Answered: he National Weather Service says that…

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 National Weather Service says that the mean daily high temperature for October in a large midwestern city is

52°F

. A local weather service suspects that this value is not accurate and wants to perform a hypothesis test to determine whether the mean is actually lower than

52°F

. A sample of mean daily high temperatures for October over the past

years yields

=x50°F

. Assume that the population standard deviation is

5.2°F

. Perform the hypothesis test at the

=α0.05

significance level.

=μ52°F

<μ52°F

Test statistic :

=z−2.4

Critical value :

=z−1.64

Reject

=:H0μ52°F

there is sufficient evidence to support the claim that the mean is less than

52°F

=μ52°F

>μ52°F

Test statistic :

=z−2.4

Critical value :

=z−1.64

Fail to reject

=:H0μ52°F

there is not sufficient evidence to support the claim that the mean is less than

52°F

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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