Amusement parks sell day passes and season passes. A day pass to Fun World costs $41 and provides admittance to the amusement park for one day. A season pass to Fun World costs $100 and provides unlimited admittance to the amusement park all season. The manager of Fun World would like to better understand how frequently patrons visit the park. At the end of the season he selects two separate random samples: one of 30 patrons that did not buy a season pass and one of 30 patrons that did buy a season pass. The parallel boxplots show the distribution of number of visits per patron for the most recent season for these two samples. (a) Write a few sentences comparing the distributions of number of visits for the sample of patrons that did and did not buy a season pass. (b) The mean number of visits per patron among those that did not buy a season pass is 1.7 visits per patron. The mean number of visits per patron among those that did buy a season pass is 2.967 visits per patron. Are these values parameters or statistics? Explain. (c) The number of visits for the 30 patrons that bought season passes are: 1111111112222222333334444457910 What proportion of these patrons would have paid less if they bought day passes rather than a season pass? Explain.

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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Amusement parks sell day passes and season passes. A day pass to Fun World costs $41 and provides admittance to the amusement park for one day. A season pass to Fun World costs $100 and provides unlimited admittance to the amusement park all season. The manager of Fun World would like to better understand how frequently patrons visit the park. At the end of the season he selects two separate random samples: one of 30 patrons that did not buy a season pass and one of 30 patrons that did buy a season pass. The parallel boxplots show the distribution of number of visits per patron for the most recent season for these two samples. (a) Write a few sentences comparing the distributions of number of visits for the sample of patrons that did and did not buy a season pass. (b) The mean number of visits per patron among those that did not buy a season pass is 1.7 visits per patron. The mean number of visits per patron among those that did buy a season pass is 2.967 visits per patron. Are these values parameters or statistics? Explain. (c) The number of visits for the 30 patrons that bought season passes are: 1111111112222222333334444457910 What proportion of these patrons would have paid less if they bought day passes rather than a season pass? Explain.

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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