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Use 0=590 for the problems_ The primary objective ofthe Study on the Efficacy ofNosocomial Infection Control (SENC Project) was determine whether infection surveill...

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Use 0=590 for the problems_ The primary objective ofthe Study on the Efficacy ofNosocomial Infection Control (SENC Project) was determine whether infection surveillance and control programs have reduced the rates ofnosocomial (hospital-acquired) infection in United States hospitals This data set (SENC.xls) consists of random sample of 113 hospitals selected from the original 338 hospitals surveyedEach line ofthe data has an identification number and provides information On 11 other variables fof

Use 0=590 for the problems_ The primary objective ofthe Study on the Efficacy ofNosocomial Infection Control (SENC Project) was determine whether infection surveillance and control programs have reduced the rates ofnosocomial (hospital-acquired) infection in United States hospitals This data set (SENC.xls) consists of random sample of 113 hospitals selected from the original 338 hospitals surveyed Each line ofthe data has an identification number and provides information On 11 other variables fof single hospital. The data presented here are for the 1975-76 study period The 12 variables are: ariable ariable Name Description Length of Stay_ Age Infection fisk Average length of stay_of all patienti_in hospital (in days) Average age ofpatienti (in Years) Average estimated probability in acquiring infection in hospital percent) Ratio of number of cultures performed to number of patients Without sign3 QI Ymptom= ofhospital-acquired infection times 100 Ratio of number of X-rays performed to number of patients without signi Qr_Symptom; of pneumonia times 100 Average qumber of beds in hospital during study period Routine culturing ratio X4 Routine chest X-ray ratio Vumber of bed: Medical schoo affiliation Region Average daily census _ Vumber of nurses 4 2 Geographic region Where:L=VE2NC Z=S A=W Average qumber of_patients in hospital pet day during study period Average number full-time equivalent registered ad licensed practical nurses during study period (number full time plus One half the number pat tine 'ercent Of 3> potential facilities and services that are provided by the hospital Xlo Available facilties and services



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Refer to the following data set: According to the U.S. Department of Health and Human Services, herd immunity is defined as "a concept of protecting a community against certain diseases by having a high percentage of the community's population immunized. Even if a few members of the community are unable to be immunized, the entire community will be indirectly protected because the disease has little opportunity for an outbreak. However, with a low percentage of population immunity, the disease would have great opportunity for an outbreak." Suppose a study is conducted in the year 2016 looking at the outbreak of Haemophilus influenzae type $b$ in the winter of 2015 across 22 nursing homes. We might look at the percentage of residents in each of the nursing homes that were immunized and the percentage of residents who were infected with this type of influenza. The fictional data set is as follows. What is the impact of the outlier(s) on this data set? Identify the outlier in this data set. What is the nursing home number for this outlier? b. Remove the outlier and re-create the scatterplot to show the relationship between $\%$ residents immunized and \% residents with influenza. c. What is the revised correlation coefficient between \% residents immunized and \% residents with influenza? d. By removing the outlier is the strength of the relationship between \% residents immunized and \% residents with influenza increased or decreased? e. What is the revised equation of the best fit line that describes the relationship between $\%$ residents immunized and \% residents with influenza?

We're given data regarding nursing home residents. What percent immunized, what percent had influenza? And we're looking to see what the relationship between those two things, as our first task was to right. A scatter platter to make a scatter plot. The scatter plot waas done using Excel. We have the, uh percent of residents with influenza on the Y axis and the percent that have been immunized on the X axis. And we can see the more that are immunized. A smaller percent get influenza. There's a negative linear trend, so we know that when we get around to finding our are is going to be less than zero. We were tasked with determining the best fits and finding out what are is so using Excel, we added what's called a trendline. That's this some dashed blue line here, and we also, uh, did what's called. We displayed the equation and we displayed the R values. So the equation is on top and they are r squared. Value is the 0.6596 Our second task was to determine our So are is going to equal the square root of our squared, but we have to give it a sign and the Sinus based on whether it's a negative association or positive ours less than zero, which means it's negative. So if we take the square root of 0.6596 and then, of course, multiplied by negative one, we're going to get negative point eight one two. So that's our our value. And that's that's fairly strong, right? We would describe. This relationship is a fairly strong it's so fairly strong, and it's negative, right? It's trending downward as X increases. Why decreases so fairly strong, negative in its linear. And our best fit equation is given to us by excel we had to do is display it on the scatter plot. So there it is, right there y equals negative 0.26 execs plus 32.196 and our is large enough weaken. Say, uh, are is large enough to make Reese Reasonable predictions are is large enough so we can make reasonable predictions. Using that best fit equations, we can make reasonable predictions. It might be some error won't be perfect. That would be reasonable

Okay, This exercise, you're given a differential equation on in part A. We have to find the equilibrium solutions. Now, remember that these are solutions. That's that is so I thought the derivative would respect. The time is zero if we use the differential equation were given. We have cereal equals off times wide, one minus y. Now, the solutions of this equation we can see that are the constants. Uh, they will be constant functions. Why gone zero on y equals one now to see if they are a synthetically stable or unstable. Let's take a look at the graph of the function. Alfa Atoms lightens one minus y. It's a problem. We know. Um, it crosses the X axes at 71 So here's the sketch of this parabola. Here's one on Syria. So the problem has positive values in the interval 01 and negative values for X greater than one on. This means that if a solution takes value between zero and one, then it has to increase on. If a solution takes a value that is greater than one, then it has to decrease on. That makes why equal zero, uh, a symptomatically unstable on Why? Cause one a synthetically stable sympathetically is stable. Okay, so now for part B, we have to solve the differential equation. No, this is a parable equation. So we can write it as the Y over wide them Swimming swab equals Alfa Times. It, um on from here on the left hand side. We can, Right. This is one minus. Oh, sorry. One of her white place. One of her one minus y. And you can do this way. Partial fractions. Uh, but it's just check. It's true on from here, we can just integrate. So we get the localism off. The absolute value of why, minus the lab, a rhythm off. The absolute value of one minus y equals up for time, Steve. Plus a constant. Now, using the properties of the love artisans, we can, um, rewrite the left hand side as the look at some of the absolute value of why everyone minus way, way have how 30 Lucy. Now we can apply the exponential to both sides on bond. Yes. Since why gives us the preparation of a population? Why everyone minus why is positive. So when applying the exponential we get, we can get rid of the absolute value. So we get why over one minus y equals a constant. I'm see today t uh them see to the Al. Fatih Sorry, Aunt Uh from here we can solve for why? Yeah and Thio. We're going to multiply everything. Times one minus y. So we get what equals 11 is why time See them? You to the Al Fatih, we can expand the right hand side e this Why I see it The Al Fatih on we can pass its last term to the other side factor. Why? So we get white times one plus c e to the city equals C Eat to the offer de Now we can divide over one pless See Eat the Al Fatih on both sides and we get this expression he did the Al Fatih Now it only is full to write this expression, uh, in a different way. So let's multiply this by one on. This one is gonna have the form e to the minus off a tea over eat minus Salvati. Andi Yeah, When multiplying we get see Time's well the product off to the Al Fatih on e to the minus. Salvatti is one. So we just get C on the numerator and then on the bottom, we get it the minus off a t plus C. Uh, yeah. So now, to find this constant, we can go back to that line in the middle. I guess it's this year. Uh huh. She lets, uh, that's but here line. Yeah, we can go back to this line on use it. Initial value were given, so we have the initial condition. Why? Evaluated at zero equals y Syria. So we use this. We get why 0/1 minus y zero equals c times E to the Alfa time, Steve. But in this case, t zero but eight today, zero, this one. So we can just get rid of this. So we get this constant on. Yeah, by using this consent in the solution we found before we have obtained, Why equals why zero off? Very one, minus y zero. Over. Eat the minus off a t plus y zero over. One man is why syria Now, to simplify this, we can again multiply, uh, by one. I want to play this term containing e to the minus Elfatih by one on that one is gonna have the form one minus y Syria over one minus 10 So that now everything is divided by one of her one minus 10 We can just cancel them. Andi. Yeah, we have now the solution. Quite zero over. Quite zero. Every gotta Syria. Harper. Okay, so 1 0/1 0 plus one minus. Why zero time? Eat the minus off at at this. Finally, as the solution of the differential equation. Now, in part C, we have to verify that. Why is a synthetically stable for that? Let's take this solution on debts. Computer limit off the solution as the ghost infinity. So we get y 0/0 plus one minus y Syria Tense it to the minus alpha T But as the ghost infinity it the minus. Alpha t goes to zero. So we get what is your over? Well, why Syria, which is one on this is the equilibrium solution we found in part A On this means that all the population will live in

All right. Hello, one. So I've written down the table. You're given Andi about a two lines s. So the first thing to do is to take the difference between the number of cases in one period on bond that of the previous period. Eso, for instance, here, uh, 220 to minus 95 gives you 100 27 on that basically gives you the number of cases. Total number of cases between the two intervals. Eso again here 417 minus 2022 gives you two and 48 and so on. But now the question asked you the average number of cases in each interval on. But then, to do that, you have to divide by the number of days in each interval and the first interval has five days and all the other ones have seven days. So you then divide here 127 by five to obtain 25.4 on That basically tells you that on average and you have 25.4 new cases in the first five days and then the following seventies eso between the fifth day and the 12 day you have 35.4 Sorry. 35.4 cases on average a zoo divide two and 48 by seven. And then you continue for all the different values. Eso Exactly. It's the same thing. You divide this number. So, for instance, this number here during eight by seven, 2, 15, 44. so I've just written down values. Um, I stopped a bit before because it basically is. It's the same thing for later values, Onda. That gives you three answer for question A on now, regarding the next question. Um, so when did the PMO just have evidence to locate the rate of new cases began to slow? Well, either you then simply have to take the average rate on DSI. When that starts to decline on approximately, it's more or less here. Okay? Because so at T equals 19. So, unfortunately, we don't have a day by day data. Uh, we only have every weekly data set. Um, but we can say that approximately after 20 days theme, the rate of inflection started to slow down as the average number of cases per day source to decline. Um, Okay, Right. So why would an expansion exponential model be inappropriate. So the two ways of seeing this firstly well, as you can see, it slows down. Whereas an exponential model, uh, simply grows forever on grows out of increasingly fast rate eso. In a way, the exponential model works quite well. In the early phases of this, um would fit quite well the data in the first few days on board. That's generally the case. And that means that is the case for logistic models, logistic growth models. Um, but as you can see, the number of cases slowly starts to decline, and then at the end, it becomes quite stable, which is definitely not the case for an exponential growth model. On. Additionally, there is some form of absurdity which arises through most exponential models is it's because exponential models grow to infinity on bond. Um, it would imply that at some point P would take the value, Let's say 10 billion and there are no there. There aren't 10 billion people on this earth. So, um, there is some form of of impossibility through expansion holds. Yeah. Um, Okay. So, um, getting so then we're told that a logistic model fits the data quite well. Um, And now regarding the inflection point, we know that the inflection point is the point at which the rate of growth starts to decline on. But that is basically equivalent to the question be, that is, as you can see again, growth here starts to decline. AT T equals 19 eso. That is our inflection point. And when it comes to limiting value of P, um, you know that the limiting value off P, um, which is the carrying capacity also of this logistic growth model, eyes twice the value taking at the inflection point. Now again, we don't have a precise, precise data set. A, we can say is that it is approximately a T equals 19. So what you do is you double the value taken by P. AT T equals 19, which is 800. So the model would predict more or less a total number infection off 1600. Now again, if we have a date today data, we would maybe see that this increase carries on the YouTube 20 40th or 21st day, and we'd have a slightly higher number on when you look at the the limiting value it seems to converge towards 1750 something. Okay, so we're not far off. Um, okay. And so were given a precise, uh, precise logistic function which fits this data in some sense. Andi, you asked for limiting value of team. So let me write down P, which is a function of time. Okay, 50 is equal to 1600 divided by one plus 17.53. Sorry. I eat to the power of minus zero point 14. 0, 80. Okay, Now, if you already familiar with realistic group logistic girls, you know that this year is the carrying capacity. Andi, that, uh, dysfunction p converges towards this point or another way of seeing this is to calculate this limit explicitly on. Do you know that e to the power of minus something which goes to infinity converges to zero. So this everything here converse to zero, and you're again left to left with 7 1760 divided by one. So 1760 which again fits the data quite well. We know that after 87 days, we're at 1000 and 55 the number of cases really seems to die out at this point. Thank Andi. Yes, that's that's it.

Hey, guys, let this problem 38. The first question is what is the effect of the absence of my society guidelines? According to this craft, yeah, removal of the society utilize jean resulting inhibition of the materials submitted to form because we see there is a drop in this, uh, blood. Therefore, as two separate allies jean removal of this gene resulting inhibition of the bacterium's ability to form granny molars in the mouse lung. Then the second question is, Do this results support those objecting part? Yeah, there's some results given if they are supporting it or not, the bacteria lacking our societal eyes are unable to grow as efficiently as those having the gene restored here. These are again unable to grow as effectively as those having the gene stress room, and this result is consistent with party then problems. CS gas. What is the purpose of the experiment in value B with reinsertion of our society? Clients gene into the bacteria from which it had been remote previously, we destroyed the normal activity, which reaffirms the notion that I society it nice is essential for the proper function of the bacteria. Therefore, when we are again giving back the associate utilized green. The material is functioning and it confirms that I suspect scrutinized is important. It is essential Also, it indicates that any other gene which might have been damaged during the removal of our society civilization is not responsible for preventing the latent infection. And the last we should ask us, why do this victory? A parish In the absence of glad Koksal lie, I was in a cycle girl. I also love cycle is used to generate carbohydrates in the plans that are necessary for the survival of bacteria. And without this ability, bacteria will perish. Therefore, without like a psycho and I also live cycle actually will. We're rich because it only have a little generated carbohydrate.


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