Question

Suppose that a particular candidate for public office is in fact favored by 49% of all registered voters in the district. A polling organization will take a random sample of 750 voters and will use p̂, the sample proportion, to estimate p. What is the approximate probability that p̂ will be greater than 0.5, causing the polling organization to incorrectly predict the result of the upcoming election? (Round your answer to four decimal places.)

Answer 1

Solution

Given that,

p = 0.49

1 - p = 1 - 0.49 = 0.51

n = 750

= p = 0.49

=  [p( 1 - p ) / n] = [(0.49 * 0.51) / 750 ] = 0.0183

P( > 0.5) = 1 - P( < 0.5 )

= 1 - P(( - ) / < (0.5 - 0.49) / 0.0183)

= 1 - P(z < 0.55)

Using z table

= 1 - 0.7088

= 0.2912