Answered: I am interested to see the average…

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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Question

I am interested to see the average weight of a bottle of sparkling water and a bottle of Coca-Cola. All bottles are the same size, conduct an interval test using a 1.0 significance interval.

Water	Coca-Cola
1.9	2.0
1.7	1.9
1.6	2.5
1.6	2.1
1.8	2.0
1.5	1.8
1.9	1.9
1.8	1.7
1.7	1.9
1.5	1.8

Expert Solution

Step 1

The hypothesis will be given as :

$H_{o} : μ_{1} = μ_{2} H_{1} : μ_{1} \neq μ_{2}$

To test if there is any difference in the average weights of the two types of bottle, with unknown standard deviations, Students' t-test will be used.

The level of significance is given to be $0.01$

The test statistics is given by :

$t = \frac{x_{1} - x_{2}}{\sqrt{\frac{{s^{2}}_{1}}{n_{1}} + \frac{{s^{2}}_{2}}{n_{2}}}} ~ t_{n_{1} + n_{2} - 2}$

The confidence interval is given as :

$C . I = (x_{1} - x_{2}) \pm t_{α / 2} . \sqrt{\frac{{s^{2}}_{1}}{n_{1}} + \frac{{s^{2}}_{2}}{n_{2}}}$

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