Answered: A population consists of the two…

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 population consists of the two numbers (7, 8). Consider all possible samples of
size 2 that can be drawn with replacement from this population. Find the following:
a. The mean of the sampling distribution of means
b. The variance of the sampling distribution
c. The standard deviation of the sampling distribution of means.
d. Illustrate the probability histogram of the sampling distribution of the
means.

The average number of liters of water that a person consumes in a month is 12 liters. Assume that the standard deviation is 4.5 liters and the distribution is
approximately normal.
a. Find the probability that a person selected at random consumes more
than 13 liters per month.
b. If a sample of 20 individuals is selected, find the probability that mean of
the sample will be more than 13 liters.

Identify the region under the t-distribution corresponding to the t-value which is 1.440 and the area is on both sides of the t-distribution.

Identify the region under the t-distribution corresponding to the t-value which is 1.725 and the area is on the right.

Identify the region under the t-distribution corresponding to the t-value which is 2.500 and the area is on the left.

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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