Question

Gallup conducted a survey from April 1 to 25, 2010, to determine the congressional vote preference of the American voters.15 They found that 51% of the male voters preferred a Republican candidate to a Democratic candidate in a sample of 5,490 registered voters. Gallup asks you, their statistical consultant, to tell them whether you could declare the Republican candidate as the likely winner of the votes coming from men if there was an election today. What is your advice

Answer 1

p ( x > 2746 ) = p ( z > - 1.4552 )

= 1 - 0.072806

= 0.9272

This shows that there is > 92% of a republican candidate winning the election hence I will advice Gallup to declare the Republican candidate winner

Explanation:

Given data:

51% of male voters preferred a Republican candidate

sample size = 5490

To win the vote one needs ≈ 2746 votes

In order to advice Gallup appropriately lets consider this as a binomial distribution

n = 5490

p = 0.51

q = 1 - 0.51 = 0.49

Hence
`n_(p)` > 5 while
`n_(q)` < 5

we will consider it as a normal distribution

From the question :

number of male voters who prefer republican candidate ( mean ) ( u )

= 0.51 * 5490 = 2799.9

std =
`√(npq)` =
`√(5490 * 0.51 *0.49)` = 37.0399 ---- ( 1 )

determine the Z-score = (x - u ) / std ---- ( 2 )

x = 2746 , u = 2799.9 , std = 37.0399

hence Z - score = - 1.4552

hence

p ( x > 2746 ) = p ( z > - 1.4552 )

= 1 - 0.072806

= 0.9272

This shows that there is > 92% of a republican candidate winning the election hence I will advice Gallup to declare the Republican candidate winner