Answered: rence between population means for gas…

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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Twelve cars were equipped with radial tires and driven over a test course. Then the same 12 cars (with the same drivers) were equipped with regular belted tires and driven over the same course. After each run, the cars' gas economy (in kilometer/liter) was measured. Data are shown below. Assume gas economy for both types of tires are normally distributed. Do the data provide enough evidence to show that radical tires produce higher gas economy? What's the difference between population means for gas economy?

Gas eco (radial) 4.2 4.7 6.6 7.0 607 4.5 5.7 6.0 7.4 4.9 6.1 5.4

Gas eco (belted) 4.1 4.9 6.2 6.9 6.8 4.4 5.7 5.8 6.9 4.7 6.0 4.9

What is the value of the test statistic? Round to 4 decimal places if necessary.

ANSWER:

What is the p-value? Round to 4 decimal places if necessary.

ANSWER:

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution

Introduction

When we are interested in the difference between two variables for the same subject, we

perform a paired t-test.

Here we have to compare gas economy using radial and belted Tyre Hence we will use paired t test

The formula for a t-statistic for two dependent samples is:

$t = \frac{\bar{D}}{\frac{S_{D}}{\sqrt{n}}}$

where $\bar{D} = {\bar{X}}_{1} - {\bar{X}}_{2}$ is the mean difference and $S_{D}$ is the sample standard deviation of the differences $\bar D = X_1^i - X_2^i$