Question

The $10\%$condition When constructing a confidence interval for a population proportion, we check that the sample size is less than $10\%$of the population size.

a. Why is it necessary to check this condition?

b. What happens to the capture rate if this condition is violated?

Short answer

a. If sample size is less than $10\%$of population, observations are closer to independent.

b. The confidence interval will be inaccurate.

Step-by-step solution

Given Information

When constructing a confidence interval for a population proportion, it is checked that sample size is less than $10\%$ of population size.

Necessity of this Condition

This condition is important due to the the fact that when sample size is less than $10\%$of population size, observations are closer to independent.

If this requirement is not met, it is not possible to calculate standard deviation of distribution.

If Population Size is not less than 10%

If this requirement is not met, it is not possible to calculate standard deviation of distribution correctly.

If standard deviation is not correct, confidence level will be inaccurate. There are less chances to obtain population parameter in confidence interval.