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d) What is the z critical value that we would use to construct a classical 95% confidence interval for p? e) Construct a 95% classical confidence interval for p? ([ f) How long is the 95% classical confidence interval for p? g) If we are creating a 95% classical confidence interval for p based upon the sample size of 4178, then what is the longest possible length of this interval?

d) What is the z critical value that we would use to construct a classical 95% confidence interval for p? e) Construct a 95% classical confidence interval for p? ([ f) How long is the 95% classical confidence interval for p? g) If we are creating a 95% classical confidence interval for p based upon the sample size of 4178, then what is the longest possible length of this interval?

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...
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What proportion of NY Monopoly scratch-off Lotto tickets are winners? We will examine this by taking a random sample of n = 4178 Monopoly scratch-offs. Of these, x = 912 were winners. Let p be the (unknown) true proportion of NY Monopoly scratch offs which are winners. We want to estimate p. X is the random variable representing the number of sampled Monopoly scratch-offs which are winners. a) What type of probability distribution does X have? O Poisson O Weibull C gamma O exponential O binomial b) What was the sample proportion, p, of sampled Monopoly scratch offs which were winners? c) What is the R formula for the expected value of X in terms of n and p? O n*p O n^2 O n*p*(1 - p) O sqrt(n*p*(1-p)) O 1/p d) What is the z critical value that we would use to construct a classical 95% confidence interval for p? e) Construct a 95% classical confidence interval for p? ( f) How long is the 95% classical confidence interval for p? g) If we are creating a 95% classical confidence interval for p based upon the sample size of 4178, then what is the longest possible length of this interval? h) Copy your R script for the above into the text box here.
Transcribed Image Text:What proportion of NY Monopoly scratch-off Lotto tickets are winners? We will examine this by taking a random sample of n = 4178 Monopoly scratch-offs. Of these, x = 912 were winners. Let p be the (unknown) true proportion of NY Monopoly scratch offs which are winners. We want to estimate p. X is the random variable representing the number of sampled Monopoly scratch-offs which are winners. a) What type of probability distribution does X have? O Poisson O Weibull C gamma O exponential O binomial b) What was the sample proportion, p, of sampled Monopoly scratch offs which were winners? c) What is the R formula for the expected value of X in terms of n and p? O n*p O n^2 O n*p*(1 - p) O sqrt(n*p*(1-p)) O 1/p d) What is the z critical value that we would use to construct a classical 95% confidence interval for p? e) Construct a 95% classical confidence interval for p? ( f) How long is the 95% classical confidence interval for p? g) If we are creating a 95% classical confidence interval for p based upon the sample size of 4178, then what is the longest possible length of this interval? h) Copy your R script for the above into the text box here.
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