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The concentrations (mg ImL) of immunoglobulin G in the blood sera of twelve donors are measured redby radial immunodiffusion (RID) and by electroimmuno-diffusion w...

Question

The concentrations (mg ImL) of immunoglobulin G in the blood sera of twelve donors are measured redby radial immunodiffusion (RID) and by electroimmuno-diffusion with the following results:Donor RID 13 1.5 0.70.8 1,0 1.10.81.8 1.40.41.3 0.70.9EID1.11.6 0.50.8 0.81.00.70.40.90.80.8Are the results of the two methods significantly different? (please use a non-parametric test)

The concentrations (mg ImL) of immunoglobulin G in the blood sera of twelve donors are measured redby radial immunodiffusion (RID) and by electroimmuno-diffusion with the following results: Donor RID 13 1.5 0.7 0.8 1,0 1.1 0.8 1.8 1.4 0.4 1.3 0.7 0.9 EID 1.1 1.6 0.5 0.8 0.8 1.0 0.7 0.4 0.9 0.8 0.8 Are the results of the two methods significantly different? (please use a non-parametric test)



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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.

The number 78 it is. Given that the normal hemoglobin level of adult females. Okay, nice button. We'll put him grounds for this. So I'm talking about human groups. Nice man. Yeah, ground decided right for normal direction. So there are too good to be a lasting to find out fiscal year two. I write an inequality to present their normal too. So you can see it is between 12-15. So if we draw a line diagram he must clear. So that destroyed. Yeah. So I destroyed yeah. Against him yet. 140 numbers here. The budget in there and see it all. Yeah. 369 Right. And so you can see yeah, the hemoglobin level 92 quarter. Yeah. Here's the chemical life. Normal Simmons. I don't. Okay, so what you can try, You can try it suppose X. m. 11 level decision in the X. So X. Can do it. X. Nice back then. What? Okay. As both political of santa clara. You can put it. Okay then. Of course the number of deep good night. What is that compound? Inequalities presenting? The Abner Mandela. So what is after wanda? I have no one ever began supposed representing that. Well, so here do a lot into that. So it is open bracket from people. Well minus and funny thanks. and again, 10 to blessing dot all other numbers. So how can they So abnormal. So abnormally does when there was a white you can write why can be presented us That is can see it is uh you can write blindness and on night to the city when forced open drop it or already been done India tend to listen to me. Okay. Okay, the second day going to write the inequality how we can try. So this is a good thing. Why? Nastya man off. Why get to them? Thanks because the americans. Okay, so again, so this is a dancer. You know, this reminds. Thank you

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.

Probleble 105 Party hired or to concentration these places from high myoglobin producing more pathetic as an ex solution with lower ph e lower be it in lungs then in issue. So hey this is a this is explanation for party now in part to be we know that had risen and concentration wherever equals two. And the log value of pds that is 7.4. Pre calculating we get the value of hard work and concentration is Pour into 10 to the power minus eight M. Now at body temperature 37° cells. Yes value of GW is two point Pull into 10 to the power minus 14. Okay. And at this temperature a neutral solution has hydrogen ion concentration. It equals to 1.5 into 10 to the power minus seven. And be it's It's equals to 6.81. You can put even through the frame of reference is a big difference at the temperature and blurred at ph 7.40 slightly basic. So we can write in a also world. You can to all the frame of reference is a bit different at this temperature, traitor blood at be it seven point poor. Each slightly basic. So this is our answer port, part B. No in part C. In bars, etc. The equilibrium in decades indicates that hi hydrogen iron concentration sip the equilibrium equilibrium towards the proton bonded drawn bonded from hammer glow being hemoglobin. A seat that is S. B. S. Plus, which means means a lower concentration dressing of HBO two in the blood. Does the ability of hammer blow being two. Transport ox season is impaired. Did so this is explanation part this is experiencing for part C.

This was probably number 68 from chapter nine 0.3. This problem deals with anemia and the Jordanian Children. It goes back to problem number 64 but they want us to do two things in this. They want us to calculate a test statistic and then find a P values and table be on a P value from our calculator. Eso first off going to the test statistic. We have two different types of tests. Statistics. We have a Z stat and a T stat Z Stats are used in proportions. T stats are used in means. So this problem deals with the means that we are going to find a T stacked. Now. We need to come up with a formula for that. So you need to have your formula sheet. You need to have your calculator. You also need to have your tea distribution chart on you. I do have him here on the slides to help us out. So to t stat going to the formula for formula sheet. And if we go down here, we have a standardized test statistic. It's called a statistic, minus the parameter, divided by standard air of the statistic now what that means here in this case, a statistic member statistic s sample s statistics come from samples in this problem for anemia mice. Statistic. My sample mean waas 11 0.3. Don't go back to the other slide. Addison also. Ah, the parameter comes from the population. The population mean here was 12 and then we're gonna divide that by the standard error of the statistic. Now, standard over this statistic is also another formula. It's on the back side of the formula sheet pot, the new formula AP former ships set up really nice here on the backside where we're looking here at, uh, uh, population mean and the standard air of the sample statistics. So we're looking at that formula right there. The standard Arab. A sample statistic is the sample standard deviation divided by square root event. So we have all those values. Here's let me get back to this slide. So the tea statistic we said was the statistic, which is 11.3 minus the parameter, which is the population mean, which was 12. We're gonna divide that by the standard air. That will be the standard deviation. The sample, which was 1.6 and we're gonna divide that by the square root of sample size, which is 50. I was going to give me on the topping negative 0.7. It's gonna get me on the bottom. Ah, zero 0.2 to 6. We divide that out, we get a value of negative 3.0 nine. That's a negative 3.9 We are allowed to have a negative test statistic here. Come back here in a minute to tell you what that means with the negative and how that works in everything. But that is the T stat value. So now, finding the P value first, we'll go to AA table, be they call it. We'll call it a T distribution table. We need to keep a couple things in mind. We need to keep that 3.9 for our tea stat value, and we also need to know our end value. Our sample size was 50. So keep those two in mind as we come over here. And here's our T distribution. Remember T distribution deals with degrees of freedom, degrees of freedom. There's a formula is n minus one, and it's a sample size minus one. That means my degrees of freedom is 49 someone to go down the degrees of freedom. But if you look here, we don't have a 49. We have 40 and we have 50. But no. 49. So what we do is we go to the next smallest value that we do know, which is 40. So we're going to use degrees of freedom of 40 here, and we go across until we find our t stat value or two numbers that are between us. We're looking for 3.9 We go across the 3.9 We get those two numbers. There's 3.9 this summer between those two numbers so that I go up top. And I know my P value is between 0.25 and 0.1 on the tee distribution charts. Hey, now, the next thing they want us to do is to find this, but using our calculator as comes back into what negative 3.9 means I have my students drawl. 80 distribution, which looks exactly like a normal distribution. That's zero. There's a negative one. There's a negative, too. And that's negative. Three negative. 3.9 Let me go back to my red color here. I dropped that down there and I'm going less senate. I'm shading that area. That they're the area is my p value. So if I can find the area of that, I'll get my P value. Now, remember, we did this with a normal curve with Z curves. We did normal C. D s or in a T distribution here. So we are going to do t c d efs. They always ask for a left side. Left side. I throw in a bunch of negative nine Negative 99999 upper value. Well, that's where we ended at negative 3.9 And the next thing they ask you for is degrees of freedom. Our sample size is 50. So my degrees of freedom is 49. You plug that into your calculator for my tea I 84 I go into distributions that second bars to get there. When I played that in, I get a P value of zero point 0016 Now, remember, on the chart, it was between 0.25 and 0.1 which is consistent


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