An article in the Journal of the American Statistical Association [Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling" (1990, Vol. 85, pp. 972-985)] measured the weight of 30 rats under experiment controls. Suppose that 12 were underweight rats. (a) Calculate a 95% two-sided confidence interval on the true proportion of rats that would show underweight from the experiment. (b) Using the point estimate of p obtained from the preliminary sample, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than 0.02? (c) If we don't have any previous information about p, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than 0.02 ? (b) Using the point estimate of p obtained from the preliminary sam- ple, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than 0.02? (c) If we don't have any previous information about p, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than 0.02?

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 58E: What is meant by the sample space of an experiment?
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An article in the Journal of the American Statistical Association ['Illustration of Bayesian Inference in Normal Data Models
Using Gibbs Sampling" (1990, Vol. 85, pp. 972-985)] measured the weight of 30 rats under experiment controls.
Suppose that 12 were underweight rats. (a) Calculate a 95% two-sided confidence interval on the true proportion of rats
that would show underweight from the experiment. (b) Using the point estimate of p obtained from the preliminary
sample, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than
0.02? (c) If we don't have any previous information about p, what sample size is needed to be 95% confident that the
error in estimating the true value of p is less than 0.02 ?
(b) Using the point estimate of p obtained from the preliminary sam-
ple, what sample size is needed to be 95% confident that the error
in estimating the true value of p is less than 0.02?
(c) If we don't have any previous information about p, what sample
size is needed to be 95% confident that the error in estimating the
true value of p is less than 0.02?
Transcribed Image Text:An article in the Journal of the American Statistical Association ['Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling" (1990, Vol. 85, pp. 972-985)] measured the weight of 30 rats under experiment controls. Suppose that 12 were underweight rats. (a) Calculate a 95% two-sided confidence interval on the true proportion of rats that would show underweight from the experiment. (b) Using the point estimate of p obtained from the preliminary sample, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than 0.02? (c) If we don't have any previous information about p, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than 0.02 ? (b) Using the point estimate of p obtained from the preliminary sam- ple, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than 0.02? (c) If we don't have any previous information about p, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than 0.02?
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