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Case Study 3 Kimberly (30 y 13S [b) completed the ACSM submaximal bike test that elicited two submaximal HRs of [ [6 and 133 beats mn at the 450 and 600 kg min stag...

Question

Case Study 3 Kimberly (30 y 13S [b) completed the ACSM submaximal bike test that elicited two submaximal HRs of [ [6 and 133 beats mn at the 450 and 600 kg min stages respectively. Calculate her predicted VOzmax using method B. Imagine the heart rates were from palpation; but the monitor actually got [22 and 139 beats min-! Recalculate VOzmax with the monitor HR How much did this change the prediction of- VOzmax from the ACSM ergometer test? cycle

Case Study 3 Kimberly (30 y 13S [b) completed the ACSM submaximal bike test that elicited two submaximal HRs of [ [6 and 133 beats mn at the 450 and 600 kg min stages respectively. Calculate her predicted VOzmax using method B. Imagine the heart rates were from palpation; but the monitor actually got [22 and 139 beats min-! Recalculate VOzmax with the monitor HR How much did this change the prediction of- VOzmax from the ACSM ergometer test? cycle



Answers

The following graph gives the heart rate of a woman before, during, and after an aerobic workout.
a. What was the difference in the woman's heart rate before the workout and after the cool-down period? b. What was her approximate heart rate 8 minutes after beginning? (GRAPH CANNOT COPY)

This exercise were given a table of data that shows the heart rate of an individual at The number of seconds right after they stop exercising. So as soon as the person stops exercising, they have a heart rate of 154 beats per minute. After two minutes it's dropped 206 beats per minute. After four minutes it's dropped to 90. Were supposed to come up with a quadratic model for this data between zero and 4 minutes. So we're going to use vertex form to find the model because we are going to take the smallest value and assume that that is the vertex of harper abla. So I'm going to rewrite this quickly to say that the rate is equal to some stretch factor Times T -4 min. So we're shifting the vertex to four And at four minutes the vertex Is at 90 beats per minute. So my ancient K values are four and 90 respectively. And that shifts the vertex to this point on our graph. Then I'm going to make this pass through time equals zero to give us 154 beats per minute. So one time equals zero. The rate equals 154. And I'm going to rewrite this equation as 154 equals. Oops. I forgot to write a squared up here. Sorry about that. Whatever the stretch factor has to be to make this work zero minus for his negative for squared plus 90 To find out what the appropriate stretch factor is. And then I'm just solving. So I subtract 90 from both sides. 150 for -90 is 64. And that equals my stretch factor A Times -4 Squared as positive 16. And if I divide both sides by 16, I get that a equals 64 divided by 16, which is four. So back to the beginning, my equation for the function that gives me the rate of the individual's heart. As a function of time. Is it going to be A? Which is four times whatever the time T is minus four minutes, quantity squared Plus 90 beats per minute. And this gives me a model for that individual's heart rate. That answers the first part of the problem. I thought that I was erasing for some reason. I apologize for that. The second part Says to Evaluate F of one. I've been writing hard but mhm. Are of one equals I'm just plugging in. Time equals 1 1 -4 squared plus 90. And then calculating that that's for Times 1 -4 is -3. That should just be a 41 minus four is negative three. Negative three squared is a positive nine plus 90 four. Times 9 is 36. plus 90 is 126. And that means that after one minute mm this person's heart rate is 126 beats per minute bpm beats per minute. That's the interpretation. The interpretation is important. We don't want to just give a number without being able to explain it. And then we're supposed to estimate when the heart rate was between 115 and 125 beats per minute. So that is 115. Yes. Less than the rate Is less than 125. Mhm. And Let's do one side first. That means that 115 is less than for times time minus four squared plus 90. Since this is in vertex form I don't have to use the quadratic formula. I can just solve it because I'll be able to take a square brute so it's attracting 90 from both sides. That means that 25 Is less than four times T -4 Squared, Dividing both sides by four. I get six and a corridor 6.25 is less than t minus four squared, taking the square root of both sides. So I'm just trying to think of how I want to do this. Let's do it this way. Square root in 6.25 Gives Me 2.5. Okay, now this is plus or minus 2.5 and then I subtract four. Oh I'm sorry I add for So 2.5 plus four would give me 6.5 minutes. Okay? Mhm -2.5 plus four would give me 1.5 minutes. My data only goes to over text of four minutes. This is only valid between zero and four minutes. 6.5 minutes is outside of valid responses, which means that it's an extraneous solution. So It's going to be 1.5 minutes Is when the heart rate is 115. Sorry, I accidentally erased that. And then the other side I'm going to have 125 is greater than four times T -4 Squared. I saw it the same way. 125 -90 is 35. I divide both sides by four And I get 35 divided by four is 8.75 equals t minus four squared. I'm sorry is greater than T -4 Squared. Okay, I take the square root of both sides. That is 2.96. And again this could be plus or -2.96 is a greater than t minus four figure. Yeah. Yeah. Yeah. and adding for it to both sides, I'm going to get either 6.96 or Which would be extraneous or 4 -2.96 is going to be 1.04 minutes. So yeah, The time because this is decreasing, this is telling me that the heart rate is between 115 and 125 when the time is greater than 1.04 minutes And less than 1.5 minutes. Yeah. Mm

Oh, the next couple questions, they're all gonna be based on the graph you see in your book. And while I cannot draw that graph, precisely, I did want to draw a loose sketch to kind of be able to refer to it. So, um, we're starting with the question of what was her heart rate at the beginning before the beginning of the workout. So what was her heart rate at the beginning? And again, this graph is showing us the heart rate. So right here, that's the beginning of the workout. It's before. Well, I should say, this is the beginning. This is before the beginning. And since it's measuring her heart rate and it's flat at 60 we know her heart rate prior to starting working out is 60 beats per minute for be were asked, How long did it take her to reach her training zone? So this is where training zone starts. So we need to measure this length of time along our X axis. So if you look, of course, this is zero. And then the change happens when we hit 10 minutes. So a 10 minutes she began training

To start this problem. The first step we need to do as we need to do something that is called the T. Test or a T statistic. That's what we're finding a T statistic. The reason why is because in order to find the p value or the significance of the test, we need to have this number. So that's where we're going to start. So to do a T. Test, there's several different equations of how to get there. I'm gonna write both down so you can use whichever one you want, but we're only going to use one. So this is one option right here, it's more of a street forward option because you just kind of get T as your answer. Remember this is the E. Right? Right here, the symbol and the symbol of E represents the sum like this and then this and over that's a bad line for the second. There we are. That's right. Um This is just a little bit bulky for my liking so I don't really do this one as much, but this is one option, like I was saying, another way that this can be performed is how we're going to do it, or how I'm going to do it. So when a bar X one minus export to over square root, remember this symbol is the standard deviation for a population over and one loss this continues right here, deviation, swear it again. But for the second, the second one over until. So that's what we're gonna use right now. And when we use that, we know there are numbers right? Um given numbers we have for regular exercise, I'll draw over here just so it's easier to see this is where regular exercise, the end we had was 40. Um for none, none for no regular exercise was 30. This is Bar X. This is gonna be um we're gonna represent regular exercise at bar X. 1 63. And then marks to which would be this number would be 71 mm like this. And okay, so this is the table that we were basically given. So now with this we can simply put things in, we have the expo we have X. To have the center deviations and we can kind of figure that out pretty nicely. So once you solve and put everything in it will look something like this 63 minus 71 over one. My ex 40 plus 1.44 over 30. And that is going to give us our t. Test um statistic which is around negative 29.61 We're going around that, it's really 609 but we just can round right there. So this is our key test answer, but that's not exactly and what they're asking for fully. So that's the relevant test of the hypothesis. But we're using this now this is the relevant test, their part A but now we need to convert that into the significance of the test. And in order to do that we need a P. Value. So I was right here baby. The p value. If you look on any chart for T. Tests and P values you can kind of match it up and see that 29.61 for a T. Test will give you a p value of zero point 0001 So that's our P value. So now that we know the p value we can answer part beat up asking to compute you observe significance of the test. This tells us the significance of the test. How because the p value is less than 0.1 So that means that we reject the null hypothesis at a 1% level of significance is what they asked for, um In addition, this also means that the sufficient evidence, there is sufficient evidence. There is sufficient evidence, um to indicate that the resting rate, um and men aged from the 18 to 25 who exercise regularly over here is more than five ft per minute, less than men who don't exercise regularly. So this is the significance of the test right here.

The pulse rate function is our defined in terms. Off T 30 is the time off lapsing out off exercise is given as 1 51 e to the power minus zero point 055 de So no solving the first part as what really leave the wrecked act t is equal to zero. So R zero is equal to 1 51 p to the power minus 0.55 multiplied by zero. So we know they eat with the power zero is equal to one. So are zero will be equal to 1 51 beard's, but minutes No. The be part is who? When will be the rate of beards as equal toe hungry? So we have to find out the time when the exercise was a star when the rate bill full act 100 beats per minute. So tea is to find out now substituting the value here in the function as hunger is equal to 1 51 eat with up over minus 0.55 de no taking the law from both sides and making the cross multiplication. So we get log hunger by 1 51 is equal to love e to the power 0.55 So this will be as De is a great too log. Engage. Why 1 51 do you make your way? 0.55 a. The town bill in minus sortie will come as 7.5 minutes hands. After 7.5 minutes, the heartbeat will come out at 100 beats per minute. No.


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