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

Step-by-step 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 :

$\text{Sampling error} =\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$\text{Sampling error} =\sqrt{\dfrac{0.48(1-0.48)}{100}}$

$=\sqrt{\dfrac{0.48(0.52)}{100}}\\\\=\sqrt{0.002496}\approx0.05$

Hence, the sampling​ error =0.05