Answered: In 2015, the average duration of…

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

In 2015, the average duration of long-distance telephone calls from a certain town was 3.9 minutes.
A telephone company wants to perform a test to determine whether this average duration of longdistance calls has changed. Fifty calls, originating from the town, was randomly selected and the
following summary minutes.
∑ ? = 205 ∑(? − ?̅)
2 = 56.43
a) Calculate the sample mean, ?̅.

) Calculate the sample standard deviation

c) Using the p value approach at the 1% level of significance, test whether the mean duration of
long-distance calls from the town had increased.

d) Construct the 99% confidence interval for the population mean duration of the long-distance
calls from the town.

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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