Question

Large Sample Proportion Problem.  Surveys were conducted in multiple countries and respondents were asked if they felt political news was reported fairly. The data for the United States is that out of 1,000 sampled, 470 indicated yes, they felt political news was reported fairly. Suppose we want to determine if the proportion for the U.S. is below .50.

What is the standard error for this hypothesis test?

SQRT((.47*.53)/1000

.4991/SQRT(1,000)

SQRT((.5*.5)/1000)

Cannot be determined from the information given.

Answer 1

Solution :

Given that,

n = 1000

x = 470

Point estimate = sample proportion = $\hat p$ = x / n = 470 / 1000 = 0.47

1 - $\hat p$ = 1 - 0.47 = 0.53

$\sigma$_{$\hat p$} =  $\sqrt$[p( 1 - p ) / n] = $\sqrt$ [(0.47 * 0.53) / 1000 ] = 0.0158

correct option is = $\sqrt$ [(0.47 * 0.53) / 1000 ]