A music manager wanted to construct a 95% confidence interval for the lenght of songs produced at his recording studio. Using data from a random sample of 47 songs, he obtained an interval of 3.05 < μ < 4.45. Which of the following is the correct interpretation of the interval?With 95% confidence, the mean width of all widgets is between 3.05 and 4.45.The mean width of all widgets is between 3.05 and 4.45, 95% of the time. We know this is true because the mean of our sample is between 3.05 and 4.45.There is a 95% chance that the mean of the population is between 3.05 and 4.45.With 95% confidence, the mean width of a randomly selected widget will be between 3.05 and 4.45.There is a 95% chance that the mean of a sample of 47 widgets will be between 3.05 and 4.45.

Given 90% CI for population mean μ 3.05 < μ < 4.45

Answered: A music manager wanted to construct a…

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 music manager wanted to construct a 95% confidence interval for the lenght of songs produced at his recording studio. Using data from a random sample of 47 songs, he obtained an interval of 3.05 < μ < 4.45. Which of the following is the correct interpretation of the interval?

With 95% confidence, the mean width of all widgets is between 3.05 and 4.45.
The mean width of all widgets is between 3.05 and 4.45, 95% of the time. We know this is true because the mean of our sample is between 3.05 and 4.45.
There is a 95% chance that the mean of the population is between 3.05 and 4.45.
With 95% confidence, the mean width of a randomly selected widget will be between 3.05 and 4.45.
There is a 95% chance that the mean of a sample of 47 widgets will be between 3.05 and 4.45.

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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