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In New York City, survey was planned to investigate the average price of "food basket" with basic needs (Ex: Bread, butter, milk; etc ); and to see whethe...

Question

In New York City, survey was planned to investigate the average price of "food basket" with basic needs (Ex: Bread, butter, milk; etc ); and to see whether food prices differ among different parts of the city. The sampling frame consisted of 408 food stores with at least 4000 square feet of retail space_ The population of stores was stratified into three strata using median household income within the zip code_ The prices of "market basket" of goods were determined for each s

In New York City, survey was planned to investigate the average price of "food basket" with basic needs (Ex: Bread, butter, milk; etc ); and to see whether food prices differ among different parts of the city. The sampling frame consisted of 408 food stores with at least 4000 square feet of retail space_ The population of stores was stratified into three strata using median household income within the zip code_ The prices of "market basket" of goods were determined for each store_ Explain why stratification by household incomc would bc uscful in thc contert of this problem



Answers

The New York City Housing and Vacancy Survey showed a total of $59,324$ rent-controlled
housing units and $236,263$ rent-stabilized units built in 1947 or later. For these rental units,
the probability distributions for the number of persons living in the unit are given
(U.S. Census Bureau website, January $12,2004$ ).
a. What is the expected value of the number of persons living in each type of unit?
b. What is the variance of the number of persons living in each type of unit?
c. Make some comparisons between the number of persons living in rent-controlled units and the number of persons living in rent-stabilized units.

Okay for this problem. We're looking at, um, housing units in Webster, New York specifically. So we are asked to create a couple different graphs are steps they're going to be to kind of organize and create our grass and then compare and contrast these two. This is categorical data as we're gonna look at a bar chart, and then we're gonna look at a first up I Kraft and that a bar chart and see which one is more informative. So let's just kind of go through this. I'm gonna basically answer these questions using this apple it here, I use this epochal stop. Let's really nice for different types of graphs. So what we're gonna do here is we're going to talk about the overall variable name. These are housing units in Webster, New York. Right. So in the category of the category, in this case is different types of, um, housing units. So the ISS's owner occupied because they don't want to live there, and we air cooled that it is 12,000 627. Second category is renter occupied so someone else owns it. But some people that live there are renters. 3803. And the third one is bacon. So no one lives there right now. It's a vacant units. And this data tells us there's 539 making units at the time. And again, if you go to stop lit dot com, you have to pick the typographic. Wanna make sense? This is categorical. Have already picked categorical I made three categories and I could been begin my analysis, um, question A says to do a pie chart. So, uh, the default is the bar chart. We're actually gonna do both, but just to go in order, I wish, uh, changed this drop down to show the pie chart. If you did this on your own, you could also do it. Um, my hand. Just have to make 360 degree circle on. You have to realize what proportion. Ah, in this case of owner occupied this so but for the time and for because it's a nice clear graph. I'm going to snap this in and show my hi chart, which is pretty all right. And we will do part B, which is going to show the bar chart. You know, snap this one over with the numbers as well, right? And so you know her application that just make this a nice big screen. So a side by side, there's party A and party. So there's a bar chart on the left. Sorry. Right. Chart pie graph on the left and the bar chart on the right and notice that kind of scale that out nicely for us. Um, And then part C just asks us which is better to kind of interpret the data. Okay, so they kind of get what you need from both grafts. But if you have to me, which one's better? I'm gonna go with, um right one. The bar chart. The bar chart tells you better relative, you kind of talk about 1000. We can visualize tens of thousands of units or the major differences. Uh, hi. Charts are better for, like, proportions in parts of holes. And we can do parts of holes, but really, this is more meaningful. So I'm going to say the bar chart bar chart better represents relative sides of the number of units. The relative difference in the number of units focus helps us out. And, uh, good luck

So the question here basically gives us a particular, um, table where we're giving a number of persons and it's frequencies here. So in order to understand this table, we need to understand what the scenario is. So what states is that from the document American Housing Survey for the United States published by the U. S. Census zero We basically obtained a following a frequency distribution for the number of persons per occupied housing units. It also states that seven is going to be in place of seven or more. So these frequencies here. So just to note, our frequencies here are gonna be in the units of million's of housing units here. So the question basically asked for a randomly selected housing unit. It wants us. Look, we want us to denote why, as a number of persons living in that unit, So for part a here it says toe, identify the possible values off the random variable. Why? So how many people can we have in that particular unit? So it's essentially just give me the person so we can have one, 23456 and then seven plus years, Um, for part B here It wants us to use random variable notation to represent event that housing has exactly three persons in it. So, essentially, if we add up all of our values here, what we're gonna get is that toe have three or, um, more people in it, or exactly three Rather people living in it are frequency is gonna be 17 million housing units, and this is going to be our random variable notation here for part C here. It wants us determine the probability off. Why is equal to three. So how do we get this? It's essentially just 17 over the sum of every single frequency that we have here. So what we get is going to be a total of 15.3. So if we just divide 17 by 105.3, we're gonna get approximately 16.14%. Um, and lastly, it wants us to determine the probably distribution of why So in other words, it just wants us to construct the hissed a gram. So what we can do is become essentially take our occupy units. So 1234567 here, and we can just draw out the relative frequencies. So that's gonna be approximately of one to this is gonna be much lower at three, even lower at four. Much lower five, six and seven here. So if we just draw a K t e or a colonel equation here density equation, we can see that it's gonna be skewed towards the left hand side. So towards the right, rather where we're essentially going to get a peek at two. So this is going to be the average or median household sighs.

Question. 12 stink. The distribution of ethnic background in the New York City population recently was this breakdown. Hispanic 28 black, 24 white, 35 Asian, 12 others 1%. The manager of this large housing complex wants know if its residents races matched population distribution. So she records data from a random sample off 800 for residents. And then we were from a cry score analysis to see if the data are significantly different. So using the table that's given, we get the expected values by multiplying 800 by the percentages I have drawn out here for you already. So it's just 800 times each of those percentages jar out here and then using the other table that's given. We just do. I squared. So we do actual minus expected about if I expected where the top is squared for all five of the different races. Add that together we get the value of twenties, explains Extreme. We want to know p value, so I just I'm using a calculator. Plug didn't and neither the P value using CD a function is significant. It's less than 0.5 But then the question asked us. How could we do it? Another analysis with us and I think something that will be interesting to look at is this other category. We only have 1% of individuals and other eight. It's still large enough to do it, guys, Great analysis. But it would be interesting to look at that group in particular and for first of all, tease out what exactly other means in these cases, can they be combined together as other? I'm sure they'd be removed completely something along those lines, or even just amp up, um, population size the number of the random sample size and get more people into that other category so that we can get some more meaningful results with the bigger ships eyes.

Question 12 were given a table. Have deserved ethnicities of people that live in this speech, your government complexes as well as he expected, um, pick ones you based off of the area's population. So we have to do is you take those They expected percentages and a couple of the actual expected numbers the multiplying them by the total number of individuals, which is 80. So I've done that here. So for Hispanic, you would expect 224 black 1 92 white to 80 Asian 96 other eight. Now we have to take archives. Great equation just observed minus accepted. And this numerator here squared to get rid of any possible on negative that could be caused by an expected value being larger than it observed and divide it by the expected value between to do this equation for all five different risk categories. Yes, we put our given observed value first to minus for Hispanic to 44. The cockpit is expected. And then you saw squared the, um, numerator and divided by 2 44 of the jam waiver. You do this for all four or five so are given to o to minus 1 92 which we calculated squared, divided by 1 92 Same thing for the next extra three com. And then you just add all five of those up to get a value up twenties explains you out. 32 Not perfect to quit the P value. You can use a calculator using the CDF equation where you put in 26.2 or 36 and then, um, 1000 calm before and it gives you a very significant P value, um, in which you conclude, conclude that there you can reject the null hypothesis that there is no difference between the observed and the expected.


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