Answered: I believe that the homeless population…

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 believe that the homeless population in Manchester, NH is .20 of the total Manchester, NH population. I asked 300 random people in Manchester, NH if they knew at least one homeless person and 67 out of the 300 people I asked knew at least 1 homeless person. Test this hypothesis at the .05 significance level.

Expert Solution

Step 1

Given Information:

Hypothesized value ( $p_{0}$ ) = 0.20

Sample size (n) = 300

Out of which X = 67 people knew at least 1 homeless person.

Significance level $α = 0.05$

Sample proportion is obtained using the formula:

$\begin{array}{rcl} \hat{p} & = & \frac{X}{n} (X i s t h e n u m b e r o f s u c c e s s e s) \\ = & \frac{67}{300} \\ = & 0.2233333333 \\ \approx & 0.22333 \end{array}$

State the Hypothesis as follows:

Null Hypothesis: $H_{0} : p = 0.20$

Alternative Hypothesis: $H_{a} : p \neq 0.20$

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