Answered: The law of large numbers states that as…

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

The law of large numbers states that as the number of observations drawn at random from a population with finite mean increases, the mean of the observed values:

	a.	tends to get closer and closer to the population mean .
	b.	gets smaller and smaller.
	c.	gets larger and larger.
	d.	fluctuates steadily between 1 standard deviation above and 1 standard deviation below the mean.

I collect a random sample of size n from a population and compute a 95% confidence interval for the proportion I observe from the population. What could I do to produce a new confidence interval with a larger width (larger margin of error) based on these same data?

	a.	I could use the same confidence level but compute the interval n times; approximately 5% of these intervals will be larger.
	b.	Nothing can guarantee absolutely that I will get a larger interval; I can only say the chance of obtaining a larger interval is 0.05.
	c.	I could use a smaller confidence level.
	d.	I could use a larger confidence level.

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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