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Q3 [16 pts] A 2004 research paper titled Are Emily and Greg More Employable Than Lakisha and Jamal? A Field Experiment on Labor Market Discrimination;' by Mari...

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Q3 [16 pts] A 2004 research paper titled Are Emily and Greg More Employable Than Lakisha and Jamal? A Field Experiment on Labor Market Discrimination;' by Marianne Bertrand and Sendhil Mullainathan aims to study discrimination in the labour market. Here's an excerpt explaining the study's methodology:Excerpt [page 991]: We send resumes in response to help-wanted ads in Chicago and Boston newspapers and measure callback for interview for each sent resume experimentally manipulate p

Q3 [16 pts] A 2004 research paper titled Are Emily and Greg More Employable Than Lakisha and Jamal? A Field Experiment on Labor Market Discrimination;' by Marianne Bertrand and Sendhil Mullainathan aims to study discrimination in the labour market. Here's an excerpt explaining the study's methodology: Excerpt [page 991]: We send resumes in response to help-wanted ads in Chicago and Boston newspapers and measure callback for interview for each sent resume experimentally manipulate perception of race via the name of the fictitious job applicant: We randomly assign very White- sounding names (such as Emily Walsh or Greg Baker) to half the resumes and very African-American-sounding names (such as Lakisha Washington or Jamal Jones) to the other half: The authors then measure the proportion of resumes that receive call for an interview (callback rate): The table below reports, for the entire sample and different subsamples of sent resumes, the callback rates for applicants with a White-sounding name (column 1) and an African - American-sounding name (column 2). Sample sizes are reported in the brackets. TABLE [ MEAN CALLBACK RATES BY RACIAL SOUNDINGNESS OF NAMES Percent callback for White names Percent callback for African-American names Sample: All sent resumes 9.65 [2,435] 8.06 [1,352] 11.63 [1,083] 9.89 [1,860] 10.46 [1,358] 8.37 [502] 8.87 [575] 6.45 [2,435] 5.40 [1,352] 7.76 [1,083] 6.63 [1,886] 6.55 [1,359] 6.83 [527] 5.83 [549] Chicago Boston Females Females in administrative jobs Females in sales jobs Males Is there statistically significant difference between the callback rates for White-sounding names and African-American-sounding names for the subsample of females in sales jobs? Also comment on the significance of your finding: Can we conclude that discrimination plays role in the difference in callback rates? Answer with hypotheses in formal notation, a quantitative analysis, and 3-4 sentence:



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Solve each problem. Several years ago, mathematical ecologists created a model to analyze population dynamics of the endangered northern spotted owl in the Pacific Northwest. The ecologists divided the female owl population into three categories: juvenile (up to $1 \text { yr old }),$ subadult $(1$ to 2 yr old ) and adult (over 2 yr old). They concluded that the change in the makeup of the northern spotted owl population in successive years could be described by the following matrix equation. $$ \left[\begin{array}{c} j_{n+1} \\ s_{n+1} \\ a_{n+1} \end{array}\right]=\left[\begin{array}{rrr} 0 & 0 & 0.33 \\ 0.18 & 0 & 0 \\ 0 & 0.71 & 0.94 \end{array}\right]\left[\begin{array}{c} j_{n} \\ s_{n} \\ a_{n} \end{array}\right] $$ The numbers in the column matrices give the numbers of females in the three age groups after $n$ years and $n+1$ years. Multiplying the matrices yields the following. $j_{n+1}=0.33 a_{n}$ Each year 33 juvenile females are born for each 100 adult females. $s_{n+1}=0.18 j_{n}$ Each year 18\% of the juvenile females survive to become subadults. $a_{n+1}=0.71 s_{n}+0.94 a_{n} \quad$ Each year $71 \%$ of the subadults survive to become adults, and $94 \%$ of the adults survive. (a) Suppose there are currently 3000 female northern spotted owls made up of 690 juveniles, 210 subadults, and 2100 adults. Use the matrix equation on the preceding page to determine the total number of female owls for each of the next 5 yr. (b) Using advanced techniques from linear algebra, we can show that in the long run, $$ \left[\begin{array}{c} j_{n+1} \\ s_{n+1} \\ a_{n+1} \end{array}\right] \approx 0.98359\left[\begin{array}{c} j_{n} \\ s_{n} \\ a_{n} \end{array}\right] $$ What can we conclude about the long-term fate of the northern spotted owl? (c) In the model, the main impediment to the survival of the northern spotted owl is the number 0.18 in the second row of the 3 $\times 3$ matrix. This number is low for two reasons. The first year of life is precarious for most animals living in the wild. In addition, juvenile owls must eventually leave the nest and establish their own territory. If much of the forest near their original home has been cleared, then they are vulnerable to predators while searching for a new home.
Suppose that, thanks to better forest management, the number 0.18 can be increased to $0.3 .$ Rework part (a) under this new assumption.

This problem is called truancy, and we need to identify the type of design that is being used in this study. So party. We're actually looking at an observational study. It's an observational study. Because there was no treatment being imposed, the researchers were simply studying traits such as attendance and mental health that already exist in the subject's. The researchers are not imposing new treatments. Barbie This is a retro perspective study because the information was obtained from school records that were already there. Part C. The subjects are the first graders fifth graders on secondary students who have been selected for three other studies party The parameters. The parameters of interest is the association between Mental Health and Truancy Party. An observational study has no random assignment, so there is no way to know whether or not there is a a casual relationship between mental health and truancy. The most we can say is whether or not in these stories there was an association

There's this problems. Meteo first convert a table of numbers in two seconds. So we have a table of minutes. So we have 1993 1995 in 1997. So it's a year, and we have the time. It's the first time is 26. They're all 26 minutes. Um so if we get 26 minutes time, 60 seconds, we can get the number of seconds And those just a minute part which is gonna be at 15. 60 and then adding the 58 38 at 15. 16. Um, but we're gonna get our 1993 value, which is going to be a 16 18 0.38 in 1995. I'm going to be adding 43.53 So me, 16 3.53 in the 1997 were adding 27.85 It's 15. 87.8, right? Okay, So, using a chart like the one they have in the book, we have it. We have a 1993. We have 1995. I'm scared of something like what's in the book? 1997. So it's gonna start kind of higher in 16. 18 a little lower 1995 and a little lower in 1997. Okay, so it's gonna be somewhere between the 16. 20 in 16. 16. Can they have? The rest of the dash is going down. Okay, that's that's about what it would look like approximately. Okay, so, um, gets the part b once, but he is the midpoint formula on 1993 and 1995 to find 1994. It's time the 1994. We'll look at the halfway point of this two times so that we're into 16. 18. You create the 16 03 three e. I don't know about Teoh. May 16.955 That's how many seconds it would be predicted for an approximation for 1994. Okay, um, so the loss making Peter Percentage era. So the actual time from 1994 was 26 minutes 52 23 sorts. Gonna add 52. 23 to ar 15 16 be 16 12.23 So I'm going to 16. 12 playing to three Prince attract 16 10.955 And divide that by 16. 12.23 Cancer in 16. 12.23 But now I'm using my calculator. 16. 10.9 Popeye, then all divided by 16. 12.2 green multiplied by 100 and our percent is gonna be 0.0 79 percent. It's a very small percent air on that one. Okay. Said my estimate was just slightly too low. Okay, um, case of part C wants me do the same thing for 95 to 97 to figure out 1996 is It's during 1996 in our halfway point between those two. So I'm gonna have 16/3 0.53 plus 15 87 28 5 What about two? So the estimate is gonna be 15 95 0.69 okay. And then, Ah, the percentage air we're gonna calculate Based off of the time given in part C, which is 26 minutes and 38 seconds. A 38.8. That's how I will be 15 98 point OK. 30. 15. 98 0.8 minus 15 95 0.69 Do. About about 15. 98 point away. So actual minus approximation, divided by actual. It's been in the calculator now and so 15. 98 point away my 15. 95.69 and then divided by 15 98. Going away looks by that about 100 and our percent ERA B 0.1 1496%. Okay, and so our estimate is just a little bit too low. Uh, actually, I was too low both times. It was just off by just off by a lot less than 1%. Okay, and then it says it is in the percent office is a little bit higher. Okay, it's in 1998. The time was an extra 22.75 seconds. So let's figure that out in seconds. I'm going to be 15 82.7 times. Okay, so it's our 1st 1 Was 16 12 approximately for 1994 when they gave us 15 98 for 96. So after the first year went down six seconds the next year went down nine seconds. The next year went down five seconds and then 11 seconds and then five seconds. So because where we haven't really seen a lot of leveling off yet. Um, uh, it mean, like, the very last time, it only went down five seconds, but because it went down five seconds before and then jumped again, it's It's hard to say just on the amount of data that they have. Um, but I would say that there's gotta be some maximum speed, so it should level off to the fastest, like, humanly possible to run it like no errors made. No missteps. There should be like a absolute fastest. Like if you designed a robot to run it, it wouldn't just keep leveling off to zero. Okay, well, thank you very much.

Okay, so in this problem, we have some background information about assisting readings, course ratings, and score on the final. Um, so I'm just gonna explain what I have on this white board so far, So in the middle, I just have this graphic that's given in the problem. And then I've written in the our values between the different lists between the different data sets. Um said our value between the, um assistant ready and the courts rating is 0.12 the R value between the course ready and the score in the final 0.46 The R value between the ready assistant reading in the score and the vital is negative 0.57 and it's all color coded. I just wrote it out in advance and calculated it in advance because it takes all the time. And I don't want to waste your time, But if you do want to tackle it, it here is the formula. But in most instances, on a test or something, you probably just check with this on your calculator through a linear regression. Eso for party says truffles on on the average dose sections that life there Ta that. Like their ta more did better on the final s. So let's just take a look at the r value between I'm between assistant rating and final score and you can see that our values negatives your 0.57 So since this our values, our senses are actually negative. Um, it actually appears that those who like their team or did worse on the final because there's a negative correlation between assistant reading and final, um, spinal squirt. So anything, uh, party would be false began. It's because there's a negative our value between course rating. Start this native our value between assistant reading and final scores. So those who like their assistant more actually did worse on the final. Uh, so for part B, it says, true falls. There was almost no relationship between the sections average reading of the assistant in the sections, average reading of the course. So that, uh, sections average rating of assistance. And we wanna find that our value, I mean, with the sections average rating of the course. And you can see that the correlation to a visions between the reading of the assistant and the reading of the course, but based on the calculation, that's our values, only 0.12 So, in fact, there is actually very little relationship between assistant rating and course rating. So be would actually be true. And finally see, says Truffles, there was almost no relationship between the sections, average reading of the course and the sections I've really score in the final. Well, again, we're looking at our bellies here so that our value, also known as correlation KeraVision between the rating and assistance and score in the final, is we start another here that we're looking at. Oh, yeah, well, I can't this called reading of the course and score in the final. So the R value between the rating of the course and the score the final is 0.46 That's not too strong, but you know there still is a relationship, so Statements C would actually be false because there is. It's at least a little bit of relationship between sections, average rating, the course and the sections average score in the final because 0.4 sixes are value between these two data sets, and it's still somewhat of a relationship. So see if he falls

Okay, so your question that yell jails juvenile population as it's a bottle and a is that a population off number off our found? Okay. And this is represented by a metrics where this is plus one year and this is the current here on this metric represent the weight ege off each type age off here. If you simplify, this will be multiply these metrics with this, we get the juvenile population at one year after his 10.33 times the adult population at that time then similarly, Sabadell population one year after its 10.1 times the general population at that time and adult population one year after is 71% off Severin population in 94% off every population. Okay, so this is what the data is given. Now what we have to assume suppose currently that is, at present, state, we have total 3000 polls out of that. Sorry. This is 6 19 juveniles and to 10 substance and 202,100 address. We need to use metrics to find total all population each year for five years. Okay. And let's take another question. So this is what we can approximate these using advance method. And from that we have to identify what will happen eventually to else eventually two old right. So this is what we need to find from this. And she's asking for if this point wanted here, which is multiplied with juvenile. So that is we're very small value and not represented. General population or face is very important for increment in our population. So if it is increased by using various reforms and using better management then and change it 2.3, then calculate part A. Okay, so let's dive in So first. Okay, so we need population hs o j n plus one s n plus one A and plus one is equals to the metrics is Zito 0.180 Zito Taito 0.71 little 0.33 Zito little 0.94 times current time. So let me die for me a j n Hessen and in Okay So first year that is an equals to zero. So J one s one and one will be equals toe the same metrics and this is values given to us. It is 6. 90 to 10 and 2100. So on solving this metrics by using matrix multiplication, we get J one j two. Sorry s one. And and one. Sorry. This is Evan, right? Evan, is it? Calls to it is 6 93 and we have won 24 2123 So total population will be addition off all this. So 693 plus 1 to 4. And this is population after a year. Plus 2, +123 And this gives us +2940 Okay, so we have this value now, using this as an input. So the second one will be that isn't J two s two a two will be called. So in metric 0.180 0.710 point 3300.94 times this. You want first year value 6931 to 4 to 123 and on solving this and calculating the total we get. T two equals two 2909 Similarly, for second year territorial, T three will give us 286134 We'll have toe 81 full and defy. That is 50 year we'll have 2767 Now we can see the population is decreasing. Continues letters from 29 to 29 09 Then 28 61 21 4, 27 67 Okay, so we found that our population is decreasing and that is a part a solution. Now we need party. So partly says we can approximate the given metrics, etc. And plus one is N plus one a and plus one as 0.98359 times J s n a n And since this value is less than one Okay, so on multiple multiplication for first year, it will be this for second or it will become square three years cube and on making it higher powers. This will approach to zero, right? So eventually the old population is going tobe Israel and they're going to get managed so that it's part B for part C. We need to change 0.1 to 0.3 into our metrics. Do you do some measures taken so he can write J n plus one s n plus one a and plus one? Is it close to 0.30 0.71 0.3300 point 94 And this is famous and J. N. Essen A. And Okay, so now we can substitute of value. So to calculate J one s one a one, this is 0.30000 point 710.3300 point 94 times the same values which we have already substituted in question number, but a Okay, so that it's 6. 19 to 10. Hm, 2100. So on solving this, we get J one s one a one s 3693 Same as because this the way same second row will change. So the answer is 207 and thorough again. Same. So we'll have same value. That is 2121 So on adding this we get first year population is 30 to 1. And if you see there is increments of 21 all because off slight change in the juveniles taking care of percentage of survival. Okay, so similar basis we can calculate to that is equals to 051 33 3079 34 This 3107 25. We get 3135 Now you can see there is a steady increase in the number of all population. Thank you.


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