Question

Candidate A is facing two opposing candidates in a mayoral election. In a recent poll of 300 residents, 98 supported candidate B and 58 supported candidate C. Construct a 95% confidence interval on the population proportion for the support of candidate A in the following election.

[0.4781, 0.4819]

[0.3942, 0.5658]

[0.4235, 0.5365]

[0.4057, 0.5543]

Answer 1

We have given,              
              
x=Candidate supported to A=300-98-58=144          
n=300          
Estimate for sample proportion=   0.48  
Level of significance is =0.05      
Z critical value(using Z table)=1.96      
              
Confidence interval formula is              
$\hat{p}\pm Z*\sqrt{\frac{\hat{p}*(1-\hat{p})}{n}}$
$=0.48\pm 1.96*\sqrt{\frac{0.48*(1-0.48)}{300}}$
=(0.4235,0.5365)
              
Lower limit for confidence interval=0.4235  
              
Upper limit for confidence interval=0.5365