Answered: on theory tells us that (choose all…

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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Sampling distribution theory tells us that (choose all that apply)

- that's as long as the sample size is greater than 10 the distribution of the sample means is about normal

- the mean and the standard deviations of the population are the same as that for the samples

- the mean of the population is the same as that for the samples means

-the standard deviation of the sample means must be adjusted by dividing sigma by SQRT(N)

-the standard deviation of the sample means must be calculated as SQRT[p(1-p)/N)]

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 + ...

Expert Solution

Step 1

The sampling distribution of a statistic is known as the probability distribution of all the possible values taken by the statistic which can be selected from the specific population.

The mean and standard deviation of the sampling distribution of the sample mean is equal to μXˉ and $σ_{\bar{X}} = σ / \sqrt{N}$ respectively.

Where,

$σ = S t a d a r d d v e i a t i o n N = S a m p l e s i z e$

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