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Complete the case study by following the prompted directions and answering Directions= Please Many questions are asking Vour opinion on the analysis the following q...

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Complete the case study by following the prompted directions and answering Directions= Please Many questions are asking Vour opinion on the analysis the following questions_ proper explanation: You therefore many answers are considered acceptable with data/graphs, do not ask for Braph explanation should turn any graphs/questions that are asked for; if ! The solutions should be numbered based on the question you are answering: itis not necessary: cannot read/understana your work or thought proces

complete the case study by following the prompted directions and answering Directions= Please Many questions are asking Vour opinion on the analysis the following questions_ proper explanation: You therefore many answers are considered acceptable with data/graphs, do not ask for Braph explanation should turn any graphs/questions that are asked for; if ! The solutions should be numbered based on the question you are answering: itis not necessary: cannot read/understana your work or thought process The solutions may be hand written (if combination of will have points deducted) or you may type Up your solutions/graphs or You THURSDAY, APRIL 25" BY 12:20 PM You both_ The due date for this case study is You decide either hand me : physical copy by this class date Or submit an electronic cOPY: Mdr PDF t0 tne appropriate drop box section to submit a electronic copy; please submit accepted: Submissions by email will not be Pictures taken on cellphones WiI not be Blackboard_ automatic for the assignment Any evidence cheating/plagiarism will result in an accepted_ and then tor every 24 hours that it is late will be Late submissions will result in 10% deduction_ another 10% deduction Case Study #3 conducted in 2017by the U.S. Census Bureau, 33.4% of Americans 25 or older According to_ poll bachelor' degree higher. This steep increase from the 28% said they had completed With so many Arnerican' carning bachelor' $ degree_ the with college degree decade a8o. Fyear collcee tuition has been highly debated and topic of student debt and overall price for platform for several political candidates. ~year college costs per vear iin New We would like Bet an idea about just how much moncy sample of the following data- The tuition is per Jersey: You t0 12 popular colleges and get You may assume the population normally distributed year far the average in state student: College Tuition (per year) Rutgers University _ 514.131 Rowan University 512,864 The Colleee New Jersey S15,466 Princeton University 543,450 Montclal State University 511,773 Stockton University S12.820 Rider Universty 538.360 Seton Hal University 538.072 Bloomfield Colleke_ 527,800 Kean University 511,581 Ramapo College 513.698 William Paterson University 512,365



Answers

The data set in VOUCHER, which is a subset of the data used in Rouse (1998), can be used to estimate the effect of school choice on academic achievement. Attendance at a choice school was paid for by a voucher, which was determined by a lottery among those who applied. The data subset was chosen so that any student in the sample has a valid 1994 math test score (the last year available in Rouse"s sample). Unfortunately, as pointed out by Rouse, many students have missing test scores, possibly due to attrition (that is, leaving the Milwaukee public school district). These data include students who applied to the voucher program and were accepted, students who applied and were not accepted, and students who did not apply. Therefore, even though the vouchers were chosen by lottery among those who applied, we do not necessarily have a random sample from a population where being selected for a voucher has been randomly determined. (An important consideration is that students who never applied to the program may be systematically different from those who did-and in ways that we cannot know based on the data.)Rouse (1998) uses panel data methods of the kind we discussed in Chapter 14 to allow student fixed effects; she also uses instrumental variables methods. This problem asks you to do a cross-sectional analysis where winning the lottery for a voucher acts as an instrumental variable for attending a choice school. Actually, because we have multiple years of data on each student, we construct two variables. The first, choiceyrs, is the number of years from 1991 to 1994 that a student attended a choice school; this variable ranges from zero to four. The variable selectyrs indicates the number of years a student was selected for a voucher. If the student applied for the program in 1990 and received a voucher then selectyrs $=4 ;$ if he applied in 1991 and received a voucher then selectyrs $=3$ and so on. The outcome of interest is mnce, the student's percentile score on a math test administered in $1994 .$
(i) Of the 990 students in the sample, how many were never awarded a voucher? How many had a
voucher available for four years? How many students actually attended a choice school for four
years?
(ii) Run a simple regression of choiceyrs on selectyrs. Are these variables related in the direction
you expected? How strong is the relationship? Is selectyrs a sensible IV candidate for choiceyrs?
(iii) Run a simple regression of mnce on choiceyrs. What do you find? Is this what you expected?
What happens if you add the variables black, hispanic, and female?
(iv) Why might choiceyrs be endogenous in an equation such as
$$m n c e=\beta_{0}+\beta_{1} \text { choiceyrs }+\beta_{2} b l a c k+\beta_{3} \text { hispanic }+\beta_{4} \text { female }+u_{1} ?$$
(v) Estimate the equation in part (iv) by instrumental variables, using selectyrs as the IV for
choiceyrs. Does using IV produce a positive effect of attending a choice school? What do you
make of the coefficients on the other explanatory variables?
(vi) To control for the possibility that prior achievement affects participating in the lottery (as well
as predicting attrition), add mnce $90-$ the math score in $1990-$ to the equation in part (iv).
Estimate the equation by OLS and IV, and compare the results for $\beta_{1 .}$ For the IV estimate, how much is each year in a choice school worth on the math percentile score? Is this a practically
large effect?
(vii) Why is the analysis from part (vi) not entirely convincing? [Hint: Compared with part (v), what
happens to the number of observations, and why? ]
(viii) The variables choiceyrs1, choiceyrs2, and so on are dummy variables indicating the different
number of years a student could have been in a choice school (from 1991 to $1994 ) .$ The dummy
variables selectyrs1, selectyrs2, and so on have a similar definition, but for being selected from
the lottery. Estimate the equation
$$m n c e=\beta_{0}+\beta_{1} \text { choiceyrs } 1+\beta_{2} \text { choiceyrs2 }+\beta_{3} \text { choiceyrs3 }+\beta_{4}$$ $$+\beta_{5} b l a c k+\beta_{6} h i s p a n i c+\beta_{7} \text {female}+\beta_{8} m n c e 90+u_{1}$$
by IV, using as instruments the four selectyrs dummy variables. (As before, the variables black,
hispanic, and female act as their own IVs.) Describe your findings. Do they make sense?

Part one out of 990 students in the sample. The number that were never awarded a voucher. R 468. And you will find that number in our by something. All the cases, this is his name of the data set dollar sign. And select years equal equal zero. You are counting the total number of cases where select years is zero. How many students had a voucher available for four years. So similarly, you find the total number of cases where selected ears double equal four. And you will get 108 students. Then how many students actually attended a choice school for four years counting all the cases were variable choice years equal equal for you get 56 party. You you run a simple regression of choice ears on select years. This is what I get. I get there slope coefficient to be minus 1.837 And this one is significant. The minus sign is not what I expect. These regression is telling us that, mm, mm hmm. Uh huh. All right. This is actually part three. All right, sir. In Part three, you run a simple regression on uh of math percentile on choice years. And this is not what I expected. Because this result is telling me being able to attend choice years actually decreases math scores. And the variable um the estimate on choice ears does not change when I add the demographic variables black, hispanic and female. Okay, so I actually accidentally skipped part two. Yeah. Let's move down to the end. In part to you. You are examining whether select ears is a good instrument for choice ears and the answer is yes. This is a regression result. This equation is telling us being selected for a voucher increases the chance of the students attending the school of choice. And the relationship is strong. Almost 1 to 1 and also highly significant. Select years can be a good instrument, assuming that it does not correlate with the error terms in the choice years. Um Now in the mass score equation let's continue with Part four. Why might choice years be endogenous in the given equation, I could think of two reasons. First one admitted bearable bias. It is possible that we have not accounted for some factors that affect both mass scores and the number of years students attending the school of choices, for example, intellectual ability and the second reason is reverse causality. The problem does not give more context on this, but it is possible that mass scores effect the ability to attend the schools of Choice, Part 56 N seven and eight. Um So for the last four parts, I put the results together and they are here in one table. This is part five, Part six and part seven. Yeah. In part five you estimate the equation in part four by instrumental variables. And Selected Years is an instrument for Choice Years does using I. V. Produced a positive effect of attending a charter school? The answer is no because the sign of the main estimate is negative. What do you make of the coefficients of the other explanatory variables? We have black, hispanic and female. As you can see the first few have negative estimates meaning students that are back and of hispanic origin tend to have significantly lower math scores. The standard error is way smaller than the estimate for variable female female dummy. This estimate is telling us being female does not affect mass scores controlling for race origin and whether attending choice schools. I wouldn't write that down about six. We at M n c E 90 the math score in 1992 the equation and we will estimate the equation by L. S. N. I. V. Now we have a positive as expected estimate on choice ears. The I. V. Estimate has a greater magnitude comparing to the old LS estimate and is actually statistically significant. I. Ve estimate is practically large each year in a school uh in a child's school is worth almost two on the math percentile score. Okay again, I will write that down about seven. So the results which has got is not entirely convincing because we have a smaller sample. So you can see from your statistical package when they run the regression in part six, they would say that 662 observations deleted due to missing. And we know that it is the missing values of the new variable M N C E 90 on a part part eight. We replaced choice years with four dummies choice here one, 23 and four. And we generate its instruments. They're instruments select years 1 to 4. We estimate the equation by ivy. This is what I get. Yeah. So we don't have choice years anymore. We don't have a constant anymore. Choice here's one is not significant. Do not significant. Three not significant. Only choice. Air Force is significant and that means being in only being in the choice school for the whole four years. The maximum amount of time matters for the math scores. So that's it and I think it's an interesting result. And you should read the paper if you have a chance to.

So between the lithium night treat, the nickel to night tree and the strong team nitrate, the one that we should actually used to precipitate the maximum out of the carbonate ions from the solution should be the strong team nitrate. And the reason for this is has the lowest ks beef value asking here. And so they gave us a case be table with the lithium carbonate, nickel to carbon and the strontium carbonate. And so adding strong human nitrate trying him carbonate is actually what we'd be making. So it would make sense for look at these case p values. And so when a case be value is closer to one, that means that the, um substance dissolves very readily and be squeak. It's only ions and it doesn't like to stay in the forms of for instance, lithium carbonate. The case be was one then what we would have is only the theme ions and only the carbonate ions. We would actually have the lithium carbonate, but here so lithium carbonate has the value closest Thorne and strong from carbonate has value closest zero, which means that it likes the state s surround him carbonate and so once we put the strontium nitrate into the solution and it reacts with the carbon e ions, we get the strong carbonate and have a lot of precipitated. Then for one beer, what we're looking at is for the carbon compound that contains the cattle on chosen in part a, which we chose as strontium nitrate, giving us drunken carbonate determine the concentration of each eye on of that compounded solution equilibrium. So this is the equilibrium, expression or equation. And so what? We have your strong him carbonate solid, solid in equal air be in, which is what these double arrows are with strong team two. Plus, it's the cat eye on and it's a quest. And then the carbon, eh? I unders and own. And that's also Equus. So then, um, what we need now is chaos P is actually just an equation, like it's just a formula that you follow. So they gave us the KSB and Cass be equals the concentration of whatever is a quest on the right side of your equation. So we have the strong tea, um, cat eye on multiplied by the concentration of the carbon A an eye on. So now since they gave us our case, P value, which is just 5.60 times 10 to the negative 10th. We're setting that equal to basically just the concentration of the strong Thiam times, the concentration of the carbonate and what we can do there is that's just x Times X giving us X squared. So now if we just take the square to both sides and we saw for eggs X equals the concentration of the strontium I on which is also equal. So the concentration of the carbonate ion, which overall is equal to 2.37 times 10 to the negative fifth Moeller. And so that's the concentration off each eye on in solution. So now moving on part C one mixing the solution should the student ensure the carbonate solution or the nitrate solution is an access. So for this, what we have to think about it, Which one of these ions would actually help us more? So we are Actual precipitated is strong team carbonated, which is as our CEO three. So we don't need more carbon ian solution because it doesn't matter how much carbonate we have, because that's just gonna stay as an eye on but for the strong tea Um, the way that we got the strong team is from the strong tea of nitrate, which is this So if we don't have enough strontium, then we can't make the strong him carbonate. So the nitrate solution should be an access because in order to create the maximum amount of precipitate, you need enough strong team I owns to react with all of the carbonate ions and having the access strontium ions in the solution doesn't affect the master of the carbonate in the virginal example. So we have a fixed amount of carbonate, but we I don't know, having more having the access won't give us the precipitate but having the excess of strong here Mayan means that we can react all off the carbon e into precipitously and then having the extras drawn to him doesn't affect anything. So then moving on to part dear after titrate and sufficient solution to precipitate out all of the carbonate ions, the student filters the solution before placing in the crucible and heating it to drive off the water after several beatings. The final mass of the precipitate it remains constant is determined be 2.2 grams. So the first thing we wanted to do is determine the number of moles of Pacific it. So what we d'oh is we take our 2.2 grams of our strong team carbonate, and we multiply that by the molar mass, which is basically just a ratio that allows us to go from grand symbols or moral stra graham. So 1 47.63 grams Uh, s or C 03 her one more and overall, that gives us okay after I put it into my calculator one point 37 times tend to the negative seven Negative, second more. And now, um, moving on determining the mass of the carbonate present in the precipitate. What we do is we take these moves that we just got and then we multiply that bye. You have one more of, um, you have one mole of the carbon e ion her one more of the strong him carbonate substance. So then, since it's just a wonder one we end up with 1.37 times tend to the negative second more of the carbonate and then what we need to do is take the Moler Mass off the carbon e ion and multiply that by the moles. And so once the molar mass of carbon e is so carbon is 12 plus the 40 the 48 from the three oxygen. So it's 60. So then once we take 60 times so 0.137 times succeed, which gives us zero point e to two grams of this carbon ee eye on. So then, um, poor E. What we need to do is determine the percent by massive carbonate in the original sample. So the 0.822 grams of the carbonate weakness around that 20.82 grams and just carry the 26 eggs and then you divide that by don't know why I did that. Um, so it's the zero point 82 grams divided by the one point 39 grams from the original sample. And then if you multiply it by 100 that's how you're gonna percent and we end up with 43.4 percent of the carbon E who of the, um carbon e i aunt in the original solution so that moving on too. Oh, you know, I did that. So then moving on to part, as is the original compound most likely lithium carbonate, which is ally to Theo. Three, um, sodium carbonate ing any to Theo three or potassium carbonate, which is you if you go through here. So what we do now is so it's the, um 60.1 for all three, um, on the numerator because what we're looking at for all of them is the carbonate. But then the only difference is the total math. So we're either dividing it by 73.89 because you had the mass of the carbonate plus the mass of dilithium or 16.1 divided by one of 5.99 or 60.1 divided by 1 38.21 Oh, and so you multiply all these by 100 and you enough with anyone 0.2% for that 56.6% for this and 45 0.4% for the pizza, potassium carbonate and

Predict the falling borders off penetration. Hey, for each group is Ah, Ortho PETA director, and she is free group that's met the director. So it's a case off consistent orientation. So that letter group enters with this Brothers Bay like trial is that met the director and this will free H is a metal director. Let's again consistent orientation in the latter group interests this position. See him in the struggle. Is it met the director. It directs into this position and horses figure is the offer. Period Director directs the order positions and the prayer position. The donor Rene's over except when it comes to orientation. Substitution to the Ortho position. Prevent Letter Group is not favorable because over stone edit from accepting activity or from in a group, so the product would contain the latter group into this position. They can be really a very minor impurities within matter. Group entering the close positions

Fennel visited, which can be produced from funeral, is less reactive than funeral in automatic. There are a few exceptions fearful. Explain what it's this, but the group is still Order Pereira director. Just like hydroxy group, you know, So I don't see a group in. Fino is a force of credit director because over too long in the pants, which supplies elections, most it through the orphan and better positions, this group still has to look natural in prayer on oxygen, which pretty X the same way as the age group. In funeral, however, the compound is less reactive because for conjugation off long and compare with adjusting Gruber. No, which most away park the church former our since one So the little there compares on oxygen become less active.


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