Answered: What is the meaning of this Probability…

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 parent association at a local high school believes that the amount of time spent on homework by students at the school, on average, is more than the schools policy of an average of 30 minutes of homework per class. To test this claim, the administrators took a random sample of 50 students, calculated the amount of time each student spent on homework per class, and tested the hypotheses:

ho u=30

ho u>30

The mean minutes spent per class of the students in the sample was 34.7 minutes and the sample standard deviation was 10.4 minutes. When the administrators performed a significance test and obtained a Probability Value of 0.0015. What is the meaning of this Probability Value in context?

Having a sample mean time spent by students on homework per class of 34.7 minutes in a random sample of 50 students, there is a probability of 0.0015 that the true mean is more than 30 minutes.

Assuming the mean time spent by students on homework per class is more than 30 minutes, there is a probability of 0.0015 of getting a sample mean of 34.7 minutes or more by chance alone in a random sample of 50 students.

Assuming the mean time spent by students on homework per class is 30 minutes, there is a probability of 0.0015 of getting a sample mean of 34.7 minutes or more by chance alone in a random sample of 50 students.

Having a sample mean time spent by students on homework per class of 34.7 minutes in a random sample of 50 students, there is a probability of 0.0015 that the true mean is 30 minutes

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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