3. The paper "Effects of Caffeine on Repeated Sprint Ability, Reactive Agility Time, Sleep and Next Day Performance"† describes an experiment in which male athlete volunteers who were considered low caffeine consumers were assigned at random to one of two experimental groups. Those assigned to the caffeine group drank a beverage which contained caffeine 1 hour before an exercise session. Those in the no-caffeine group drank a beverage that did not contain caffeine 1 hour before an exercise session. That night, participants wore a device that measures sleep activity. The researchers reported that there was no significant difference in mean sleep duration for the two experimental groups. In the context of this experiment, explain what it means to say that there is no significant difference in the group means. A) The difference in mean sleep duration for the caffeine and no-caffeine groups could have occurred by chance just due to the random assignment, assuming there is a real difference between the treatment means. B) The difference in mean sleep duration for the caffeine and no-caffeine groups could not have occurred by chance just due to the random assignment, assuming there is no real difference between the treatment means. C) The difference in mean sleep duration for the caffeine and no-caffeine groups could have occurred by chance just due to the random assignment, assuming there is no real difference between the treatment means. D) The difference in mean sleep duration for the caffeine and no-caffeine groups could not have occurred by chance just due to the random assignment, assuming there is a real difference between the treatment means. In particular, explain if this means that the mean sleep durations for the two groups are equal. A) It does not mean that the mean sleep durations for the two groups are equal, but there is convincing evidence that they are equal. B) It means that the mean sleep durations for the two groups are equal, because there is convincing evidence that they are equal. C) It does not mean that the mean sleep durations for the two groups are equal, but there is not convincing evidence that they are different. D) It does not mean that the mean sleep durations for the two groups are equal, but there is convincing evidence that they are different.

3. The paper "Effects of Caffeine on Repeated Sprint Ability, Reactive Agility Time, Sleep and Next Day Performance"† describes an experiment in which male athlete volunteers who were considered low caffeine consumers were assigned at random to one of two experimental groups. Those assigned to the caffeine group drank a beverage which contained caffeine 1 hour before an exercise session. Those in the no-caffeine group drank a beverage that did not contain caffeine 1 hour before an exercise session. That night, participants wore a device that measures sleep activity. The researchers reported that there was no significant difference in mean sleep duration for the two experimental groups. In the context of this experiment, explain what it means to say that there is no significant difference in the group means. A) The difference in mean sleep duration for the caffeine and no-caffeine groups could have occurred by chance just due to the random assignment, assuming there is a real difference between the treatment means. B) The difference in mean sleep duration for the caffeine and no-caffeine groups could not have occurred by chance just due to the random assignment, assuming there is no real difference between the treatment means. C) The difference in mean sleep duration for the caffeine and no-caffeine groups could have occurred by chance just due to the random assignment, assuming there is no real difference between the treatment means. D) The difference in mean sleep duration for the caffeine and no-caffeine groups could not have occurred by chance just due to the random assignment, assuming there is a real difference between the treatment means. In particular, explain if this means that the mean sleep durations for the two groups are equal. A) It does not mean that the mean sleep durations for the two groups are equal, but there is convincing evidence that they are equal. B) It means that the mean sleep durations for the two groups are equal, because there is convincing evidence that they are equal. C) It does not mean that the mean sleep durations for the two groups are equal, but there is not convincing evidence that they are different. D) It does not mean that the mean sleep durations for the two groups are equal, but there is convincing evidence that they are different.

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) The difference in mean sleep duration for the caffeine and no-caffeine groups could have occurred by chance just due to the random assignment, assuming there is a real difference between the treatment means.

B) The difference in mean sleep duration for the caffeine and no-caffeine groups could not have occurred by chance just due to the random assignment, assuming there is no real difference between the treatment means.

C) The difference in mean sleep duration for the caffeine and no-caffeine groups could have occurred by chance just due to the random assignment, assuming there is no real difference between the treatment means.

D) The difference in mean sleep duration for the caffeine and no-caffeine groups could not have occurred by chance just due to the random assignment, assuming there is a real difference between the treatment means.

In particular, explain if this means that the mean sleep durations for the two groups are equal.

A) It does not mean that the mean sleep durations for the two groups are equal, but there is convincing evidence that they are equal.

B) It means that the mean sleep durations for the two groups are equal, because there is convincing evidence that they are equal.

C) It does not mean that the mean sleep durations for the two groups are equal, but there is not convincing evidence that they are different.

D) It does not mean that the mean sleep durations for the two groups are equal, but there is convincing evidence that they are different.

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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