression, Uh, or rather below the innovative below the regression and innovative. And in over two remember novels just analysis of variance. We're looking at the variations in prediction. So this table hard the for efficient value. Um, and the intercept values, uh, together, together with if you value just like the on over people. For those who don't have the exact spaceship, you could use your t r A 84 or 85 California. So, uh, and the process is similar. The only difference is that you're gonna end up using. Mm hmm. Um, that, uh, so starts and then heritage and then input dependent on l one column input independent on l. Too common. After that, go back to go back to start how to meet Carl, and then he likes Uh huh. The fourth option would say a linear regression. Linear regression. So So culturally, she select of the fourth option linear regression. Um, with it was the X You're going to get the same results So you can either use an Excel spreadsheet or you could use, uh, data. You could use data from, uh, linear regression. So once you run your results, um, you can get value for the internet on the slope, so they don't want which is the, you know, eyes given us trend points 8 to 9. And then beta, not which is the Intersect. Uh, given us 6.514 And so you're the prediction. Why height? Mm. A Y eyes family 6.514 plus 10.8 to 9. And then you wanna have your ex your independent so you have your dependent and, uh, independent values when it comes to hypothesis. Testing, remember, was declared thio. Uh, slope is either zero or the now hypotheses and then alternative hypotheses. Two tailed tests where your slope is not equal to zero. So it could be either less than zero, which means it's negative. Or it could be greater than zero, which is positive. So the first day with compute on the test statistic. Um, and like we said, you don't have to compute the test statistic or or the, uh, using the long method if you already have results from the table. But just for purposes off, uh, computation you're gonna have you're gonna have the T valley, which is the test statistic is better Heart one minus data one all of radical and regression. This is for the model on then the, uh, standing there for the model. Remember, when you're testing the hypotheses, you can either use critical or Alfa off 0.5. Uh, this is n minus wanted the degrees of freedom that you're using. Uh, since hypothesized meal is devil, this formula just collapses, too. Radical Emmett's regression all over x x, x that under now. And so you're gonna get your t value being the same non 6.336 Um, and your T value, which is connected to the T value, become 0.0 244 And like I said, you're gonna find these numbers from your table. So from your regression results after Iran Excel or T I 80 4 85 and for your conclusion is that since since since the Peabody, which is the same of 0.244 is less than Alfa, which is 0.5 Member Alfa is the critical region, a critical region that's the region off rejection. So you're saying if you have a distribution like that and this is critical, all of this guy's gonna be your Alfa, which is 105 And then you're, uh p your p with the value is that so you can see your P falls inside the critical region. So you're saying, Oh, it's too far from the hypothesized slope. The difference between your test statistic t Ln your t critical or hypothesized slope is too far. So you're your data. Your data is showing a different kind off slope coefficient, which is way off from zero. And so because that happens because there's a huge gap between the slope that your data defines and the slope that you hypothesized. So this is, uh, from the data on this is the hypothesized Uh huh. There's a huge gap and why they're huge gap because you could see falls inside the critical region where I'll 1st 0.5 eso Your conclusion is we uh huh We we reject the now hypothesis and provide groans. Uh, provide grounds. Two supports the all eternity over Jackman off. And so, uh, our test is or rather than our test detest Oh, uh, there is off significant relationship between X and y, which is between a deal trend, which is the y. And uh huh, our act value to specific, specific gravity. So we do have those relationships between X and Y our being strength and specific gravity. Okay, so there's not not just any kind of relationship, but a linear relationship. We want to call that, um, and that becomes a conclusion and then put fee his, but see way do have another aspect where we have to get the 90 90% confidence if you want to think of it that way. So we're looking for Mm. We're looking for 90% confidence that but he So, um, we're gonna see. So we're a 0.5 line viewable. Those are the numbers we're looking at. So why? Why? Um why equals two beta not plus. Wait a one X. So why is the same month beta? Not if you go back. There was 10 point something. So let's let's go back. You know, 6.51 ft, 6.514 twice plus 10.8 tonight. 10.8 tonight. And then we wanna plug in, Uh, wanna plug in the value back, which is 0.5 90 and let's see what we get. So 10 10.8 to 9 times 0.59 level. Uh, plus 6.514 We got 12 points. 12 points. 92311 That's coming Number. And now we need to compute the 90% confidence intervals of it for this value. Uh, need to compute the 90% confidence interval for this body. So we have, you know, Ah, y plus minus margin of error. And, uh, the the goal off the problem is, how are we going to get of the 90 90% margin off ever for this particular problem? Um, using all the data using all the data that we have from so again, you go back to your cult later and you look, you look up your data. Uh, so for using using the results table form your exhale or T I 84 85 output. You're gonna see something. You're gonna see that? Why? Since this is a prediction, you could call it Wyatt because we predicted violence. So why heart plus minus the margin off era. So our white hot is what you really predicted. 12.93 11 Okay, that's all. Why? Heart? Hmm. And imagine off era from the table from the confidence 90% confidence interval. So you have to select. I need to send confidence. Uh, interval. So that gives you plus minus a 0.35989 on. Then your interval will run between 12.544 to 13.263 That's over 90% confidence. So once again, we had a problem. He was hmm. On elaborate problem where were provided the data of x and y. And we have to compute a regression model. So using Excel, we had a series of steps, uh, using the data knowledge, Tupac, you select data and then select data analysis on then to let progression on in the input y winds. So, like the column with strength and put act like specific gravity on, then click OK. And you have an outfit on over table on the regression table has all the results in me. You could repeat the same process using tear 80 45 start and then added Input the Dependent, the Independent and then linear regression. Again, you get the results. You could also around the 90 different confidence at the same time. From that data from the results table, you're gonna be able to identify the intercept the coefficient. So in the coefficient column, you get the Intersect and the floor the slope will be next to are the variable description because it's the smoke that live the X and the Y variable, and then testing for the hypotheses that now means there's no relationship. Those high into the relationship again. You could either use the long method. Get the T values for that. But these numbers also available in the results table. So with the P being left on offer, he tossed a significant on. So there's a linear relationship between X and Y, and now we make a prediction when access 0.59 at 90% confident the body we get in 12 point why I becomes 12.9 do 311 and this one plus minus will give us three intervals. Hope you enjoy the problems will be to send any questions department and have a wonderful day


Similar Solved Questions

5 answers
Moving to another question will save this responseOlestonQuestion20 points5A projectile is thrown with an initial speed Vo at an angle 0 =220 as shown in the figure; At time the projectile reaches the point with coordinates (d.h)nere d-38.3m and h-9.Zm In the given coordinate system Given (8,d,h,g}, find Vo (Take 8-9 _ 8 m/s2) Express your answer using wo decimaLplases(d,h)Que-tonMoving to another question will save this response
Moving to another question will save this response Oleston Question 20 points 5 A projectile is thrown with an initial speed Vo at an angle 0 =220 as shown in the figure; At time the projectile reaches the point with coordinates (d.h)nere d-38.3m and h-9.Zm In the given coordinate system Given (8,d...
2 answers
LblLEALLLEAL'PlanoDlamotor (kilomutorstAvorago-dlstance-trom-Sun (kllometersh WalhaxMmallyAHHVt12I00104 2 ulhaxHEAuI2dl14470 Wlhax4,790 14,col227.9 MlHJunkFta J Wlhax54nue13 41427 ulhaxMcae526ChenMauNtct44 400
LblLEALLLEAL' Plano Dlamotor (kilomutorst Avorago-dlstance-trom-Sun (kllometersh Walhax Mmally AHH Vt 12I00 104 2 ulhax HEAu I2dl 14470 Wlhax 4,790 14,col 227.9 MlH Junk Fta J Wlhax 54nue 13 4 1427 ulhax Mcae 526 ChenMau Ntct 44 400...
5 answers
Problem 7.8 (Recursive to Explicit). Let (an Jnz1 be the sequence which is recursively defined by 00 = [ and Cn 3an-1 11 for all 2 1. Use mathematical induction to prove that the same sequence can be explicitly defined by 3"+1 an for all n > 0.
Problem 7.8 (Recursive to Explicit). Let (an Jnz1 be the sequence which is recursively defined by 00 = [ and Cn 3an-1 11 for all 2 1. Use mathematical induction to prove that the same sequence can be explicitly defined by 3"+1 an for all n > 0....
1 answers
HQMEWORK 2For the general displacement formulation with no body forces show that Navier's equations reduce t0 the form Mj,kk Wkki = Zv and thus the field equation formulation will now only depend on the single elastic constant: Poisson ralio For the ese with only displacement boundary conditions. this fact would imply that the solution would also only depend on Poisson $ ratio.
HQMEWORK 2 For the general displacement formulation with no body forces show that Navier's equations reduce t0 the form Mj,kk Wkki = Zv and thus the field equation formulation will now only depend on the single elastic constant: Poisson ralio For the ese with only displacement boundary conditi...
5 answers
Uestion 14ot yet IsweredA particle is projected from the ground level with initial velocity (range in m) on the Vi-35i+45j Find the horizontal distance ground level: (g=1Om/s))arked out ofFlag questionViRSelect one: a.315b. 240c.300d. 500360
uestion 14 ot yet Iswered A particle is projected from the ground level with initial velocity (range in m) on the Vi-35i+45j Find the horizontal distance ground level: (g=1Om/s)) arked out of Flag question Vi R Select one: a.315 b. 240 c.300 d. 500 360...
5 answers
The circuit in Figure $mathrm{P} 28.39$ has been connected for several seconds. Find the current (a) in the $4.00-mathrm{V}$ battery, (b) in the $3.00-Omega$ resistor, (c) in the $8.00-mathrm{V}$ battery, and(d) in the $3.00-mathrm{V}$ battery. Find (c) the charge on the capacitor.
The circuit in Figure $mathrm{P} 28.39$ has been connected for several seconds. Find the current (a) in the $4.00-mathrm{V}$ battery, (b) in the $3.00-Omega$ resistor, (c) in the $8.00-mathrm{V}$ battery, and (d) in the $3.00-mathrm{V}$ battery. Find (c) the charge on the capacitor....
5 answers
Classify each of the following substances as either strong or weak acid, strong or weak base, or a soluble Or insoluble salt:Clear AlIstrong acidHNO,weak acidCuCO,strong baseNaOHweuk baseHNOzsoluble saltAgsPO4insoluble salt
Classify each of the following substances as either strong or weak acid, strong or weak base, or a soluble Or insoluble salt: Clear AlI strong acid HNO, weak acid CuCO, strong base NaOH weuk base HNOz soluble salt AgsPO4 insoluble salt...
5 answers
Points) Given the matrix_3find all values of a that make |A| = 0. Give your answer as comma -separated listValues of a:
points) Given the matrix _3 find all values of a that make |A| = 0. Give your answer as comma -separated list Values of a:...
1 answers
Calculate the $\mathrm{pH}$ of a solution that is $1.00 \mathrm{M} \mathrm{HCN}$ and $1.00 \mathrm{M}$ HF. Compare the concentration (in molarity) of the $\mathrm{CN}^{-}$ ion in this solution with that in a $1.00 \mathrm{M}$ HCN solution. Comment on the difference.
Calculate the $\mathrm{pH}$ of a solution that is $1.00 \mathrm{M} \mathrm{HCN}$ and $1.00 \mathrm{M}$ HF. Compare the concentration (in molarity) of the $\mathrm{CN}^{-}$ ion in this solution with that in a $1.00 \mathrm{M}$ HCN solution. Comment on the difference....
5 answers
Solve the following Homogeneous Ainear Systemn uslng any method of your choice. X1 + 3x2 4X4 Ii+ 4r2 2x3 32n2 " 2x3 - ~X4 2x1 ~4x2 " + K3 + X4 Mi - .2x2" X3 | Xa
Solve the following Homogeneous Ainear Systemn uslng any method of your choice. X1 + 3x2 4X4 Ii+ 4r2 2x3 32n2 " 2x3 - ~X4 2x1 ~4x2 " + K3 + X4 Mi - .2x2" X3 | Xa...
5 answers
1 1 h Homework: 10.2 Hypothesis Tests for 1 a Population Proportio1 1 1
1 1 h Homework: 10.2 Hypothesis Tests for 1 a Population Proportio 1 1 1...
5 answers
Q2. Use substitution to show that x #is a solution to the equation cos?(x) - 1 =0 Show all your work:03. Use substitution to show that x = Tr is a solution to the equation sin(x) cos(x) = 1. Show all your work: Find two other solutions to the equation.04. a) Solve the equation ab-a = 0.b) Using the factoring vou found in part a) along with the substitutions solve the equation tan(x) sin(x) sin(x) = 0 on the interval [0, 3n)tan(x)and b = sin(x) to
Q2. Use substitution to show that x #is a solution to the equation cos?(x) - 1 =0 Show all your work: 03. Use substitution to show that x = Tr is a solution to the equation sin(x) cos(x) = 1. Show all your work: Find two other solutions to the equation. 04. a) Solve the equation ab-a = 0. b) Using t...
5 answers
(e} A + 0 FX1(Q 24 + 5 F3(g) A - 5 FE
(e} A + 0 FX1 (Q 24 + 5 F3 (g) A - 5 FE...
5 answers
Suppose that an object is moving along a vertical line. Itsvertical position is given by theequation L(t)=2t2+5t−9L(t)=2t2+5t-9, where distance ismeasured in meters and time in seconds. Find the approximate valueof the average velocity (accurate up to three or more decimalplaces) in the given time intervals.between t1=5 sand t2=10 s : msmsbetween t1=4 sand t2=6 s : msmsbetween t1=1 sand t2=7 s : msms
Suppose that an object is moving along a vertical line. Its vertical position is given by the equation L(t)=2t2+5t−9L(t)=2t2+5t-9, where distance is measured in meters and time in seconds. Find the approximate value of the average velocity (accurate up to three or more decimal places) in the g...
5 answers
When 1.25 L of 0.6SM Hydrofluoric acid (HF; Ka-6.6xl0-4) is titrated with 5.OM KOH, what is the pH _ after the addition of 42.OmL KOH?
When 1.25 L of 0.6SM Hydrofluoric acid (HF; Ka-6.6xl0-4) is titrated with 5.OM KOH, what is the pH _ after the addition of 42.OmL KOH?...
5 answers
Suppa Lha given by v(t)object moving uoug axis and that its velocity (in feet per second) at time 4L. Use this information answer the questions Inckt points cach):Sketch graph the velocity fuctiunthe first Scuds of trarelUse the graph from abott trhveldutermine the distance the object has traveledthe first seconds 0lWhatchange the object 8 posilion over the first Beconds of travel?Find antidezitative; st} Ior Ue
Suppa Lha given by v(t) object moving uoug axis and that its velocity (in feet per second) at time 4L. Use this information answer the questions Inckt points cach): Sketch graph the velocity fuctiun the first Scuds of trarel Use the graph from abott trhvel dutermine the distance the object has trav...

-- 0.017774--