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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> In an opinion poll it is assumed that an unknown proportion <math>p</math> of the people are in favor of a proposed new law and a proportion <math>1-p</math> are against it. A sample of <math>n</math> people is taken to obtain their opinion. Th...") |
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In an opinion poll it is assumed that an unknown proportion <math>p</math> of the people are in favor of a proposed new law and a proportion <math>1-p</math> are against it. A sample of <math>n</math> people is taken to obtain their opinion. The proportion <math>{\bar | |||
of the people are in favor of a proposed new law and a proportion <math>1-p</math> are against | |||
it. A sample of <math>n</math> people is taken to obtain their opinion. The proportion <math>{\bar | |||
p}</math> in favor in the sample is taken as an estimate of <math>p</math>. Using the Central Limit | p}</math> in favor in the sample is taken as an estimate of <math>p</math>. Using the Central Limit | ||
Theorem, determine how large a sample will ensure that the estimate will, with | Theorem, determine how large a sample will ensure that the estimate will, with | ||
probability .95, be correct to within .01. | probability .95, be correct to within .01. | ||
Latest revision as of 00:00, 15 June 2024
In an opinion poll it is assumed that an unknown proportion [math]p[/math] of the people are in favor of a proposed new law and a proportion [math]1-p[/math] are against it. A sample of [math]n[/math] people is taken to obtain their opinion. The proportion [math]{\bar p}[/math] in favor in the sample is taken as an estimate of [math]p[/math]. Using the Central Limit Theorem, determine how large a sample will ensure that the estimate will, with probability .95, be correct to within .01.