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17. An investigator assessed the association between diabetes (yes and no) and cancer (yes and no). In this study, investigator evaluated 50 cancer patients and 50 ...

Question

17. An investigator assessed the association between diabetes (yes and no) and cancer (yes and no). In this study, investigator evaluated 50 cancer patients and 50 healthy controls. Among 50 cancer patients, 30 patients rcported to have diabetes while 10 had diabetes in controls_ Compute odds ratio and risk ratio for having cancer (outcome yes and no) in relation to diabetes (exposure-diabetes yes and no)_

17. An investigator assessed the association between diabetes (yes and no) and cancer (yes and no). In this study, investigator evaluated 50 cancer patients and 50 healthy controls. Among 50 cancer patients, 30 patients rcported to have diabetes while 10 had diabetes in controls_ Compute odds ratio and risk ratio for having cancer (outcome yes and no) in relation to diabetes (exposure-diabetes yes and no)_



Answers

Type 2 diabetes is becoming increasingly common in the United States. The primary risk factor for type 2 diabetes is a history of obesity. Statistics show that children are becoming obese at an alarmingly high rate, and this correlates with increased rates of type 2 diabetes. When young children become overweight, the blame is often placed on parents and the nutrition and exercise choices they make for their children. Why do you think today's parents have a harder time feeding their children nutritious meals and providing an exercise program than did parents of previous generations? What can be done to solve this problem? Additionally, diabetes is more common in low-income populations than in wealthy populations. What are possible reasons for this?

We have 89 number problem ledges with devotees that we have began. Group 14.6 million are diagnosed. Well, 6.2 million, sir. On dino sore. Total number of people with diabetes will be our base. 14.6. Place 6.2, that is 20 point eight million people is diagnosed with ah, his total number off diabetes patient and of the hell to find of what percent of Americans with devotees have not been diagnosed. So we will be having the amount that is the number of people which have not been diagnosed the 6.2 million. Okay, so we need to calculate percent the percent we need to find out. So let us as young this to be n okay, we will be using percentage question are not present in prison proportion. This really better, which is percent Oh, uh 100 equal to amount over this, we have en over 100. Quito amount six point 2/20 6.0.8. So we have an equal to 6.2 in 200 over 20.8, which will be 4 to 6.22 under 4.8 29.0 76 So we have and approximately will toe 29 point 8%. This is the percent off the Americans for damages have not been diagnosed with mental disease. Thank you so much.

Okay. So C. Is defined as Between five and 10 where we want to be at least five. At least five means that we have a close parentheses on this end and an open one on on that most tent. So when we're reversing this this means that we will have an open prints here on five and a closed one on 10. So we're gonna be looking for values that are less than five. But at most looking at our table we have exactly nine values that meet this criteria. Now moving on to A. And B. Hey is defined as the event that the state has diabetes prevalence percentage of at least eight And be event that the state has a diabetes prevalence percentage of less than 7%. So we're looking at values that are less than 7% and that are at least 8%. However, we might have spotted the loophole there is that There isn't a number that is greater than seven but less than eight. Wait no no no I said that wrong. Um We have a loophole here that just says we're looking for At least eight. Less than seven AIDS here. seven is there And we're going different ways there's no way overlap of these two. So A. And B. Is the empty set now for C. Or D. We're definitely get an answer for this one. C. is at least 5% but less than 10%. So I'm gonna write it like this 5 10. Yeah And then D is the event that we are less than 9%? So we're gonna write that as nine. They will probably put like zero or I don't know like this so they overlap C. Or D. Is going to be 5678 and nine. So that's gonna be mhm. Yeah and I read that wrong we're actually just looking for Um anything that's less than 10%. So this is our high end and then the low end is just gonna be basically zero. So we're looking for anything that is less than 10%. Which looking at our table here You look on the left column 10 UNDER 11. It's just one of those states that His outside of that. So that's going to be 50 -1 of states. I saw a total of 49 states Are less than 10%. Prediabetic. Okay. And now we got an extra question of C. And B. So when you write that down here So c. is between five and 10 including five And b. is just being less than seven. So less than seven. So that's just pretty much means that we're looking for rates between five including 5 and that are less than seven. Looking at our table here, 25 states satisfied that. Yeah. Yes. Mhm.

Probleble seven dysfunction represented the distribution of a test at school. We want to find the values of A and B. That makes this a probability density function. A probability density function has the area under the function equals one. Let's get this area knowing that in the problem, given 25% received the scores between 50 and 100, which means this area is 25 And 75% received the scores between zero and 50. Then this dotted area is 75 Or 4.75. Let's start by .75. All .75 equals the dotted area. That area equals an area of our Wrangler height multiplied by So it's how it is A Depoted by the wits is 50. Then we can get equals 4.75 divided by 15 Equals o point or 15 for barbie. Sorry, let's get the value of the first. We use the information that 25% scores Between 50 and 100. Then the area of this shaded rectangular equals we're going to fire equals the bees. Multiplied by height or the width multiplied by the bet is 100 minus 50 Not to buy Buy the right which is B. Then we can get B equals 4.25. divided by 50 Equals 4.05. This for birdie for barbie. We want to find the median test score The definition of the medium that the integration from 0 to the media. For the dynasty function equals one half. Let's integrate The integration from 0 to T. Of course lawyers in this area Because this area is open 75 and this area is open to five. Then we know that T. Is below 50. Then the integration from 0 to T. Will be for P. Of X. In the first the first area B of X is defined as horizontal line. A constant value At a point or 15 Equals 0.5. Let's integrate its 0.015. To blow by X. This substance through from zero to T equals half. Then We substitute by the upper limit. 1st t minus zero Equals 0 .5, then T equals 0.5 divided by oh point 15. It equals 33 point three. And we should we should check that. It's a great it's smaller than 50. It's as expected. It will be less than 50. Then the median is 33.3. Well. But see we want to find the means. Test the score. You by definition equals integration from the minimum value which is zero To the maximum value which is 100 for B. Of X. Dx. But here we have two definitions for b of x, one from 0 to 50 And one from 50 to 100. The first definition is able to blow it. You? Sorry? It's X. Multiplied by B of X dx. Then we have X multiplied by the constant E. And here we have X multiplied by the constant B. The X. Of course we have here the X. Let's integrate. We add one to the power, then divide by the new bar from 0 to 50 plus the same. We add one to the board and divide by. The new book equals four point oh 75 Mr. Institute. By the upper limit. 1st 50 squared minus zero Plus 4.025 deployed by 100 square minus 50 squared. Then it equals 37.5. Find any full body. We want to grab the cumulative distribution function C d e f for these scores. The community of distribution function is the undid derivative of the of the probability density function. If here we have access to school, here is the fractions And we have scores from 0 to 50 And from 50 to 100. We integrate the constant lying here. The integration of horizontal line is a straight line with a bust of his troops, then it's from zero to face with this slope and the slope will be A. And we know that the area at 50 Equals 0.75, then Here is a .75. After then We have a straight line between 50 and 100. And at the end of a distribution function, we know that it's very equal warm, then it has a straight line like this, then it goes one And the slope of this line is the value of B, which is all .05. And this is they're required. The cumulative distribution function

So in this problem, we're gonna be looking at how out wires impact a scatter plot. I'm gonna be doing this in Excel. However, you need to do this in a graphing calculator. I will include the steps for that at the end. So first, we're gonna be making a scatter plot of the data. I'm gonna do free because later on in the problem, we're gonna need to separate the data into these three sections. The all right. So here is the data set and excel. I just highlight two columns go to insert, and then over here are the scatter quiets. So this is gonna be the one of all of them. The next one we want is without number 15. So to do that, I'm gonna highlight all of arm and hold control on Mac. It might be different, maybe, Commander, and then click on the two. We want to get rid of so the same thing again and start in your scattered quite. And I'll reach title this one without 15 a. So now I'm gonna make one without 18 on all title this one accordingly and next, we need to find the correlation for all three categories and then I'm gonna do the first part of part C at the same time, we're gonna make the regression line for all three categories of doing this and excel. We could just click on the crab if this plus fun in it. Check the trendline, barks and go to more options. And from there will put display equation on charts and display r squared on charts and I'll move those up here. So I'm just gonna go and do that with the over to now and trendline equation and r squared value if either too small to see all right them down at the end of China. So don't worry if you can't see you trendline more options equation and r squared. I don't now, don't this copy these down? This is our square that we don't want our squared. We want our The reason why R squared is called R squared is because it's literally just are square. So to get our all we have to dio is take the square root of r squared. So I'm gonna go back into a problem and I'll write down what we have so far. So our first equation put these in. Warrior Bar is equal to point or 82 and why is equal to 10 points or 08 x plus 66.4 to 9. So about 15 we get our is equal 2.568 and why is equal to 8.924 x, who s 69.487? Let about 18. We get our is equal 2.53 free and why is equal to 12 0.194 x plus 53.913 So let's take a look at the second half of part B. Do either of these outliers influence the correlation? Why did our change with these points? So as we're looking at these points, if you notice are seems to be higher without 15 18 however, it's not really that that big of a difference. So do either of these out wires influence the correlation. A little banza. It raises it a little bit. Now, why does it raise it a little bit? Well, without those out, wire points are graph is now able to be a lot more accurate at measuring all the other points, so any correlation we get is going to be much more accurate. So these two higher numbers are likely to be more accurate. So now we're going to make our regression line already did that. Do either of these outliers influence the lying? So we just take a look at them. We don't see a heavy amount of influencia. So again, the answer is a little bag. What we do see, though, is that the slope appears to be changing either up or down. Our default was 10 of the slope when we removed 15 it went down to about nine and then we were removed, 18 it up to about 12. So removing these out wires gave us a changing swell. So, for example, and this one we lost this high point out wire over here went away about 15 resulting in a lower slope because now the average point is a little bit lower. Whereas in this bottom graph, it went up a little bit because that point far off to the right as it is on the lower half. So removing it raised Arsal ova. So that looks like that's everything you need for this line. Here are the calculator steps to do this, you could take a screenshot off this, that this will explain how to enter data into your calculator, how to make a scatter plot to get r and r squared. And this is a one time setting. So if you've already done this, you can skip this and then finally, how to make the regression equation, which will have our in our square. And there are some pictures to help you do that, too. If you aren't using a T I calculator, most books will usually have a tutorial on how to do stuff like this for various different calculators. So you might be able to find these steps in your textbook till, and I think we're going.


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