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Polltlcl curdidate has asked you conduct Poll - detetinine whut pcrcentagepeople suppont her:It the candidaie only wants 596 nuargin af erar at a 9036 conlidence le...

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Polltlcl curdidate has asked you conduct Poll - detetinine whut pcrcentagepeople suppont her:It the candidaie only wants 596 nuargin af erar at a 9036 conlidence level,whu sice smple [s netrkcd?Co not rourd between sleps, Use tec hnology Mlu| z scotc. Givc your wns#cr whok pcoplc: Make sutt" YQU Use' Ihe comx ( rurding nk: for samples sze

polltlcl curdidate has asked you conduct Poll - detetinine whut pcrcentage people suppont her: It the candidaie only wants 596 nuargin af erar at a 9036 conlidence level,whu sice smple [s netrkcd? Co not rourd between sleps, Use tec hnology Mlu| z scotc. Givc your wns#cr whok pcoplc: Make sutt" YQU Use' Ihe comx ( rurding nk: for samples sze



Answers

A survey organization takes a simple random sample of $1,500$ persons from
the residents of a large city. Among these sample persons, $1,035$ were renters.
(a) The expected value for the percentage of sample persons who rent is ______ 69$\%$
(b) The SE for the percentage of sample persons who rent is ______ 1.2$\%$
Fill in the blanks, and explain. Options:
(i) exactly equal to $\quad$ (ii) estimated from the data as

In this question, a questionnaire is mailed to 150 households to know about their ice cream eating habits and flavor preferences. And out of the 1 50 questionnaires that are mailed only for our return. So again, what is your sample size? You wish to get the responses from 150 people, but out of that, only four off them respond. Okay, so we're here again. We see that this is a non response bias. Why? Because this is sort of a voluntary response service sort of thing. So in this case, the most common type of biases non response, whether user actually chooses if he wants to respond or not. How can you improve this? What are the ways to remedy this? One of the ways is callbacks. What is the meaning of call backs? You have mailed them once you will mail them again as a reminder. So this is nothing but a follow up method in which you follow up with the people. Mhm follow ups. Right? And what is the other way? The other way is the introduction of rewards. The introduction off rewards. So by using rewards such as cash payments for completing a questionnaire or incentives that state that the responses to the questionnaire will be determined. Future policy. You can encourage people to respond, or you can also give them some sort of discounts in your new shop, So this is how we can remedy this.

Now in this case, does the order affect the survey? Yes, because in part B, we can see that the ah classroom is a place in which kids study so and every child, every child that study in a classroom is treated equal or should be treated equal. And hence the question in part B has a bit off. More important, Okay, in other places of employment, you should should not allow that is a different thing. But in a classroom, there definitely should not be any kind of discrimination or any, but he should not feel left out. So Part B should be the first question. So what we cannot do over here, it's simply switch the order. So, yes, the order over here will affect the survey results. And there is also another question over here, which is about the choice of the word prohibit. Now, the thing over here is prohibit is a very strong word. Instead of prohibit, we can use the word not allowed right. We can use the word not allow in this case, Uh, because most people are not willing to prohibit something, but, you know, they are willing to not allow something

We're testing to see if there is an association between race and Internet use, and I have reproduced a table that summarizes the responses to the question. Did you use the Internet yesterday? Now this data represents a population categorized on two variables. So this is a question of independence. So we're testing for independence. For her part, A were asked under the no hypothesis, What are the expected values? So the no hypothesis is that your answer to that question, yes or no is not dependent on your race. So we would expect every race to have the same breakdown of yes and no. So to figure out what the expected numbers would be for each cell. First week in total, the columns and total of the rose. So this comes out to 3291. This is 1176 and that gives the total number of people pulled as 4467. So if we wanted to know regardless of race, what the proportion what? Your likelihood of answering yes, is we just take the total number of people answered yes, and divided by the total number of people that comes out to you 73.7%. And so for no. Then that's the compliment. So that's 26 0.3%. So now if we want to fill in the sales with the expected numbers, so let's let's do white First, let's say there's 3402 whites, and we're expecting that 73.7% would answer yes. So that comes out to 2000 506 0.38 So basically, we took a total number of people in that category times the total number of people who answer the proportion of people answered, yes, multiply them to get the expected counts for the cell, and you can see it varies a little bit from the actual observed counts. So if we do that for each cell, we would get these answers here. So I just place this table here. So this table includes the expected counts for each cell now moving on to Part B, were asked to compute the chi squared statistic. So that is a summation across all sales of the observed counts minus the expected counts squared, divided by the expected counts And so again, these air, the expected counts, these air the observed counts. And I've used software Teoh to calculate the chi squared statistic for us, it comes out to 11.176 and for part C were asked, What are the degrees of freedom for our test for the chi scored statistic? Remember, that is a number of rows minus one times the number of columns minus one. So we have two columns and three rolls, so that means it's two times one or two degrees of freedom and were asked to calculate a P value. So I use many tab to calculate this, and they gave me a P value of 0.4 which is obviously a small P value. So I e. When we're asked to state or conclusion, we can say, based on the small p value, we reject the no hypothesis, and we conclude that there is evidence to suggest that your answer to the question did you use Internet yesterday is dependent on race

So the question here basically states that we have a website which basically publishes results of new surveys each day. So the first particular part of this question here asked us to identify the population of interest. So in this particular case, we know that through telephone interviews that we have national adults that are aged 18 or over art basically conducted or investigate in this particular case. So for a here, it's going to be the national, um, adults aged 18 plus in this particular case for be here. It's asking for the sampling frame. So the sampling frame is the method through which this particular website does its research. So in this particular case, it's going to be through telephone interviews, Um, and that part see here and asked what, um problems can we potentially have in terms of the sample on the sampling frame? So in this particular case, we're going to undergo something called under coverage bias, which is a particular bias where we don't have enough particular samples from a greater variety of sample sizes. So in this particular cage on the case, rather, we might be able to get a particular sample size where we might get, For example, um, participants that are aged, for example, 50 plus, however, we don't get as many below that particular range, so we might get that buys in that particular sense.


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