People end up tossing 12% of what they buy at the grocery store (Reader's Digest, March 2009). Assume this is the true population proportion and that you plan to take a sample survey of 540 grocery shoppers to further investigate their behavior. Use z-table. a. Show the sampling distribution of (P), the proportion of groceries thrown out by your sample respondents (to 4 decimals). Can assume to be normally distributed because np>=5 and n(1-p)>=5 p = .12 standard error of the proportion o( p ) = b. What is the probability that your survey will provide a sample proportion within +.03 of the population proportion (to 4 decimals)?

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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People end up tossing 12% of what they buy at the grocery store (Reader's Digest, March 2009). Assume this is the true population
proportion and that you plan to take a sample survey of 540 grocery shoppers to further investigate their behavior. Use z-table.
a. Show the sampling distribution of (P), the proportion of groceries thrown out by your sample respondents (to 4 decimals).
Can assume to be normally distributed because np>=5 and n(1-p)>=5
p =
.12
standard error of the proportion o( p) =
b. What is the probability that your survey will provide a sample proportion within +.03 of the population proportion (to 4 decimals)?
c. What is the probability that your survey will provide a sample proportion within +.015 of the population proportion (to 4
decimals)?
.7154
Transcribed Image Text:People end up tossing 12% of what they buy at the grocery store (Reader's Digest, March 2009). Assume this is the true population proportion and that you plan to take a sample survey of 540 grocery shoppers to further investigate their behavior. Use z-table. a. Show the sampling distribution of (P), the proportion of groceries thrown out by your sample respondents (to 4 decimals). Can assume to be normally distributed because np>=5 and n(1-p)>=5 p = .12 standard error of the proportion o( p) = b. What is the probability that your survey will provide a sample proportion within +.03 of the population proportion (to 4 decimals)? c. What is the probability that your survey will provide a sample proportion within +.015 of the population proportion (to 4 decimals)? .7154
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