Question

Suppose that a particular candidate for public office is in fact favored by 48% of all registered voters in the district. A polling organization will take a random sample of 300 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

Answer :

given data :-

random sample = 300

n = 300

P^ = 0.5

fact favored by of all registered voters in the district = 48%

p = 48/100

p = 0.48

P(p^ > 0.5)

now we need to find out the approximate probability that p̂ will be greater than 0.5, causing the polling organization to incorrectly predict the result of the upcoming election

we know that

Z = (p^ - p)/(sqrt(p(1-p)/n)

= (0.5-0.48)/sqrt(0.48*(1-0.48))300

= 0.02/sqrt(0.48*0.52)300

= 0.02/sqrt(0.249/300

= 0.02/sqrt0.000832

= 0.02/0.0288

z = 0.694

from the z normal table

P(Z>0.694) = 0.2451