Question

In a recent survey of 47 youth soccer players, 32 said that their favorite position to play is goalkeeper. Find the standard error for the sample proportion of soccer players whose favorite position is goalkeeper.

Answer 1

0.0737

Explanation:

Given that

people surveyed = n = 47

Number of players who said that their favorite position to play is goalkeeper=32

p = Sample proportion of players that their favorite position to play is goalkeeper=
`(32)/(47) =0.6809`

q = Player who did not say that their favorite position to play is goalkeeper=1-p = 0.3191

Sample proportion is following normal distribution with mean =
`p \\SE =\sqrt{(pq)/(n) } \\`

Std error of sample proportion=
`\sqrt{(0.3191(0.6809))/(47) } \\=0.0737`