Answered: The time needed for students to…

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

The time needed for students to complete a paper and pencil maze is normally
distributed with a mean of 45 seconds and standard deviation of 5 seconds. You
wish to see if the mean completion time is decreased by vigorous exercise. You
will have a group of 10 students exercise vigorously for thirty minutes and then
complete the maze and test your hypothesis at the 1% significance level.

a. Suppose you observe a mean time of 41.7 seconds. What is your
conclusion regarding the true average time necessary to complete this
maze. What are the null and alternative hypothesis for your test?

a.μ > 45, μ <= 45

b.μ >= 45, μ < 45

c.μ <= 45, μ > 45

d. μ == 45, μ =/= 45

b. What is the p-value, significance, level and conclusion of your test?

c. What is the power of your test against the one-sided alternative value of 40 seconds?

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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