Answered: Because of safety considerations, in…

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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Because of safety considerations, in May 2003, the Federal Aviation Administration (FAA) changed its guidelines for how small commuter airlines must estimate passenger weights. Under the old rule, airlines used 180 pounds as a typical passenger weight (including carry-on luggage) in warm months and 185 pounds as a typical weight in cold months. The Alaska Journal of Commerce (May 25, 2003) reported that Frontier Airlines conducted a study to estimate mean passenger plus carry-on weights. They found a sample mean summer weight of 183 pounds and a winter sample mean of 190 pounds. Suppose that these estimates were based on random samples of 100 passengers and that the sample standard deviations were 21 pounds for the summer weights and 24 pounds for the winter weights.

A) Construct a 95% confidence interval (in pounds) for the population mean summer weight (including carry-on luggage) of Frontier Airlines passengers. (Round your answers to three decimal places.)

B)Construct a 95% confidence interval (in pounds) for the population mean winter weight (including carry-on luggage) of Frontier Airlines passengers. (Round your answers to three decimal places.)

Because of safety considerations, in May 2003, the Federal Aviation Administration (FAA) changed its guidelines for how small commuter airlines must estimate passenger weights. Under the old rule,
airlines used 180 pounds as a typical passenger weight (including carry-on luggage) in warm months and 185 pounds as a typical weight in cold months. The Alaska Journal of Commerce (May 25,
2003) reported that Frontier Airlines conducted a study to estimate mean passenger plus carry-on weights. They found a sample mean summer weight of 183 pounds and a winter sample mean of
190 pounds. Suppose that these estimates were based on random samples of 100 passengers and that the sample standard deviations were 21 pounds for the summer weights and 24 pounds for the
winter weights.
In USE SALT
(a) Construct a 95% confidence interval (in pounds) for the population mean summer weight (including carry-on luggage) of Frontier Airlines passengers. (Round your answers to three decimal
places.)
Ibs
Interpret the interval.
There is a 95% chance that the summer weight (including carry-on luggage) of Frontier Airlines passengers falls directly in the middle of this interval.
We are 95% confident that the true mean summer weight (including carry-on luggage) of Frontier Airlines passengers falls within this interval.
We are 95% confident that the summer weight (including carry-on luggage) of Frontier Airlines passengers falls within this interval.
There is a 95% chance that the true mean summer weight (including carry-on luggage) of Frontier Airlines passengers falls directly in the middle of this interval.
There is a 95% chance that the summer weight (including carry-on luggage) of Frontier Airlines passengers falls within this interval.
(b) Construct a 95% confidence interval (in pounds) for the population mean winter weight (including carry-on luggage) of Frontier Airlines passengers. (Round your answers to three decimal
places.)
Ibs
Interpret the 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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