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3.Twelve blood specimens are randomly assigned into three groups. Group receives the treatment of anticoagulant A; Group receives the treatment of anticoagulant B: ...

Question

3.Twelve blood specimens are randomly assigned into three groups. Group receives the treatment of anticoagulant A; Group receives the treatment of anticoagulant B: Group receives the treatment of anticoagulant C. For each blood specimen, the erythrocyte sedimentation rate(ESR) after receiving the treatment measured The results are showed in Table 3. please teSt whether the three mean ESRs are significantly diflerentTableErythrocyte sedimentation rate(ESR m/h)AnticoagulantESR

3.Twelve blood specimens are randomly assigned into three groups. Group receives the treatment of anticoagulant A; Group receives the treatment of anticoagulant B: Group receives the treatment of anticoagulant C. For each blood specimen, the erythrocyte sedimentation rate(ESR) after receiving the treatment measured The results are showed in Table 3. please teSt whether the three mean ESRs are significantly diflerent Table Erythrocyte sedimentation rate(ESR m/h) Anticoagulant ESR



Answers

An article titled “Naturally Occurring Anticoagulants and Bone Marrow Transplantation: Plasma Protein $\mathrm{C}$ Predicts the Development of Venoocclusive Disease of the Liver" (Blood) compared baseline values for antithrombin III with antithrombin II values 7 days after a bone marrow transplant for 45 patients. The differences were found to be nonsignificant. Suppose 17 of the differences were positive and 28 were negative. The null hypothesis is that the median difference is zero, and the alternative hypothesis is that the median difference is not zero. Use the 0.05 level of significance. Complete the test and carefully state your conclusion.

In problem 43. Given the mean in the standard division, off the blood platelet counts of women, the mean equals 25 200 and 55.1 counts. I understand that division is equals 65.4. Using ships, ships, the're, um we will calculate the percentage of women with literally comes that are within three standard divisions of the meat using ships of fear. Um, we can determine only the minimum their centers of women we can't define on exact percentage or a maximum. We define the minimum, Then the minimum percentage equals one minus one, divided by a squared multiplied boy 100. Where K is the number of a standard divisions we want toe, calculate it for okay equals three or three Standard division. Then we're substitute by K equals three. You have one mind swan divided by nine multiplied by 100 which equals 89%. This is the minimum percentage of women that are within three standard deviations off the milk and to calculate the minimum and the maximum politically counts. Minimum 43 Standard division equals export minus three or the boy bystander division and the maximum. Of course, will be export plus three multiplied by a standard division. Export equals 255.1 minus three multiplied by 65.4 on we have here 155.1 plus the MTA buoyed by 65.4. And this gives 400. This is 451.3 and the minimum value is 58 0.9. Then the minimum percentage that lies between these two values are 89%. This is a final answer off our problem.

11 Good chili on that it is called is equal toe. The X value one is the me over understanding deviation which, approximately equal to negative one So negative one is one of than is one of than that for which and for which and be, um does the score is equal to the X value minus the mean over the standard Division, which actually is equal to a negative to so that that many here is is smaller than negative for seen. Uh, depending here is four minus four point 8/1 4.0.3, which is negative, 2.67 and then for the other many is 5.54 point eight over opened three. She's a toe. So this is where you would like between negative 2.67 and 2.33 for preaching the, um, the X very equal to the mean minus 1.44 time open three, which is 4.36 eight. So the expert is smaller than 4.36 eight. For questions in me, the X daily is equal toe me 4.8 plus, uh, doesn't the score multiplied by Son of deviation, which is equal to 5.18 four. So 5.18 for is smaller than X. The X value is equal toe the mean minus 2.2 15 times 4.3, which is 4.125 and it's ready for other friend is 4.8 using one. The meaning is one times open three, which is 4.5. So 4.1 toe Find explosives between these two values. Question regime. So this the score is equal toe X radio, minus the mean over the summer, the energy 3.6 seven. So the usual values are written to something division off, I mean, and thus have this call between negative 70.2. So that is 3.6. So it's not just than two, so 5.1 is unusual number.

For this problem, we are asked to use the empirical rule to find the percentage of observations that fall within a certain number of standard deviations of the mean. The empirical rule states that if there is a normal distribution with mean X. Bar and standard deviation s, approximately 68% of observations fall within one standard deviation of the mean, 95% fall within two standard deviations and 99.7 Percent fall within three standard deviations of the mean. In this problem, the mean is 255.1 And S is 65.4. For part A. We want to know the percentage of observations within two standard deviations. And based on the empirical rule, We know that the answer is 95%. For part B. We want to know what percentage of observations are between 189.7 And 320.5 first we have to find out how many standard deviations these numbers are from the mean. We subtract the mean of 255.1 from 3 20.5 And we get 65.4, And then we can also subtract 255.1 -189.7, Which also gets us 65.4, Since 65.4 is equal to the standard deviation in this problem. We know that observations falling between 189.7 and 320.5 are within one standard deviation of the mean. Using the empirical rule, 68% of observations are within one standard deviation of the mean, So the answer to part B is 68%.

So as we introduced normal distributions, there's something called the empirical rule which states that in our normal distribution, 68% of our data is gonna be within one standard deviation of the mean or the mean is centered right in the middle? All do not mean by this meal right here. So for red, that's going to be one standard deviation away from the mean. Which is going to hold about 68% of all our data. at two standard deviations away, We are going to encompass two standard deviations or 95% of all the data. Yeah, It might be helpful to draw these arrows right here. So that's going to encompass 95 and 68% is going to be within this At the 3rd standard deviation We're going to get 99.5% of our data. I didn't really make my alliance long enough, but you get the idea, Yeah, we're gonna have most of our data. All but half of a percent of our data is going to be within three standard deviations. Now, for part A it asks, what is the approximate percentage of women with platelet counts that are within two standard deviations of the mean? So that's gonna be two standard deviations or 98%. So there we go, that's gonna be 95%. Yeah. And then for part B Between 215 and 345, well now we have to interpret this. Okay, if our mean is 280 and our standard deviation is 65. What are our bounds? Well, let's go out one Let's start with 280 And add 65 to that. What do we end up getting? Well, it's gonna be 20 to get to 300 plus the 45 that are left, so that's going to make 345 for our upper bound, Let's ask, see what they're asking. 345. Okay, so reasonably 215 is going to be 65 away from 280. This means that we are one standard deviation From the mean, and therefore that is going to have 68% of our data, So that's gonna be 345 and 2 15, Okay.


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