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We wish to examine the average daily weight gain by calves sired by four bulls selected at random from population of bulls. Bulls denoted A through D were mated wit...

Question

We wish to examine the average daily weight gain by calves sired by four bulls selected at random from population of bulls. Bulls denoted A through D were mated with randomly selected cows_ Average daily weight gain by the calves is given below: B D 1.46 1.17 98 95 1.23 1.08 1.06 1.10 1.12 1.20 1.15 1.07 1.23 1.08 1.11 1.11 1.02 1.01 83 89 1.15 86 86 1.12 Test the null hypothesis that there is no sire to sire variability in the response Find 90% confidence intervals for the error variance and th

We wish to examine the average daily weight gain by calves sired by four bulls selected at random from population of bulls. Bulls denoted A through D were mated with randomly selected cows_ Average daily weight gain by the calves is given below: B D 1.46 1.17 98 95 1.23 1.08 1.06 1.10 1.12 1.20 1.15 1.07 1.23 1.08 1.11 1.11 1.02 1.01 83 89 1.15 86 86 1.12 Test the null hypothesis that there is no sire to sire variability in the response Find 90% confidence intervals for the error variance and the sire to sire variance



Answers

Recall that the beef cattle described in Exercise 17 had a mean weight of 1152 pounds, with a standard deviation of 84 pounds.
a) Cattle buyers hope that yearling Angus steers will weigh at least 1000 pounds. To see how much over (or under) that goal the cattle are, we could subtract 1000 pounds from all the weights. What would the new mean and standard deviation be?
b) Suppose such cattle sell at auction for 40 cents a pound. Find the mean and standard deviation of the sale prices for all the steers.

All right, That's the question. 19 together. So by the definition off T given in the question, devalue is equal. Teoh rations a mine. An inspiration. Be. So now we're going to first find out each battle over t Respect Teoh. Um, age subject. So for the first subject, the TS uh 65 minus 58 show it's seven. And the second is negative two ni to to to negative six and eight. All right, now we're going to calculate for the D Square as well, because, um, we will use a value for D Square in the following the steps so that he square for seven is 49 4 81 four for the hundreds, 36 64. Oh, right. And notice that our sample side here is eight. So and is eight. And because our confidence level is 95%. So our alibis equal to barrel buying. Oh, by all right. Now we can calculate summation off D, which iss 30 and summation off. He square is equal to 342 and in were like, if, uh, if we want to calculate for this dinner deviation off the we also need to know the square off summation de, which is square off 30 and it is equal to night Haggard. All right, By having this much information, we're be able to calculate its in their deviation from t. How? Just write down the only alert. So it is. Summation off the square, Linus Square off Summation D divided by and over and minus one. All right, so we just fucking this numbers 34 to my nose. 900 over eight, divided by eight minus one. And you get the value people to five points. Well, to six. All right. Okay. And we also launch of buying the critical T value as well. So let's recall the definition for the degree Afraid out, which is equal to a minus one. So it's eight minus 17 here and our our outsized there. A 170.5 and our t value. Aziz two point 36 Okay, um, now we're be able to calculate the maximum Will arrow here he is equal to t times Standard deviation off sti over square would off pen hands this 2.36 times 5.726 over square leg off. Eight and we won't get this number to be four point slab night, all right? And we also need to know the deep are in order to calculate our confidence Interval bounds. So deep are is just summation off t divided by and summation up the 30 and is eight. So 30 minus eight. There are 30 people divided. Right? Fades because you go to 3.75 Okay, Now were able to calculate the bounds. All right, The lower pals is he quote to t far minus E in which is negative. One point narrow for and the upper bells is equal to t far plus e, which is 8.54 So the final answer for our 95 Compton 95% confidence interval as from minus 1.4 to 8.54 All right,

Other question here wants us to go over the particular statements from the students and explain if there are any missed interpretations. So for the first one here, it states that 95% of cow studied gained between 45 £65. And in this particular case, this is going to be an incorrect statement. So they here is going to be incorrect. Due to the fact that when we look at are 95% confidence interval, that does not necessarily mean that it's plus or minus from the averages, plus or minus from any single point that you look for me. Here is as were 95% share that cow fed. The supplement will gain between 45 £67 is also going to be incorrect as there is going to be. There's gonna be margin of error here, and that not every single cow here is gonna be in between those particular values. So, um, for a C here it's going to be the same as it's essentially saying. The same thing for D Here's is the average weight gain of Castro. The supplement will be between 45 67% £67 rather at 95% of this time. This does not really make sense, even though the average weight gain is given to us is 56. So therefore, this is also gonna be incorrect for you here, it says. If the supplement is tested on another sample of cows, there is a 95% chance that their average weight gain will be between those two values. And again, the logic is in corrected. The fact that we are given the average weight gain, which is 56 95% here, is just the margin of error or the confidence level that it's going to be in between a particular value.

Alright, guys. So this magazine, this is a longer question. So we're looking at low. I sure Campbell And we look that different characters Day quiz show of the team's distribution. And we actually kept like the clearances and that was calculating the table. That again you can see here, but you can see in your book. So we want to do two things. One a or three things able to capture the bride and their sincere builds character would be in the population animal study which paratroopers on Mr Selection and then as a life force and then see ah, projects I'm taking to try to decrease me. That hunting hurt the me fat contents currently template 5%. And so he arable the means of 645 is in fact, in a pre his parents for the next generation of what me. That content can be expected in descendants of these animals, So this is literally a combination of a lot of questions. We've already the first witness process. Harry Mills, who was remember just to keep in mind, measures the the portion of total Marion's that's due to genetic variance. And so this is this madman was H two equals genetic variant GDP divided by unity in various. Then this further broken down Teoh pools Miss teen minus Yeah, Use in narrow sense just tells us the total variation population due to address the genes alone. And so that's usually looks like Lopez age. So a square equals Azem Gene Variation a G Bye bye energy variation Plus don't this variation pleasant Barmal marriage. So Devi pleasant And then, mathematically, this looks like I'm gonna refresh this page so you may want to stop here. You around is now we have a lot of after that. So the first everyone calculates is for the mysteries characterised is shake that so h two and I worked one. I just keep this up Song equals by this in Mali students coming from that is what you want And now narrow sense every look You just need to find the value from the table which I've already mentioned, and then just plug and play. So that's the shape I'm going to see that at this point just because we have a lot to do. So Nik, there were looking at you and then that content in General Elsie content So that's a hamster. A. That's the trying to keep you for excessive. So looking at me, remember be wants us to answer in the public mammal stated wish Cantor We respond based selection. So if you didn't isolation, we're gonna only a narrow Since this Narrow says, Corley knows the selection. And so the larger value that age to the Grand Duke between selected pants and population is the hope and more characterises response. So fact there'll be announcement. Fans love this one. So that comes to and then I'll see what one that we need for us election response. Because we need to know. I asked This question of the project is undertaken to decrease me pack hunting, and so that would be so. Select response is r equals H two times was called selection differential. Now, aides to for that when we already have 1.400 and in this election differential, it's the percentages. Uh, well, exemptions are tip on 5% and these happen question when we had a If we look at the question, we saw that we were looking for Temple, perhaps, and people five, those two values in the questions so just these ants attract those in the the second part. So simple. 5%. My 6.5. And then how you waas a 1.6% decrease, in fact. And where were they in fact tennis? An example. This alone. But it was a lot doing one problem.

Okay for this problem, we're going to refer back to some context that we had previous problem about cattle weight. So for this problem, we knew that we have had a weight. £1152 We're gonna do is we're gonna talk about how much money some people could make at auction these cows. And we want a certain goal weight for them and to see how the costs are affected. Um, how much money they could make on average. So we know we have these two pieces of information eso What they want to know is they want to know what the new mean would be. Um, and we also want to have cows over £1000 trying to get an idea how much money they can make. You want to know the new meaning, the new standard deviation. But that would be okay. So our plan is going to be what we need to do it for the first step. It is Just do it. What's called linear transformation. So we can actually take that 11 52. I mean, we can just subtract 1000 critical of a 50 to minus 1000 that is £152. That's the new mean. You're gonna just the mean by a pure subtraction. It's called linear transformation. Now for the standard deviation, the new standard deviation the same as the old standard deviation. So £84. Because the standard deviation is a difference between two values, we actually don't have to multiply way, way. Don't subtract the 1000 so that the standard deviation is really unchanged. That's an important fact to know, because just the difference If we take away the 1000 the difference doesn't change. So that was really like part a of this problem. So I put a over here is to make sure we're clear, and that's with part B. So for part B, what they really wanted to do, they were told that they could sell these cows at 40 cents a pound is a sale price. Okay, so they want how much money they're gonna make on average, so we can take that, um, sale price. Yeah, this is a linear transformation that you take the whatever price you're making. 40 cents per pound. You're going to take the 1 1152 and That's how much money you're going to make for that for stealing an average weight of a cow. So if you take those two things multiply together, they would make a profit. They would make We're in $60.80 on average. So for the standard deviation of difference and what they would make again, we're not going to do that. So from the standard deviation, you actually take that same value over here, the 84 it's still 40 cents. So we're gonna find the difference so he could make depending on the difference of the cow weights or how much the cat weights. Very. So that's not gonna change. So really, the math you're doing here is just 0.40 times 84. We take that The difference. It's a variation in price, maybe $33.60. That's typically Okay, so that's what we haven't


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