suppose that the actual proportion of students at a particular college who use public transportation to travel to campus is 0.17. In a study of parking needs at the campus, college administrators would like to estimate this proportion. They plan to take a random sample of 80 students and use the sample proportion who use public transportation, p̂, as an estimate of the population proportion. (a) What is the standard deviation of p̂? (Round your answer to four decimal places.) b) If for a different sample size, σp̂ = 0.0323, would you expect more or less sample-to-sample variability in the sample proportions than for when n = 80? I would expect more sample-to-sample variability when σp̂ = 0.0323 because the standard deviation of the sampling distribution of p̂ is smaller than when n = 80.I would expect more sample-to-sample variability when σp̂ = 0.0323 because the standard deviation of the sampling distribution of p̂ is larger than when n = 80. I would expect the same sample-to-sample variability when σp̂ = 0.0323 because the standard deviation of the sampling distribution of p̂ is smaller than when n = 80.I would expect less sample-to-sample variability when σp̂ = 0.0323 because the standard deviation of the sampling distribution of p̂ is smaller than when n = 80.I would expect less sample-to-sample variability when σp̂ = 0.0323 because the standard deviation of the sampling distribution of p̂ is larger than when n = 80. (c) Is the sample size that resulted in σp̂ = 0.0323 larger than 80 or smaller than 80? Explain your reasoning. The sample size that resulted in σp̂ = 0.0323 is larger than 80 because smaller standard deviations of the sampling distribution of the sample proportion correspond to smaller sample sizes.The sample size that resulted in σp̂ = 0.0323 is larger than 80 because smaller standard deviations of the sampling distribution of the sample proportion correspond to larger sample sizes. The sample size that resulted in σp̂ = 0.0323 is smaller than 80 because smaller standard deviations of the sampling distribution of the sample proportion correspond to smaller sample sizes.The sample size that resulted in σp̂ = 0.0323 is smaller than 80 because smaller standard deviations of the sampling distribution of the sample proportion correspond to larger sample sizes.
suppose that the actual proportion of students at a particular college who use public transportation to travel to campus is 0.17. In a study of parking needs at the campus, college administrators would like to estimate this proportion. They plan to take a random sample of 80 students and use the sample proportion who use public transportation, p̂, as an estimate of the population proportion. (a) What is the standard deviation of p̂? (Round your answer to four decimal places.) b) If for a different sample size, σp̂ = 0.0323, would you expect more or less sample-to-sample variability in the sample proportions than for when n = 80? I would expect more sample-to-sample variability when σp̂ = 0.0323 because the standard deviation of the sampling distribution of p̂ is smaller than when n = 80.I would expect more sample-to-sample variability when σp̂ = 0.0323 because the standard deviation of the sampling distribution of p̂ is larger than when n = 80. I would expect the same sample-to-sample variability when σp̂ = 0.0323 because the standard deviation of the sampling distribution of p̂ is smaller than when n = 80.I would expect less sample-to-sample variability when σp̂ = 0.0323 because the standard deviation of the sampling distribution of p̂ is smaller than when n = 80.I would expect less sample-to-sample variability when σp̂ = 0.0323 because the standard deviation of the sampling distribution of p̂ is larger than when n = 80. (c) Is the sample size that resulted in σp̂ = 0.0323 larger than 80 or smaller than 80? Explain your reasoning. The sample size that resulted in σp̂ = 0.0323 is larger than 80 because smaller standard deviations of the sampling distribution of the sample proportion correspond to smaller sample sizes.The sample size that resulted in σp̂ = 0.0323 is larger than 80 because smaller standard deviations of the sampling distribution of the sample proportion correspond to larger sample sizes. The sample size that resulted in σp̂ = 0.0323 is smaller than 80 because smaller standard deviations of the sampling distribution of the sample proportion correspond to smaller sample sizes.The sample size that resulted in σp̂ = 0.0323 is smaller than 80 because smaller standard deviations of the sampling distribution of the sample proportion correspond to larger sample sizes.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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suppose that the actual proportion of students at a particular college who use public transportation to travel to campus is 0.17. In a study of parking needs at the campus, college administrators would like to estimate this proportion. They plan to take a random sample of 80 students and use the sample proportion who use public transportation, p̂, as an estimate of the population proportion.
(a)
What is the standard deviation of p̂? (Round your answer to four decimal places.)
b)
If for a different sample size ,
σp̂ = 0.0323,
would you expect more or less sample-to-sample variability in the sample proportions than for when
n = 80?
I would expect more sample-to-sample variability when σp̂ = 0.0323 because the standard deviation of the sampling distribution of p̂ is smaller than when n = 80.I would expect more sample-to-sample variability when σp̂ = 0.0323 because the standard deviation of the sampling distribution of p̂ is larger than when n = 80. I would expect the same sample-to-sample variability when σp̂ = 0.0323 because the standard deviation of the sampling distribution of p̂ is smaller than when n = 80.I would expect less sample-to-sample variability when σp̂ = 0.0323 because the standard deviation of the sampling distribution of p̂ is smaller than when n = 80.I would expect less sample-to-sample variability when σp̂ = 0.0323 because the standard deviation of the sampling distribution of p̂ is larger than when n = 80.
(c)
Is the sample size that resulted in
σp̂ = 0.0323
larger than 80 or smaller than 80? Explain your reasoning.The sample size that resulted in σp̂ = 0.0323 is larger than 80 because smaller standard deviations of the sampling distribution of the sample proportion correspond to smaller sample sizes.The sample size that resulted in σp̂ = 0.0323 is larger than 80 because smaller standard deviations of the sampling distribution of the sample proportion correspond to larger sample sizes. The sample size that resulted in σp̂ = 0.0323 is smaller than 80 because smaller standard deviations of the sampling distribution of the sample proportion correspond to smaller sample sizes.The sample size that resulted in σp̂ = 0.0323 is smaller than 80 because smaller standard deviations of the sampling distribution of the sample proportion correspond to larger sample sizes.
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