Answered: Test the following claim. Identify the…

Name: Test the following claim. Identify the null hypothesis, alternative
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Description: Test the following claim. Identify the null hypothesis, alternative hypothesis,, P_value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. A manual states that in order to be a hit, a song must be no l

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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Test the following claim. Identify the null hypothesis, alternative hypothesis,, P_value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.

A manual states that in order to be a hit, a song must be no longer than three minutes and

twenty seconds (or 200 seconds). A simple random sample of 40

current hit songs results in a mean length of 245.0 sec. Assume the population standard deviation of song lengths is 54.5 sec. Use a 0.01 significance level to test the claim that the sample is from a population of songs with a mean greater than 200 sec. What do these result suggest about the advice given in the manual?

a) What are the null and alternative hypotheses?

b) Does this reject or fail to reject H0?

c) Is there sufficient evidence to support the claim that the sample is from a population of songs with a mean greater than 200 sec?

d) does this result suggest thaat the advice given in the manual is or is not sound?

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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