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Hypertension It has been found that 26% of men 20 years and older suffer from hypertension (high blood pressure) and 31.5% of women are hypertensive- random sample ...

Question

Hypertension It has been found that 26% of men 20 years and older suffer from hypertension (high blood pressure) and 31.5% of women are hypertensive- random sample of 147 of each gender was selected from recent hospital records_ and the following results were obtained_ Can You conclude that a higher percentage of women have high blood pressure? Use a = 0.01_Men43 patients had high blood pressure Women 57 patients had high blood pressureUse P1 for the proportion of men with high blood pressure an

Hypertension It has been found that 26% of men 20 years and older suffer from hypertension (high blood pressure) and 31.5% of women are hypertensive- random sample of 147 of each gender was selected from recent hospital records_ and the following results were obtained_ Can You conclude that a higher percentage of women have high blood pressure? Use a = 0.01_ Men 43 patients had high blood pressure Women 57 patients had high blood pressure Use P1 for the proportion of men with high blood pressure and round all intermediate calculations to at least three decima places;



Answers

Medical: Hypertension This problem is based on information taken from The Merck Manual (a reference manual used in most medical and nursing schools). Hypertension is defined as a blood pressure reading over $140 \mathrm{mm}$ Hg systolic and/or over $90 \mathrm{mm}$ Hg diastolic. Hypertension, if not corrected, can cause long-term health problems. In the college-age population $(18-24$ years), about $9.2 \%$ have hypertension. Suppose that a blood donor program is taking place in a college dormitory this week (final exams week). Before each student gives blood, the nurse takes a blood pressure reading. Of 196 donors, it is found that 29 have hypertension. Do these data indicate that the population proportion of students with hypertension during final exams week is higher than $9.2 \% ?$ Use a $5 \%$ level of significance.

Hey, part normal value is equals to 1 25 on the actual. This Doleac, they said, is the question 116. So, really, that is the difference can be given US B minus 1 25 more on that is 116 minus 1 25 full board is because tomorrow minus nine articles to nine. So the difference oppressors equals to nine be part were given with their difference. Really, that is equal to 17 on the normal present values given us 1 20 so we will calculate actual systolic pressure. We know marta P minus one point days because toe clearly that is 17 so B minus 1 20 vehicles to 17 40 minus 1 20 degrees to minus 70. Solving both we get being is equals to 1 20 plus 17. Or he's because +21 20 minus 70 means the value peas either 1 37 are easy close to 103

So in this problem, we're dealing with that blood pressure equation. We have the blood pressure at a particular point in time is equal to 100 plus 20 times the sign of seven pi over three t and we know that the amplitude is 20. We know that the middle of the graph is our it's vertically shifted at 100 it will rise up to 120 it will drop 20 below and go down to 80. So our our picture of our graph which were not given instructions on this faras whether to do this totally algebraic Lee or to do this with a calculator. So I'm going to do it based on using our calculator. So I put my calculate in my calculator Ah, window that when asl oas 80 and when as high as 120 because again, I know the graph is oscillating along the line y equals 100 and I have the 20 as the amplitude. So from 100 it's going to go up 20 and down 20. And then we were on Lee interested in the graph from zero toe one. So when I graft. This the graph does something like this and it comes up and it comes down and it comes back up. And we know that the period of the graph, the period of the graph is two pi. It doesn't ask us about this, but just for review purposes. That two pi divided by this coefficient is what our period did, which was to be two pi times. 3/7 pi thighs would cancel, so it takes six seventh of a time period to complete one cycle. So that would be what this point right here would be at 6/7. And so if we look at this little picture here, we know that everyone Fourth, we could actually figure out either by graphing using our graph for or with this type pubs set up. We know when it's going to end up equaling zero and 100. Uh, at time, zero, it's gonna be at 100 then half away later, it's gonna be at 100 half away later. It's gonna be 100. So this is going to take place at 3/7. So we know at zero and at three. Seventh and at 67 we're gonna end up having it at a time of zero. So that was our first question. And we didn't even use really the graph for to find that. But we wanted to find When will this blood pressure be at 100? And I can see that those times are going to take place at time zero and at time, three sevens and at times 6/7. And you could get the death with approximations for that. And I have to look. But now we want to look at the 1 20. When will the blood pressure be up to 120. And again, if I know that this is at 3/7 and one thing I do for my students is I make them find how often the we have critical points. We have critical points every 1/4 of the period and the period waas 6/7. So ATS and that will reduce down. So every 3/14 of a time unit. So at time, zero. This is at 3/14. This is at 6/14 which is 37 and then we confined when it's gonna equal 80 by adding on again 3 14 and add on 3/14 again, We'll be back here into the metal. So So anyway, we know that that time is gonna end up taking place. And right up here at 3/14 Um, and decimal wise, I think that comes out to be about 0.214 and then we want to define when is this going to end up being between 100 and 105? So when is that PMT going to be in between those those values air from that to that value. So what I did on my calculator is already know what these times are, but I didn't know what 105 watts and I could have algebraic Lee saw. But I would still have to use my calculator to figure it out. And I had it graph Why equals 105 as like why some too. And I needed to find this point and this point and this point and so I can see that this is an interesting part of my graph. This is an interesting part of my graph, and this is an interesting part of my grab, and I've found the location of this point to be and 0.34 time units. And this one came out to be 10.394 And this one came out to be 10.89 So I would have quite a few time intervals. I would have if zero is to t is 2.34 that in that time frame we would have our blood pressure in this range. If we go from 0.394 to this point, which is at 3/7 that would also work. And then from 6/7 which again you could get the decimal approximation 2.89 Those would also be locations. So? So we did much of it without graphing without the graph for but a little bit of it, you would have to use that that intersect feature to find those points.

So you're, uh if I talk about, uh I mean, before I start with the part, let me just consider the history graham that they have given us in the question. So I'm gonna take the history. I'm here first. Yeah. So you just resize this fast. Yeah. So does becomes easy for us to reform in resolving the problem now. So, uh, now if you observe over here if we start with the first question that it's been asked. So by observation, you can see that the area under the history Graham between say, 1 30 over here. This is 1 30 and ah, one sixties over here. So this is about 1/4 of the total area. So the idea of the blocks of the history Graham did a prison percentages over? Sure. Andi, I would therefore say that the person did off the women with the blood pressure. Uh, pressures above 1 30 Mm. All right is around. See 25 person because you can see that it forms the almost quarter of the Tokyo area. So this is the first part again, moving on its second part again. If you observe the historical, um uh between the Rangers and 90 and one sixties averages over. Sure. This is 90 on 1 60 over here is the last. So you can see it's a bold the old lady off in front of totally go off all the area off the blocks which have been given to us in the history. Graham and individually, they all represent percentages. Fight. So that is why you can see that in this case, the boss and age Well, women with blood pressure's between nine demon. I want 60. Mm. Oh, is around, say 99% as you can see the diagram. Sure. Right now, moving on to the next part for the bar to see again. You observe this telegram. Uh, you can take the range of 1 to 31. 40 to 1 50 Here. It appears to be more than that is compared to ah 1 35 to 1 40 this 1 35 years. I wondered if I do fork one forties, this part and, uh, this is 1 40 to 1 50 Right? So it means that there are moving mill Indian double 1 40 to 1 50 So, And would you write down that part. You're that, uh, from the history. Graham again, huh? The idea. The dream 1 41 50 Mm. Appears Toby more than that between 1 35 1 40 Mm. Right. So therefore, we say that there are more women in the in. Double off, one for Deacon, 1 50 Mm. Right. Yeah, No morning. Under the next part, the party we're going to check over the interval again, who are from 7 35 1 40 Which is this one doesn't double, but it And you can see that it appears to be taller than the block over the double 1 40 to 1, which is this one. Right? So we see that this interval over here is more crowded, right? So I would therefore say that since the indoors off 1 35 to 1 40 mm is a dollar, then the in double off 1 40 to 1 50 Mm. Right. So we therefore conclude that the interval off 1 35 to 1 40 is more crowded. Oh, yeah. No going on to the next part. The fifth part here, Or if you see that each one millimeter in double between or 1 25 year old is the line for 1 25 and wanted Tim. Millimeter contains about 2.1 positive women. So I can say that from 1 25 millimeters toe 1 30 millimeters, there are about 2.1% off women. And there are five of these in one millimeter in troubles between 1 25 and 1 30 So the difference over here, you can see is off for five millimeters. So that is why I can therefore, counselor, the percentage of women that have blood pressures and this interval last 2.1 and we can do five. So this gives me approximately 10.5% as the answer for the bod ee. And, uh, next is if I talk about the part, if again from the history. Graham, you can see that the block in trouble from homeland to 203. Mm. So over here it's between 100 100. And then Okay. That is going to be Ah, dollar blow. Here. You can see this block a stall over, then double from 97 to 90. It's this and this is the comparison here. So we difficult route. That 102 103 millimeter. Have more women. Right? So therefore, we conclude that 100 to 203. Mm. Have more women, Right? And next, I'm moving on to the bar G for the bar G. You can master that, which is a Peter. Well, the history ram is highest. So the history Graham is highest overtaken double from, say, 100 and 15. 220 as you can see here. So I'm going to write that in double this. 115. 220. Mm. Where the history Graham is of the highest. Yeah. So we've done that, simplifying all the questions that


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