Marijuana Use The Gallup poll reported that 45 % of Americans have tried marijuana. This was based on a survey of 1021 Americans and had a margin of error of plus or minus 5 percentage points with a 95 % level of confidence. a. State the survey results in confidence interval form and interpret the interval. b. If the Gallup Poll was to conduct 100 such surveys of 1021 Americans, how many of them would result in confidence intervals that did not include the true population proportion? c. Suppose a student wrote this interpretation of the interval: “We are 95 % confident that the percentage of Americans who have tried marijuana is between 40 % and 50 % . ” What, if anything, is incorrect in this interpretation?
Marijuana Use The Gallup poll reported that 45 % of Americans have tried marijuana. This was based on a survey of 1021 Americans and had a margin of error of plus or minus 5 percentage points with a 95 % level of confidence. a. State the survey results in confidence interval form and interpret the interval. b. If the Gallup Poll was to conduct 100 such surveys of 1021 Americans, how many of them would result in confidence intervals that did not include the true population proportion? c. Suppose a student wrote this interpretation of the interval: “We are 95 % confident that the percentage of Americans who have tried marijuana is between 40 % and 50 % . ” What, if anything, is incorrect in this interpretation?
Solution Summary: The author explains the 95 % confidence interval for population proportion, which indicates that the true population parameter lies within the confidence limit.
Marijuana Use The Gallup poll reported that
45
%
of Americans have tried marijuana. This was based on a survey of 1021 Americans and had a margin of error of plus or minus 5 percentage points with a
95
%
level of confidence.
a. State the survey results in confidence interval form and interpret the interval.
b. If the Gallup Poll was to conduct 100 such surveys of 1021 Americans, how many of them would result in confidence intervals that did not include the true population proportion?
c. Suppose a student wrote this interpretation of the interval: “We are
95
%
confident that the percentage of Americans who have tried marijuana is between
40
%
and
50
%
.
”
What, if anything, is incorrect in this interpretation?
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Hypothesis Testing - Solving Problems With Proportions; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=76VruarGn2Q;License: Standard YouTube License, CC-BY
Hypothesis Testing and Confidence Intervals (FRM Part 1 – Book 2 – Chapter 5); Author: Analystprep;https://www.youtube.com/watch?v=vth3yZIUlGQ;License: Standard YouTube License, CC-BY