Question

President

u

d

d

u

u

d

a

a

d

u

d

d

Table above shows 12 students took a survey for for President Obama election decision

letters means the following  

"A" = Approve
"D" = Disapprove
"U" = Undecided

1. Is it reasonable to assume that the 12 people that responded are a representative sample of all adults aged 21 or more years living in the United States at that time? Clearly, but briefly, state why or why not.

2. Regardless of your answer to part c), assume that the 12 people that responded are a representative sample of all adults aged 21 or more years living in the United States at that time. Give and interpret a 95% confidence interval for President Obama’s approval rating for this population on that date, 1/16/15.

Answer 1

a) No, it is not reasonable to assume that the 12 people that responded are a representative sample of all adults aged 21 or more years living in the United States at that time.

The sample size is too small to represent the whole population. The sample size must be at least 30 .

b)

n = 12, x = 2, p̅ = x/n = 0.1667

95% Confidence interval :

At α = 0.05, two tailed critical value, z_c = NORM.S.INV(0.05/2) = 1.960

Lower Bound = p̄ - z_c*√( p̄ *(1- p̄ )/n) = 0.1667 - 1.96 *√(0.1667*0.8333/12) = -0.04 = 0

Upper Bound = p̄ + z_c*√( p̄ *(1- p̄ )/n) = 0.1667 + 1.96 *√(0.1667*0.8333/12) = 0.38