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1349 andrew gelman stats-2012-05-28-Question 18 of my final exam for Design and Analysis of Sample Surveys


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Introduction: 18. A survey is taken of 100 undergraduates, 100 graduate students, and 100 continuing education students at a university. Assume a simple random sample within each group. Each student is asked to rate his or her satisfaction (on a 1–10 scale) with his or her experiences. Write the estimate and standard error of the average satisfaction of all the students at the university. Introduce notation as necessary for all the information needed to solve the problem. Solution to question 17 From yesterday : 17. In a survey of n people, half are asked if they support “the health care law recently passed by Congress” and half are asked if they support “the law known as Obamacare.” The goal is to estimate the effect of the wording on the proportion of Yes responses. How large must n be for the effect to be estimated within a standard error of 5 percentage points? Solution: se is sqrt(.5*.5/(n/2)+.5*.5/(n/2)) = 1/sqrt(n). Solve 1/sqrt(n) = .05, you get n = (1/.05)^2 = 400.


Summary: the most important sentenses genereted by tfidf model

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1 A survey is taken of 100 undergraduates, 100 graduate students, and 100 continuing education students at a university. [sent-2, score-0.82]

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4 Introduce notation as necessary for all the information needed to solve the problem. [sent-6, score-0.665]

5 Solution to question 17 From yesterday : 17. [sent-7, score-0.11]

6 In a survey of n people, half are asked if they support “the health care law recently passed by Congress” and half are asked if they support “the law known as Obamacare. [sent-8, score-2.325]

7 ” The goal is to estimate the effect of the wording on the proportion of Yes responses. [sent-9, score-0.667]

8 How large must n be for the effect to be estimated within a standard error of 5 percentage points? [sent-10, score-0.945]


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same-blog 1 1.0 1349 andrew gelman stats-2012-05-28-Question 18 of my final exam for Design and Analysis of Sample Surveys

Introduction: 18. A survey is taken of 100 undergraduates, 100 graduate students, and 100 continuing education students at a university. Assume a simple random sample within each group. Each student is asked to rate his or her satisfaction (on a 1–10 scale) with his or her experiences. Write the estimate and standard error of the average satisfaction of all the students at the university. Introduce notation as necessary for all the information needed to solve the problem. Solution to question 17 From yesterday : 17. In a survey of n people, half are asked if they support “the health care law recently passed by Congress” and half are asked if they support “the law known as Obamacare.” The goal is to estimate the effect of the wording on the proportion of Yes responses. How large must n be for the effect to be estimated within a standard error of 5 percentage points? Solution: se is sqrt(.5*.5/(n/2)+.5*.5/(n/2)) = 1/sqrt(n). Solve 1/sqrt(n) = .05, you get n = (1/.05)^2 = 400.

2 0.49121362 1352 andrew gelman stats-2012-05-29-Question 19 of my final exam for Design and Analysis of Sample Surveys

Introduction: 19. A survey is taken of students in a metropolitan area. At the first stage a school is sampled at random. The schools are divided into two strata: 20 private schools and 50 public schools are sampled. At the second stage, 5 classes are sampled within each sampled school. At the third stage, 10 students are sampled within each class. What is the probability that any given student is sampled? Express this in terms of the number of students in the class, number of classes in the school, and number of schools in the area. Define appropriate notation as needed. Solution to question 18 From yesterday : 18. A survey is taken of 100 undergraduates, 100 graduate students, and 100 continuing education students at a university. Assume a simple random sample within each group. Each student is asked to rate his or her satisfaction (on a 1–10 scale) with his or her experiences. Write the estimate and standard error of the average satisfaction of all the students at the university. Introd

3 0.43169364 1348 andrew gelman stats-2012-05-27-Question 17 of my final exam for Design and Analysis of Sample Surveys

Introduction: 17. In a survey of n people, half are asked if they support “the health care law recently passed by Congress” and half are asked if they support “the law known as Obamacare.” The goal is to estimate the effect of the wording on the proportion of Yes responses. How large must n be for the effect to be estimated within a standard error of 5 percentage points? Solution to question 16 From yesterday : 16. You are doing a survey in a war-torn country to estimate what percentage of unemployed men support the rebels in a civil war. Express this as a ratio estimation problem, where goal is to estimate Y.bar/X.bar. What are x and y here? Give the estimate and standard error for the percentage of unemployed men who support the rebels. Solution: x is 1 if the respondent is an unemployed man, 0 otherwise. y is 1 if the respondent is an unemployed man and supports the rebels, 0 otherwise. The estimate is y.bar/x.bar [typo fixed], the standard error is (1/x.bar)*(1/sqrt(n))*s.z, whe

4 0.25530908 1361 andrew gelman stats-2012-06-02-Question 23 of my final exam for Design and Analysis of Sample Surveys

Introduction: 23. Suppose you are conducting a survey in which people are asked about their health behaviors (how often they wash their hands, how often they go to the doctor, etc.). There is a concern that different interviewers will get different sorts of responses—that is, there may be important interviewer effects. Describe (in two sentences) how you could estimate the interviewer effects within your survey. Can the interviewer effects create problems of reliability of the survey responses? Explain (in one sentence). Can the interviewer effects create problems of validity of the survey responses? Explain (in one sentence). Solution to question 22 From yesterday : 22. A supermarket chain has 100 equally-sized stores. It is desired to estimate the proportion of vegetables that spoil before being sold. Three stores are selected at random and are checked: the percent of spoiled vegetables are 3%, 5%, and 10% in the three stores. Give an estimate and standard error for the percentage of spo

5 0.2471444 1333 andrew gelman stats-2012-05-20-Question 10 of my final exam for Design and Analysis of Sample Surveys

Introduction: 10. Out of a random sample of 100 Americans, zero report having ever held political office. From this information, give a 95% confidence interval for the proportion of Americans who have ever held political office. Solution to question 9 From yesterday : 9. Out of a population of 100 medical records, 40 are randomly sampled and then audited. 10 out of the 40 audits reveal fraud. From this information, give an estimate, standard error, and 95% confidence interval for the proportion of audits in the population with fraud. Solution: estimate is p.hat=10/40=0.25. Se is sqrt(1-f)*sqrt(p.hat*(1-.hat)/n)=sqrt(1-0.4)*sqrt(0.25*0.75/40)=0.053. 95% interval is [0.25 +/- 2*0.053] = [0.14,0.36].

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Introduction: 18. A survey is taken of 100 undergraduates, 100 graduate students, and 100 continuing education students at a university. Assume a simple random sample within each group. Each student is asked to rate his or her satisfaction (on a 1–10 scale) with his or her experiences. Write the estimate and standard error of the average satisfaction of all the students at the university. Introduce notation as necessary for all the information needed to solve the problem. Solution to question 17 From yesterday : 17. In a survey of n people, half are asked if they support “the health care law recently passed by Congress” and half are asked if they support “the law known as Obamacare.” The goal is to estimate the effect of the wording on the proportion of Yes responses. How large must n be for the effect to be estimated within a standard error of 5 percentage points? Solution: se is sqrt(.5*.5/(n/2)+.5*.5/(n/2)) = 1/sqrt(n). Solve 1/sqrt(n) = .05, you get n = (1/.05)^2 = 400.

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Introduction: 17. In a survey of n people, half are asked if they support “the health care law recently passed by Congress” and half are asked if they support “the law known as Obamacare.” The goal is to estimate the effect of the wording on the proportion of Yes responses. How large must n be for the effect to be estimated within a standard error of 5 percentage points? Solution to question 16 From yesterday : 16. You are doing a survey in a war-torn country to estimate what percentage of unemployed men support the rebels in a civil war. Express this as a ratio estimation problem, where goal is to estimate Y.bar/X.bar. What are x and y here? Give the estimate and standard error for the percentage of unemployed men who support the rebels. Solution: x is 1 if the respondent is an unemployed man, 0 otherwise. y is 1 if the respondent is an unemployed man and supports the rebels, 0 otherwise. The estimate is y.bar/x.bar [typo fixed], the standard error is (1/x.bar)*(1/sqrt(n))*s.z, whe

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Introduction: 23. Suppose you are conducting a survey in which people are asked about their health behaviors (how often they wash their hands, how often they go to the doctor, etc.). There is a concern that different interviewers will get different sorts of responses—that is, there may be important interviewer effects. Describe (in two sentences) how you could estimate the interviewer effects within your survey. Can the interviewer effects create problems of reliability of the survey responses? Explain (in one sentence). Can the interviewer effects create problems of validity of the survey responses? Explain (in one sentence). Solution to question 22 From yesterday : 22. A supermarket chain has 100 equally-sized stores. It is desired to estimate the proportion of vegetables that spoil before being sold. Three stores are selected at random and are checked: the percent of spoiled vegetables are 3%, 5%, and 10% in the three stores. Give an estimate and standard error for the percentage of spo

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Introduction: 19. A survey is taken of students in a metropolitan area. At the first stage a school is sampled at random. The schools are divided into two strata: 20 private schools and 50 public schools are sampled. At the second stage, 5 classes are sampled within each sampled school. At the third stage, 10 students are sampled within each class. What is the probability that any given student is sampled? Express this in terms of the number of students in the class, number of classes in the school, and number of schools in the area. Define appropriate notation as needed. Solution to question 18 From yesterday : 18. A survey is taken of 100 undergraduates, 100 graduate students, and 100 continuing education students at a university. Assume a simple random sample within each group. Each student is asked to rate his or her satisfaction (on a 1–10 scale) with his or her experiences. Write the estimate and standard error of the average satisfaction of all the students at the university. Introd

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Introduction: 22. A supermarket chain has 100 equally-sized stores. It is desired to estimate the proportion of vegetables that spoil before being sold. Three stores are selected at random and are checked: the percent of spoiled vegetables are 3%, 5%, and 10% in the three stores. Give an estimate and standard error for the percentage of spoiled vegetables for the entire chain. Solution to question 21 From yesterday : 21. A country is divided into three regions with populations of 2 million, 2 million, and 0.5 million, respectively. A survey is done asking about foreign policy opinions. Somebody proposes taking a sample of 50 people from each reason. Give a reason why this non-proportional sample would not usually be done, and also a reason why it might actually be a good idea. Solution: Nonproportional sampling is usually avoided because it makes the analysis more complicated and it results in a higher standard error for estimates of the general population. It might be a good idea her

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