Answered: A research team interested in the…

Name: A research team interested in the proportion of patients at a local ho
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Description: A research team interested in the proportion of patients at a local hospital that are admitted to the emergency room without any form of healthcare insurance. Supposed to team hypothesizes that the proportion of these patients was 19%, and conducted

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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A research team interested in the proportion of patients at a local hospital that are admitted to the emergency room without any form of healthcare insurance. Supposed to team hypothesizes that the proportion of these patients was 19%, and conducted a sample of 298 participants to find that 109 were without any insurance at 95% confidence. What was the power of the tests conducted?

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Step 1

Given
Sample size = n $= 298$
number of patients with out insurance be X $= 109$
The proportion of patients with out insurance $= \frac{109}{298} = 0.3658$

Null hypothesis $H_{o} : p = 0.19$
Alternate hypothesis $H_{a} : p \neq 0.19$

As the alternate hypothesis has ≠ , the hypothesis test is two tailed test.
The test statistic is calculated as shown below
$Z = \frac{\hat{p} - p}{\sqrt{\frac{p (1 - p)}{n}}} Z = \frac{0.3658 - 0.19}{\sqrt{\frac{0.19 (1 - 0.19)}{298}}} = 7.734$

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