Answered: Long races, like a marathon, have…

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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Use the prompt and answer question 1

Long races, like a marathon, have hydration stations about 2-3 miles apart. When it comes to getting ready for the big race, runners must decide whether the water provided by the hydration stations is enough to get them through the race or whether they should carry their own supply of water. Some runners believe carrying additional weight (like a water bottle) will slow them down and therefore they decide to rely on the hydration stations along the race.

To put this theory to the test, a random sample of 466 marathon runners is selected and various variables are recorded including the runner’s completion time in minutes and whether or not the runner carried water during the race.

A 10% significance level is to be used.

Here's a definition of the parameters:

µ₁: the population mean marathon completion time in minutes when the runner is not carrying their own water bottle
µ₂ : the population mean marathon completion time in minutes when the runner is carrying their own water bottle.

Recall the Steps for Testing Hypotheses:
Question 1: State the hypotheses (the significance level has been selected to be 10%).

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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