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Playing Giddy Up - Go: Standard Deviation of Proportion

APSTAT-GC1RSE

Giddy Up - Go is a hot new game app that can be downloaded on smartphones. Researchers wanted to know what proportion of smartphone users have downloaded the app. They believe that the actual proportion is $0.10$ and have decided to investigate.

After surveying a random sample of $225$ smartphone users, the researchers determined that $27$ had downloaded the app.

In constructing a confidence interval, which of the following shows how to calculate the standard deviation of the sample proportion?

A

$\sqrt { \cfrac { (0.10)(0.90) }{ 225 } } $

B

$\sqrt { \cfrac { (0.12)(0.88) }{ 225 } } $

C

$\cfrac { (0.10)(0.90) }{ \sqrt { 225 } } $

D

$\sqrt { (225)(0.10)(0.90) } $

E

$\sqrt { (225)(0.12)(0.88) } $