Answered: Practice For Two Sample T Test…

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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Practice For Two Sample T Test Procedure: Go through all of the hypothesis test steps in order to answer the question below: Example: Suppose we want to compare the true mean stopping times of two different types of brakes at 50 mph of a car of a certain type. The first type of brake is made from an enhanced synthetic material that is thought to improve braking distances. The second type of brake is made from material that has been in use before the enhanced material was designed. Do the following data support the claim that the brakes made from the enhanced material are superior to the brakes made from the other material? Sample on enhanced brakes: 6 cars tested, average braking distance 115.7 ft with a standard deviation of 5.03 ft. Sample on existing brakes: 7 cars tested, average braking distance 121.3 ft with a standard deviation of 5.38 ft. Before you begin the steps: What do you have to assume about the populations that are being sampled here? (This is important! You can’t do a t-test without these assumptions!) After you finish the steps: Calculate a 95% confidence interval on the mean difference in braking distance for the brakes.

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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