Question

The proportion of items in a population that possess a specific attribute is known to be 0.40. If a simple random sample of size 100 is selected and the proportion of items in the sample that contain the attribute of interest is 0.46​, what is the sampling​ error?

Answer 1

Answer:

The sampling error =  0.06

Step-by-step explanation:

From the given information:

Let represent $\beta$ to  be the population proportion = 0.4

The sample proportion be P = 0.46   &

The sample size be n = 100

The population standard duration can be expressed by the relation:

Population standard duration $\sigma = \sqrt{\dfrac{\beta(1- \beta)}{n}}$

$\sigma = \sqrt{\dfrac{0.4(1-0.4)}{100}}$

$\sigma = \sqrt{\dfrac{0.4(0.6)}{100}}$

$\sigma = 0.049$

The sample proportion = 0.46

Then the sampling error  = P - $\beta$

The sampling error  = 0.46 - 0.4

The sampling error =  0.06