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The drug OxyContin is used to treat patients with severe pain. However, it is extremely addictive and can be lethal. In a clinical trial, 216 subjects were given Ox...

Question

The drug OxyContin is used to treat patients with severe pain. However, it is extremely addictive and can be lethal. In a clinical trial, 216 subjects were given OxyContin as part of their treatment Of those 216 treated, 56 developed nausea. Another 123 patients were given a placebo and of those, subjects developed nausea_5. (Submit a screenshot of your written or typed answer:) Use a 0.05 significance level to test the claim that the population proportion of those taking the placebo and gettin

The drug OxyContin is used to treat patients with severe pain. However, it is extremely addictive and can be lethal. In a clinical trial, 216 subjects were given OxyContin as part of their treatment Of those 216 treated, 56 developed nausea. Another 123 patients were given a placebo and of those, subjects developed nausea_ 5. (Submit a screenshot of your written or typed answer:) Use a 0.05 significance level to test the claim that the population proportion of those taking the placebo and getting nauseous is smaller than the population proportion of those who are nauseous and take OxyContin: Use the provided information to find point estimate for the population proportion of subjects with nausea and were given the placebo, P1, and the point estimate for the population of subjects with nausea and were given OxyContin pz- b. State the null and alternative hypotheses. Indicate the significance level: Use the Brock Excel calculator to test the claim. Submit a screenshot of that sheet; including all input values and output results. d_ What is the P-Value from the test? Explain whether or not the null hypothesis is rejected. Write a concluding statement that addresses the claim_ Explain what it would mean in this context to make a Type error g. Explain what it would mean in this context to make a Type I| error h Based on the conclusion of the hypothesis test; which error(s) could have been made? Explain_



Answers

Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.
OxyContin (oxycodone) is a drug used to treat pain, but it is well known for its addictiveness and danger. In a clinical trial, among subjects treated with OxyContin, 52 developed nausea and 175 did not develop nausea. Among other subjects given placebos, 5 developed nausea and 40 did not develop nausea (based on data from Purdue Pharma L.P.). Use a 0.05 significance level to test for a difference between the rates of nausea for those treated with OxyContin and those given a placebo. a. Use a hypothesis test. b. Use an appropriate confidence interval. c. Does nausea appear to be an adverse reaction resulting from OxyContin?

So we know that this is a right tail test. With our null hypothesis being P is equal to 0.2 on our alternative hypothesis, P is greater than 0.2. And since our critical value I'm sorry, are critical value of the significance. Level off is equal to 0.5 And the question on the critical value for a right tail test is C. I think she go to one point 65 Telegraph would look something like this distribution here. This is the region February concerned with this. So if you use I bought this, this test results we get the Z test statistic is equal to 1.0 95 on Super G. It's the rejection region. Is Z is greater than 1.65 She right here. Sure. Okay, she's going over 165 And since it has observed the Z is equal to 1.5 which is less than 1.65 it could be concluded that the no hypothesis is not rejected. So therefore, there's not enough evidence to claim that more than 20% of OxyContin users develop nausea

Now we have to find the proportion out of 227 subjects. 50 to develop nausea. So what is my proportion? 52 by 2. 27. These other people who developed nausea. So this will be my p cap. So this is 52 divided by 2. 27 or 0.229 Okay, this is 0.229 Let's write this. 2291 Okay. Now we want to construct a 95% confidence interval to estimate how many off them developed nausea to examine it. To approximate the proportion of the people developed nausea. So I have my P cap. What is going to be my cue cap? What is my cue cap? My cuchara will be one minus this value. So this is going to be 0.7709 This is going to be 0.770 7709 Okay, now we know the formula for E. That is marginal, Federer. Zl for way too. The alphabet route over. Speak up. Que capped by N What is my end? It is a sample size to 27. I want a 95% confidence interval, which means my Alfa by 20.25 help A by two is 0.0 to fight. And if I use a calculator to find my Alfa value here it is 1.96 So this is going to be 1.96 into Rudo. Er pick up que kabai and Okay, so let me just use a calculator rule over zero point 291 into 0.7709 divided by 2. 27. Right? And I want to multiply this by 1.961 point 96 So this is 0.546 0.546 Okay, now how do I find the interval? My interval will be confidence interval at 95%. This is going to be 0.2291 0.22910 0.91 minus eat that 0.546 So this is 0.1745 0.1745 And what is this? 0.2291 plus 0.2291 plus 0.546 This is 0.28370 point +2837 This is my confidence interval. Okay, Now we want to compare this results to a 95% confidence interval for five subjects who developed nausea among 45 subjects. And these were given placebo instead of the medicine. And in this case, are P waas zero point 01 19. In this case, it waas zero point 0193 to zero point 2 to 0.2. Again. We see that over here the intervals overlap. Nate? Yeah. Over here, in both of these intervals, we can see that there is a new will happen. Hence we cannot conclude anything concrete. We cannot say that. Okay? The medicine or this drug OxyContin is any better than the placebo. Right? So we cannot say that the drug is effective.

Okay. So for this problem, we start out by looking at this first structure here and you'll notice that this structure has an R group here. So if this R. Is hydrogen, then the structure is morphine. If this our group is a muscle group and then instead of it being morphine, its actually its own methylated derivative known as codeine. So these two drugs are among the most effective painkillers that are used today. However, they do have drawbacks, including the fact that they are addictive and if you use them over and over again, you can kind of build up a tolerance and so they become less effective. As a result, a lot of research has gone in to studying in trying to synthesize other derivatives that might not have these same drawbacks. So These are three such additional drugs. So if you're looking at these structures, you can see that there are several structural similarities. So for example, you have this nitrogen here in all cases gonna draw this where attached to a missile group and in all cases you have a fennel ring here and I think looking at all of them, but that's pretty much the extent of the structural similarities. You know, if you look at this first structure Demerol um this ring is closed, so you have this carbon carbon bond here, um I guess there's a carbon here for all of them as well. However, you have this group here, which doesn't appear exactly on any of the other structures. Instead, you have kind of this key tone or this group here. Um also you'll notice these second structures for methadone and pro poxy thing. Um Like I mentioned, it's not a six member id ring. Um and these two groups also have an additional subtle ring. So here attached right to this carbon or with another carbon in between. So this is the main structural similarity that all of you share. And what you'll notice is that this corresponds to the Beckett Casey rules. So the Beckett Casey rules are a set of rules that kind of define whether these structures are or rather to predict structures that are able to buy into the morphine receptors in your body and if they buy into the morphine receptors, then they can be used um as effective painkillers in theory. So what you want to look at in terms of structure is you want to make sure first that you have an aromatic ring and in this case you do but specifically want this aromatic ring to be bonded to a quaternary carbon. So a carbon That is bonded to four other carbons and one of these carbons is going to be a federal ring. So if we look at this is our structural similarity. So we see our final ring is attached to this carbon here, um and I guess, you know, so we want to look at this carbon here. So this carbon is a quaternary carbon. This carbon has a federal attached to a coronary carbon. This carbon has a federal group attached to ordinary carbon. And even if we go back up to our original morphine and codeine an example, you have this carbon here is attached to this federal ring is attached to a quaternary carbon. So for all four of these structures, we have fulfilled the first two of the Beckett. Okay, see rules and the last one is that you have to have a nitrogen that's at a distance equal to two carbon carbon single bond lengths away from the quaternary Catalan center. Not kind but quaternary carbon center. Um so let's actually change this degree. So you'll see that you have this nitrogen, so you have this carbon carbon bond here and you have this carbon carbon bond here. And so basically what it's saying is that you have a nitrogen attached to this carbon and a federal attached to this carbon of your carbon carbon bond. And you can see that that's the case for all of these carbon carbon to carbon carbon bonds. And even up here you have to carbon carbon bonds. So according so you can see the structural similarities. Very importantly, they all have this carbon carbon bond, you have this mental ring attached to quaternary carbon and just from the structural similarities, you can see that they all follow the Beckett Casey rules. So at least theoretically if you were in the lab and synthesizing these structures, you could feel pretty confident that they would be good alternative structures to work as painkillers to be able to bind to the morphine receptors

We're told that a company is testing a new type of pain relief, new headache medicine called pain free. And they're running a test to see whether this works or not. Okay. And so were given this matrix appear to begin with a focus on just this matrix for now. So we can see that it says when people took pain free, we can see who actually got pain relief and who did not. And then when people took the placebo meaning nothing Riel, how many of them were pain free and how many of them were not okay? And the first question it asks is of those who took the placebo. So right off the bat, we know we're on. Lee focused on this bottom row. So of the people that took the placebo, how many got relief? Meaning, yes, there was pain relief. Well, if we look at the intersection of the placebo row and the yes column, the answer to part A would be that we have eight people that were pain free, right? Right here. That's where we'd be looking at. So the answer for part A is eight for Part B. It says of those who took the new medication. I mean, now we're focused on the people from the pain free call row of those who took the new medication. How Maney got no relief. So the no call and we can see that the intersection between the pain free row and the No column is three. So our answer for Part B is three for part C. It says the test was repeated on three Mawr groups of 50 patients each, which is all of this data that we have down here. All three of these matrices. It says it would like us to find the total results for all 200 patients. Not be careful here because recognized. It said that each of these three groups down here represented 50 groups are 50 people 50 patients each when it asked for all 200. It is also including our original matrix. So make sure you repeat that down here as well. 22 3 8 17. You should have all four matrices you've been given down here now. Besides that, it is simply asking for the total results, which is another way of saying they want us toe. Add all of these together. Remember, when you are adding matrices, you simply combine the corresponding entries meaning I'm going to start by taking the top left entry top left element of every matrix and add those together. So if you take 21 plus 19 plus 23 plus 22 you would get 85. Then I'd combine all the top right elements. Top right entries. So four plus six plus two plus three. If you take four plus six plus two plus three, you would get 15. Then we're gonna take the bottom left elements and add those together. If you take six plus 10 plus three plus eight, you would get 27. And finally we will combine all the bottom right elements. And if you take 19 plus 15 plus 22 plus 17 you would get 73. That is your matrix for part C. Final part Part D is just simply a question of analyzing the data. And it asked, Does it appear that pain free is effective? Remember, the first row represented pain free. The bottom row represented placebo. And this was the people that got relief. This was the people that did not. Well, if we look at our first row are placebo or, I mean, are pain free row. Clearly, the majority of people did experience pain relief. Yes, they got pain relief. If you compare that to our bottom row are placebo row? More people did not receive pain relief or did not report pain relief as those that did so. It looks pretty clear to us that yes, pain free does work because more people on pain free had pain relief than those that didn't.


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