Question

​If, based on a sample size of 850​, a political candidate finds that 471 people would vote for him in a​ two-person race.

a. A 90% confidence interval for his expected proportion of the vote is ____ , ____

b. Would he be confident of winning based on this​ poll?

Answer 1

Solution :

Given that,

n = 850

x = 471

Point estimate = sample proportion = = x / n = 471/850=0.554

1 - = 1-0.554=0.446

At

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645}

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.645(((0.554-0.0.446) /850 )

= 0.028

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.554-0.028 < p <0.554+0.028

0.526<p<0.582

(b)

Standard normal deviate for α = Z_α = 1.645

Proportion of positive results = P = x/N = 0.554

Lower bound = P - (Z_α*SEM) = 0.526

Upper bound = P + (Z_α*SEM) = 0.582