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Paulcatipay560go
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in your study, the size of your population is 5250 respondents. what is the size of your sample if you allow 5% margin of error?​

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Hanimeyago

SAMPLE SIZE

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Problem

  • in your study, the size of your population is 5250 respondents. what is the size of your sample if you allow 5% margin of error?

Given

  • N = 5,250.00
  • e = 5%
  • n = ?

Solution

Determine the sample size using the formula in which n is the sample size, N is the population and e is the acceptable sampling error

  • [tex]\bold{Formula\:||\:Sample_{Size} = \frac{N}{1\:+\: {N}^{2} } }[/tex]
  • [tex]\large\tt{\red{Sample_{Size}} = \frac{5,250}{1 \:+\: (5,250){(0.05)}^{2} } }[/tex]

Substitute the values of n and e to the formula and solve for the product at the denominator then simplify

  • [tex]\large\tt{Sample_{Size} = \frac{N}{1\: + \:{N}^{2} }}[/tex]

  • [tex]\large\tt{Sample_{Size} = \frac{5,250}{1 \:+ \:(5,250) (0.05)²}}[/tex]

  • [tex]\large\tt{Sample_{Size} = \frac{5,250}{ 1 \:+ \:(5,250) (0.0025) }}[/tex]

  • [tex]\large\tt{Sample_{Size} = \frac{5,250}{14.12}}[/tex]

  • [tex]\underline{\large\tt\red{371.81= Sample_{Size}}}[/tex]

Final Answer

  • Therefore, The size of your sample if you allow 5% margin of error is 371

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