Answered: A psycho-linguist has been studying the…

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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A psycho-linguist has been studying the frequency of text-speech (e.g., R U Ok?, LOL ) has been progressing into EMAIL correspondence. He collects a sample of 121 EMAIL messages and computes the mean (average) number of examples of text-speech per message. He also has a huge library of archived EMAIL messages from the year 2001. From these he is able to calculate the population average and standard deviation. Compute a inferential statistic to evaluate the hypothesis that the use of text-speech has increased in the years since 2001. Use an alpha level that would insure a maximum of a %5 risk of rejecting a true null hypothesis.

These are the obtained values:

Population Mean from 2001: 1.6

Population Standard deviation from 2001: 1.25

Sample mean from this year: 1.98

Calculate and properly report your calculated statistic, and interpret your conclusion in one or two sentences.

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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