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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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I am having trouble with this question. My textbook is not doing a very good job at explaining it for me. This is one question with multiple parts: known and unknown for both concepts....

Explain the following concepts related to the inference between population means when the standard deviation is known and unknown: (a)Interval Estimation (b)Hypothesis testing using the mean

Expert Solution

Step 1

Test of significance for difference of means

Let ${\bar{x}}_{1}$ be the mean of size $n_{1}$ population with mean $μ_{1}$ and variance $σ_{1}^{2}$

${\bar{x}}_{2}$ be the mean of size $n_{2}$ population with mean $μ_{2}$ and variance $σ_{2}^{2}$

${\bar{x}}_{1}$ ~N( $μ_{1}$ , $σ_{1}^{2}$ / $n_{1}$ ); ${\bar{x}}_{2}$ ~N( $μ_{2}$ , $σ_{2}^{2}$ / $n_{2}$ )

Also ${\bar{x}}_{1}$ - ${\bar{x}}_{2}$ , the difference of two independent normal variates is again a normal variate

Hence Z = $\frac{(x_{1} - x_{2}) - E (x_{1} - x_{2})}{S . E (x_{1} - x_{2})} ~ N (0, 1)$

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