Reducing the sample size to one-third, increases the error by √3.
The margin of error is given by:
[tex]E=z_\frac{\alpha}{2} *\frac{\sigma}{\sqrt{n} } \\\\where\ z_\frac{\alpha}{2} \ is \ the \ confidence\ level\ z\ score, \sigma\ is \ mean\ and\ n\ is\ sample\ size.\\\\n=360, hence:\\\\E=z_\frac{\alpha}{2} *\frac{\sigma}{\sqrt{360} } \\\\E=0.0527(z_\frac{\alpha}{2} *\sigma)\\\\For\ n = 1/3 * 360=120:\\\\\\E=z_\frac{\alpha}{2} *\frac{\sigma}{\sqrt{120} } \\\\E=0.09122(z_\frac{\alpha}{2} *\sigma)[/tex]
Reducing the sample size to one-third, increases the error by √3.
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