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For a population, [tex]N = 3700[/tex] and [tex]p = 0.31[/tex]. A random sample of 100 elements selected from this population gave [tex]\hat{p} = 0.56[/tex]. Find the sampling error.

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Sampling error =

Answer :

The sampling error is 0.25.

Sampling error is the difference between the actual population parameter value and the value of the sample statistic that is used to estimate the population parameter.

It is computed as the difference between the sample statistic and the true value of the population parameter.

Here, we need to find the sampling error.

The formula for the sampling error is;

Sampling error (i) = p - Pwhere p is the sample proportion and P is the population proportion.

Given that the population, N = 3700 and p = 0.31.

A random sample of 100 elements selected from this population gave p = 0,56.

Therefore, the population proportion is given by P = (3700)(0.31) = 1147.The sample proportion is p = 0.56.Using the formula above, the sampling error is;i = p - P = 0.56 - 0.31 = 0.25

Therefore, the sampling error is 0.25.

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