Answered: David McCandless, Lee Byron, and their…

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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Formulating directional and nondirectional hypotheses

David McCandless, Lee Byron, and their team scanned more than 10,000 Facebook status updates and set out to learn more about the timing of relationship breakups. They found that there was a peak in breakups on Valentine’s Day and Mondays with a dip on Christmas Day. [Source: McCandless, D. (July 2010). The beauty of data visualization. TEDGlobal talks.]

Suppose you are a researcher. You conduct a hypothesis test to determine whether the mean number of breakups on Wednesdays is greater than the mean number of daily breakups. Assume that the mean number of daily breakups is 10.3 breakups (the population mean). You obtain a sample of 10,000 Facebook status updates, which yields a sample mean of M = 11.4 breakups.

Let μ denote the mean number of breakups on Wednesdays. Formulate your null and alternative hypotheses by selecting the appropriate values in the blue dropdown menus that follow.

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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