A musicologist is attempting to determine the mean length of modern pop songs. She conducts a sample of 40 songs, and finds a sample mean of 214 seconds., with a standard deviation of 10 secods. Assume that the distribution of lengths of pop songs is nearly normal.Define your variable:Let p be the proportion of pop song that are seconds long.Let μμ be the mean length of the sampled pop songs, in seconds.Let μμ be the mean length of pop songs, in seconds..Let p be the proprotion of songs in the sample.Create and interpret a 95% Confidence Interval. Round your answers to one decimal place. and seconds.What is the margin of error? Round your answer to one decimal place. seconds.According to Google, the mean length of pop songs is 210210. What do you think of this claim?The claim is inside the interval. It is reasonable.The claim is above the sample mean, so there is no way it can be true.The claim is inside the interval. It must be true.That claim is not in our interval. We do not believe it.

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Answered: Define your variable: Let p be the…

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 musicologist is attempting to determine the mean length of modern pop songs. She conducts a sample of 40 songs, and finds a sample mean of 214 seconds., with a standard deviation of 10 secods. Assume that the distribution of lengths of pop songs is nearly normal.

Define your variable:

Let p be the proportion of pop song that are seconds long.
Let μμ be the mean length of the sampled pop songs, in seconds.
Let μμ be the mean length of pop songs, in seconds..
Let p be the proprotion of songs in the sample.

Create and interpret a 95% Confidence Interval. Round your answers to one decimal place. and seconds.

What is the margin of error? Round your answer to one decimal place. seconds.

According to Google, the mean length of pop songs is 210210. What do you think of this claim?

The claim is inside the interval. It is reasonable.
The claim is above the sample mean, so there is no way it can be true.
The claim is inside the interval. It must be true.
That claim is not in our interval. We do not believe it.

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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