Question

From the records of a health-insurance companies in Pennsylvania, it is known that 58% of the accounts include dental coverage. A researcher would like to take a random sample of 500 accounts to review. Find the standard deviation of the sample proportion in this situation. Give your answer to 4 decimal places. For help on how to input a numeric answer, please see "Instructions for inputting a numeric response."

Answer 1

Answer: 0.0221

Explanation:

We know that the formula to find the standard deviation of the sample proportion is :

`\sigma_p=\sqrt{(p(1-p))/(n)}`

, where p = proportion of success.

n= sample size.

As per given , we have

p=0.58

n= 500

Then, the standard deviation of the sample proportion in this situation would be :

`\sigma_p=\sqrt{(0.58(1-0.58))/(500)}\\\\=\sqrt{(0.2436)/(500)}\\\\=√(0.0004872)\\\\\approx0.0221`

Hence, the standard deviation of the sample proportion in this situation is 0.0221 .