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For your political science class, you'd like to take a survey from a sample of all the Catholic Church members in your city. A list of churches shows 17 Cathol...

Question

For your political science class, you'd like to take a survey from a sample of all the Catholic Church members in your city. A list of churches shows 17 Catholic churches within the city limits. Rather than try to obtain a list of all members of all these churches, you decide to pick 3 churches at random. For those churches, you'll ask to get a list of all current members and contact 100 members at random.a) What kind of design have you used?b) What could go wrong with vour desion?

For your political science class, you'd like to take a survey from a sample of all the Catholic Church members in your city. A list of churches shows 17 Catholic churches within the city limits. Rather than try to obtain a list of all members of all these churches, you decide to pick 3 churches at random. For those churches, you'll ask to get a list of all current members and contact 100 members at random. a) What kind of design have you used? b) What could go wrong with vour desion?



Answers

The Pew Research Center's Social \& Demographic Trends project found that 46$$\%$$ of U.S. adults would rather live in a different type of community than the one where they are living now (Pew Research Center, January $$29,2009$ ). The national survey of 2260 adults asked: "Where do you live now? and "What do you consider to be the ideal community?Response options were City (C). Suburb (S), Small Town (T), or Rural (R). A representative portion of this survey for a sample of 100 respondents is as follows. Where do you live now?

What do you consider to be the ideal community?


a. Provide a percent frequency distribution for each question.
b. Construct a bar chart for each question.
c. Where are most adults living now?
d. Where do most adults consider the ideal community?
e. What changes in living areas would you expect to see if people moved from where
they currently live to their ideal community?

For a problem like this. It's important to read each part of the question closely because there are two categories of students being pulled Democrats and Republicans. There's an added dimension to finding this probability First, for a person who does not favor the amendment, we're searching for simply someone who doesn't favorite. It does not matter whether they're Democrat or a Republican. That gives us 25 Democrats and nine Republicans for a total of 34 students out of 100 who do not favor the bills. If we're searching simply for any Republican, we are looking at all Republicans whether they are in favor, not in favor or unsure. This gives us 32 that are in favor, nine that are not in favor and four then are unsure for a total of 45 Republicans out of all 100 students. Finally, when selecting a Democrat who is in favor of the amendment, we are looking at a much more specific problem than the last two parts. So we're looking for out of a total of 55 Democrats. How many are in favor of the amendment, so we're not looking at those who are not in favor. We can cancel 25 out. We're not looking at those who are unsure, so we can cancel seven. But we are looking at those who are in favour, which is 23. We will have 23 out of 100 students who are both Democrats.

We're considering a gallop poll about, uh, people who go to church or synagogue. Um, the number of respondents is 1700 80 five. And in our sample, 44% of the respondents said that they go to church or synagogue. But we're going to say, Let's just say that we know that in reality 40% of people actually attend church or synagogue. So the answer to a what is the mean of the sample we're the mean of the sample is the mean of the population. So it is 0.4 because it is a random sample and is therefore unbiased. Be okay. Were asked to calculate the standard deviation for our sample right down the equation. Which is p. Times one minus p over end the square root of that. But 44 hundreds? No, not 44 hundreds. I just used the wrong one. Glad I caught myself there. We're using this. The population, um percent. So 0.4 one minus p rips the guy switched colors one minus P. One minus point Forrest 10.0.6 and is 1700 80 five. If we calculate this, we get zero decimal 011 5954 That All right, check if the 10% condition is met. Um, well, our sample size must be less than or equal to 10% of the population size. And I assure you that there are more than millions of people in the United States, So 1785 is definitely less than 10%. See? Okay, we're gonna check if our sample is normal. So end times p must be greater than 10. Also end times one minus p. Must be greater than 10. Well, p is point for and one minus P s 10.6. So the lower of the two is going to be P 1785 times 0.4 4/10 is 714 which is much greater than 10. So we're good. We can assume we're gonna proximate this with random. I mean, with a normal distribution. Okay, d, if we calculate the z score to figure how likely it is to get a response of ah, 44% or greater, we would put in the 44% which is above the population mean of 40%. We would divide by the standard deviation 0.11 59 54 and we would get a Z score of 3.4. There's a very high C score nine 64 very high Z score. So the probability of getting responses that are less than this Z score if we calculate with our normal distribution tables, would be 0.99 nine 719 So it's almost certain that you're going to get less than 44% of the respondents to say that they go to church or synagogue. If we want to consider Maur, then then 44% of the respondents saying that they go to church or synagogue. We have to so track that from line 100% minus 99.919714% it means that that's an eight having trouble writing. Okay, let's try that again. 0.2 807 percent of the time. We should get responses that are 44% or greater, so again at zero point zero two eight 07 percent of the time. So it's extremely unlikely that we would get a response of 44% or higher, so I would question

If we look back at question 36 b, we see that the standard deviation, huh? That we calculated was zero point 011 5954 We want the new standard deviation to be 1/3 of that. So 0.11 5954 divided by three is 0.0 zero 3865 13 So all I did was I, uh, divided that standard deviation by three. So that's gonna be our new standard deviation. We use the same equation as in question 36 0.4. Time 0.6 and we divide by the new. And so what I'm gonna dio is I'm going to square both sides of the equation like this, uh, and I get 1.4 9393 times 10 to the negative. Fifth power is 4/10 time, 6/10 over an I'm now going to take the reciprocal of both sides, which means I'm just gonna flip it over. I could put over one if I wanted to. And so that gives me 66,937 on the left side. Okay. Equals and over 0.4 times 0.6. Okay, All that's left is the multiply by 4/10 and 6/10 on both sides, and that gives me an answer of n equals 16,000 65 which is the new sample size.

Question 45. We're looking at pretty much bias. So bias is anything that has an influence on the results. So here are answered. Choice is choice, see?


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