Answered: Researchers working for a sports drink…

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

Researchers working for a sports drink company would like to know if a new blend if its popular sports drink can help improve marathon runners' final running time. Marathon times, Y, are known to follow a Normal distribution. Suppose thatrunners using the old blend sports drink have a mean finishing time of 300 minutes(u = 300 minutes). A random sample of 20 runners was selected to use the newblend of sports drink in a marathon, finishing with an average time of 270 minutesand a standard deviation of 20 minutes (y = 270 min, s = 20 min). Can it be claimed thatthe new blend lowers finishing times? Or is it possible that random chance alone canexplain the discrepancy? Carry out a hypothesis test of the true mean u using the 4-step procedure. Set your alpha-level to 0.05.

a. Which is the correct null hypothesis?

b. Which is the correct alternative hypothesis?

c. Which test statistic and sampling distribution under the null should we use?

d. What is the critical value associated with an alpha-level of 0.05?

e. Calculate the value of the test statistic. (round to 2 significant digits, 1.23)

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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