Answered: Compute the 95% confidence interval…

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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Three friends are having a debate. They recently read that on average Americans drive 16 miles each way when computing to work by car (ABC News, 2007). Friend A suspects that the mean for Colorado residents is likely lower than the national average because the population density of Colorado increases the likelihood that people live closer to their jobs, while friend B suspects the mean for Colorado residents is likely higher than the national average. Friend C does not find either argument very convincing and instead suspects that the mean for Colorado residents is no different from the US population mean. The three friends bet a dinner at Alinea and set out to resolve the debate. Using a random sample of 20 Colorado residents, they calculate the mean for their sample to be 14.23 miles with a standard deviation of 2.34. The three friends did not pay very close attention in their statistics class, so they need your help making sense of these numbers.

Compute the 95% confidence interval around the u for Colorado residents. Be sure to state your results in statistical notation.
Do you reject or fail to reject the null? Why/why not?
State the findings in plain language. Who gets a free dinner at Alinea?: Friend A, Friend B, or Friend C?

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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