Answered: Simple random sampling has been used to…

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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Simple random sampling has been used to obtain a sample of 50 elements from a population of 800. The sample mean was 21.5, and the sample standard deviation was found to be 20.

Estimate the population mean.

Estimate the standard error of the mean.

iii. Develop an approximate 95% confidence interval for the population mean

b. A county had 724 corporate tax returns filed. The mean annual income reported was 161.22 with a standard deviation of 31.3. How large a sample will be necessary next year to develop an approximate 95% confidence interval on mean annual corporate earnings? The precision required is an interval width of no more than

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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