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The permissible sampling error is required to determine sample size for:
- a)Estimating a Proportion
- b)Estimating a Mean
- c)Both (a) & (b)
- d)None
Correct answer is option 'C'. Can you explain this answer?
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The permissible sampling error is required to determine sample size fo...
Estimating a Proportion and Estimating a Mean
To determine the sample size required for estimating a proportion or mean, we need to consider the permissible sampling error. The permissible sampling error is the maximum amount of error that we are willing to accept in our estimate.
Estimating a Proportion:
When estimating a proportion, the sample size calculation is based on the formula:
\[ n = \frac{{p(1-p)(Z^2)}}{{E^2}} \]
Where:
- \( n \) = sample size
- \( p \) = estimated proportion
- \( Z \) = Z-score corresponding to the desired level of confidence
- \( E \) = permissible sampling error
Estimating a Mean:
When estimating a mean, the sample size calculation is based on the formula:
\[ n = \frac{{Z^2 * σ^2}}{{E^2}} \]
Where:
- \( n \) = sample size
- \( Z \) = Z-score corresponding to the desired level of confidence
- \( σ \) = standard deviation of the population
- \( E \) = permissible sampling error
Both (a) & (b):
Since the permissible sampling error is required to determine the sample size for estimating both a proportion and a mean, the correct answer is option 'C' - Both (a) & (b).
In conclusion, the permissible sampling error plays a crucial role in determining the sample size needed to estimate a proportion or mean accurately. It helps in ensuring that the sample is representative of the population and that the results are reliable.
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