An opinion poll asks a sample of 200 adults (an SRS) whether they favor giving parents of school-age children vouchers that can be exchanged for education at any public or private school of their choice. Each school would be paid by the government on the basis of how many vouchers it collected. Suppose that in fact 55% of the population favor this idea. (a) What is the mean of the sampling distribution of p̂, the proportion of adults in samples of 200 who favor giving parents of school-age children these vouchers? (b) What is the standard deviation of p̂? (c) Check that you can use the Normal approximation for the distribution of p̂. (d) What is the probability that more than half of the sample are in favor? Show your work.
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An opinion poll asks a simple random sample of 500 adults whether they favor giving parents of school-aged children vouchers that can be exchanged for education at any public or private school of their choice. Each school would be paid by the government on the basis of how many vouchers it collected. Suppose that in fact 45% of the population favor this idea. a. What are the mean and standard deviation of the sampling distribution of p^, the proportion of adults in samples of 500 who favor giving parents of school-aged children these vouchers? b. Justify the use of a normal approximation for the sampling distribution of p^ in this setting. c. What is the probability that more than 55% of the sample are in favor? Show all work including z-score.
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Mrs. Bracken asks a random sample of 400 adults whether they favor giving vouchers to parents of school-age children that can be exchanged for education at any public or private school of their choice. Each school would be paid by the government on the basis of how many vouchers it collected. Suppose that 47% of the population favor this idea. (a) What is the mean of the sampling distribution of p̂, the proportion of adults in samples of size n = 400 who favor giving parents of school-age children these vouchers? (4 points) (b) What is the standard deviation of the sampling distribution of p̂? Interpret this value. (5 points) (c) Check that you can use the Normal approximation for the sampling distribution of p̂. (4 points) (d) What is the probability that more than half of the sample are in favor? Show your work. (4 points)
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