Question

The proportion of items in a population that possess a specific attribute is known to be 0.45. a. If a simple random sample of size nequals100 is selected and the proportion of items in the sample that contain the attribute of interest is 0.48​, what is the sampling​ error?

Answer 1

Answer: 0.05

Explanation:

• Sampling error is the error occurs by considering sample for study instead of entire population.

Given : The proportion of items in a population that possess a specific attribute is known to be 0.45.

Sample size : n= 100

Sample proportion of items in a population that possess a specific attribute :
`\hat{p}=0.48`

Now, the formula to find the sampling error :

`\text{Sampling error} =\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}`

`\text{Sampling error} =\sqrt{(0.48(1-0.48))/(100)}`

`=\sqrt{(0.48(0.52))/(100)}\\\\=√(0.002496)\approx0.05`

Hence, the sampling​ error =0.05