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Readme [11.4K]
3 years ago
12

A prior study determined the point estimate of the population proportion as 58% ( = 0.58). The analysts decide to conduct a seco

nd study on the same topic and would like its margin of error, E, to be 4% when its confidence level is 95% (z*-score of 1.96).
What is the minimum sample size that should be used so the estimate of will be within the required margin of error of the population proportion?
Mathematics
2 answers:
ICE Princess25 [194]3 years ago
4 0

Answer:

<em>Minimum Sample size  'n' = 585</em>

Step-by-step explanation:

<u>Explanation</u>:-

Given Estimate of the population proportion as 58% ( = 0.58)

P = 0.58

Given margin of error, E, to be 4%

M.E = 4 % = 0.04

<em>margin of error of the population proportion is determined by</em>

<em></em>M.E = \frac{Z_{\frac{\alpha }{2} }\sqrt{p(1-p)}  }{\sqrt{n} }<em></em>

Z- score = 1.96

0.04 = \frac{1.96\sqrt{0.58(1-0.58)}  }{\sqrt{n} }

Cross multiplication , we get

0.04 \sqrt{n} = 1.96 X  0.4935

\sqrt{n} = \frac{0.4935 X 1.96}{0.04} = 24.18

<em>Squaring on both sides, we get</em>

<em>n = 584.7≅585</em>

<u><em>Conclusion</em></u><u>:-</u>

<em>minimum Sample size  'n' = 585</em>

Arturiano [62]3 years ago
4 0

Answer:

585

Step-by-step explanation:

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