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

The sampling error = 0.06

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{(\beta(1- \beta))/(n)}`

`\sigma = \sqrt{(0.4(1-0.4))/(100)}`

`\sigma = \sqrt{(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