Question

The probability of winning a prize from a scratch

off card is 60%. A sample of 30 cards is taken.
What is the standard error of the proportion,
rounded to the nearest thousandth?

Answer 1

The standard error of the proportion is

`E=0.089`

Explanation:

Assuming that the size of population N is large enough, and with a sample
`n = 30`, so that:

`(n)/(N)\leq0.05` then the standard error of the proportion is:

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

Where

`n = 30\\\\p= 0.6\\\\E = \sqrt{(0.6(1-0.6))/(30)}\\\\E =\sqrt{(0.6(0.4))/(30)}\\\\E=(√(5))/(25)=0.089`