Answered: A sports marketing company is…

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

A sports marketing company is interested in how many hours teenagers in a town spend watching sports. They randomly select 40 teenagers from this town and ask how many hours per week they spend watching sports. The mean amount is 6.25 hours with a standard deviation of 4.33 hours. Which of the following correctly interprets the 90% confidence interval for the true mean number of hours teenagers from this town watch sports? 90% of all teenagers from this town watch sports for the number of hours that lie between the values in the interval. In repeated sampling, 90% of the time, the true mean number of hours teens from this town watch sports will be 6.25 hours. The sports marketing company can be 90% confident that the constructed interval captures the true mean number of hours teens from this town watch sports. In repeated sampling, 90% of the time the true mean number of hours teens from this town watch sports will be captured in the constructed interval.

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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