Question

12. Mrs. Bracken asks a random sample of 500 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 45% of the population favor this idea. (a) What is the mean of the sampling distribution of p?, the proportion of adults in samples of size n = 500 who favor giving parents of school-age children these vouchers? (b) What is the standard deviation of p?? Interpret this value. (c) Check that you can use the Normal approximation for the distribution of p?. (d) What is the probability that more than half of the sample are in favor? Show your work.

          12. Mrs. Bracken asks a random sample of 500 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 45% of the population favor this idea.

(a) What is the mean of the sampling distribution of p?, the proportion of adults in samples of size n = 500 who favor giving parents of school-age children these vouchers?

(b) What is the standard deviation of p?? Interpret this value.

(c) Check that you can use the Normal approximation for the distribution of p?.

(d) What is the probability that more than half of the sample are in favor? Show your work.

Show more…

12. Mrs. Bracken asks a random sample of 500 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 45% of the population favor this idea.

(a) What is the mean of the sampling distribution of p?, the proportion of adults in samples of size n = 500 who favor giving parents of school-age children these vouchers?

(b) What is the standard deviation of p?? Interpret this value.

(c) Check that you can use the Normal approximation for the distribution of p?.

(d) What is the probability that more than half of the sample are in favor? Show your work.

Added by Kevin C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert David Nguyen

01/15/2022

Step 1

So, the mean is 0.45. (b) The standard deviation of the sampling distribution of the proportion is given by the formula sqrt[p(1-p)/n], where p is the population proportion and n is the sample size. Substituting the given values, we get sqrt[0.45(1-0.45)/500] = Show more…

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12. Mrs. Bracken asks a random sample of 500 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 based on how many vouchers it collected. Suppose that 45% of the population favor this idea. What is the mean of the sampling distribution of the proportion of adults in samples of size n = 500 who favor giving parents of school-age children these vouchers? (b) What is the standard deviation? Interpret this value. (c) Check that you can use the Normal approximation for the distribution. (d) What is the probability that more than half of the sample are in favor? Show your work.

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Transcript

00:01 Hi, i'm david and i'm here to help me answer your question.

00:03 Now let me pick up the question here.

00:06 In this question, we'll discuss about the distribution of the sample proportion.

00:12 Let me remind you that if we have the end is large, and then we will have the sample proportion p.

00:21 Hart, it will follow by the normal, when the mean under p .ht equal to the population proportion, the standard division under p heart, it will equal to the square root of the p times 1 minus b divided by n.

00:39 And in this question here, we are given that the n equal to the 500, and we will have the population proportion p equal to the 45%, which is 0 .45.

00:54 And the question i ask can let you find the mean of the sampling distribution be hard.

00:58 It means that we want to find the mule on the p heart.

01:03 And by the formula, it will equal to the p, and it will equal to the 0 .45.

01:10 In the question b, we want to find the standard division in the p heart, and then it will be the standard division of pheap, equal to this formula.

01:22 So we have the square root of the p times 1 minus b, divided by n.

01:29 Therefore, we have a square root of 0 .45 times 1 minus 0 .45, divided by n.

01:38 And if we compute it, we have 0 .45 times 0 .55, divided by n will be the 500, taking the square root equal to the 0 .0 ,0, 2, 2.

01:55 2 and this is the average difference between the each sample proportion and the population now for the question c check that if you can use the normal approximation for the distribution on the p...

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