Answered: A polling organization polls n = 400…

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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Question

A polling organization polls n = 400 randomly selected registered voters to estimate the proportion of a large population that intends to vote for Candidate Y in an upcoming election. Although it is not known by the polling organization, p = 0.67 is the actual proportion of the population that prefers Candidate Y.

(a) Give the numerical value of the mean of the sampling distribution of p̂.
Mean =

(b) Calculate the standard deviation, s.d., of the sampling distribution of p̂. (Round your answer to the nearest hundredth.)
s.d. =

(c) Use the Empirical Rule to find values that fill in the blanks in the following sentence. (Round all answers to the nearest hundredth.)
In about 99.7% of all randomly selected samples of n = 400 from this population, the sample proportion preferring Candidate Y will be between and .

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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