Question

In state A, 19% of the people drink coffee. In state B, 27% of the people drink coffee.

We take a random sample of 50 from state A, and 60 from state B, and find the sample proportions spA and spB (spA is the sample proportion of those who drink coffee from state A, which in the notation of the textbook would be    )

What is the standard deviation of spA? (write it as a decimal fraction, not a percentage; provide three decimal places)

Answer 1

Solution

Given that,

sample proportion = = 0.19 ( spA )

= 1 - = 1 - 0.19 = 0.81

sample proportion = = 0.27 ( spB )

n = 50 ( spA )

n = 60 ( spB )

=  [( 1 - ) / n] = [(0.19 * 0.81) / 50 ] = 0.055 ( spA )