7. A political poll is taken to determine the fraction p of the population that would support a referendum requiring all citizens to be fluent in the language of probability and statistics. (i) Assume p = 0.5, use the central limit theorem to estimate the probability that in a poll of 25 people at least 14 people support the referendum. With p unknown and n the number of random people polled. Let xn be the (ii) fraction of the polled people who support the referendum. What is the smallest sample size n in order to have a 90% confidence that x, is within 0.01 of the true value of p?

7. A political poll is taken to determine the fraction p of the population that would support a referendum requiring all citizens to be fluent in the language of probability and statistics. (i) Assume p = 0.5, use the central limit theorem to estimate the probability that in a poll of 25 people at least 14 people support the referendum. With p unknown and n the number of random people polled. Let xn be the (ii) fraction of the polled people who support the referendum. What is the smallest sample size n in order to have a 90% confidence that x, is within 0.01 of the true value of p?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

7. A political poll is taken to determine the fraction p of the population that would
support a referendum requiring all citizens to be fluent in the language of
probability and statistics.
(i)
Assume p = 0.5, use the central limit theorem to estimate the probability
that in a poll of 25 people at least 14 people support the referendum.
With p unknown and n the number of random people polled. Let xn be the
(ii)
fraction of the polled people who support the referendum. What is the
smallest sample size n in order to have a 90% confidence that x, is within
0.01 of the true value of p?

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