Answered: Recent studies have shown that about…

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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Recent studies have shown that about 20% of American adults fit the medical definition of being obese. A large medical clinic would like to estimate what percentage of their patients are obese, so they take a random sample of 100 patients and find that 16 are obese. Suppose that in truth, the same percentage holds for the patients of the medical clinic as for the general population, 20%. Give a numerical value for each of the following concepts.

(a) The population proportion, p, of obese patients in the medical clinic.
p =

(b) The proportion of obese patients, p̂, for the sample of 100 patients.
p̂ =

(c) The standard error, s.e., of p̂. (Round your answer to four decimal places.)
s.e.(p̂) =

(d) The mean of the sampling distribution of p̂.
mean =
(e) The standard deviation, s.d., of the sampling distribution of p̂. (Round your answer to four decimal places.)
s.d.(p̂) =

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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