Answered: Two ride-sharing companies are…

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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Two ride-sharing companies are competing for business in a large city. To help customers compare the companies, a data scientist selects a random sample of 40 completed rides from each of the two companies. From each sample, he computes the mean amount of time that passed between when the request for a pickup was placed and when the customer was picked up. Company A took, on average, 18 minutes to pick up customers with a standard deviation of 4 minutes. Company B took, on average, 12 minutes to pick up customers with a standard deviation of 10 minutes. (a) Construct and interpret a 98% confidence interval for the difference in mean response time for these two ride-sharing companies (b) The results of the study are particularly meaningful to customers if one company is found to be significantly different from the other company regarding response time. Based upon the 98% confidence interval, is there reason to believe that the two ride-sharing companies have different mean response times? 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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