Question

In a random sample of 400 registered voters, 144 indicated they plan to vote for Candidate A.

Determine a 95% confidence interval for the proportion of all the registered voters who will vote for Candidate A.

Value from the appropriate table=   

Margin of error=  

Lower limit of C.I.=   

Upper limit of C.I.=  

Answer 1

n = 400

= proportion of registered voters who vote A

= 144/400

= 0.36

Margin of error = critical value SE

SE = [(1- )/n]^1/2  

= [0.36(1 - 0.36)/400]^1/2  

= 0.024

Margin of error = 1.96 0.024

= 0.04704

95% confidence interval is given by

+/- 1.96 [(1- )/n]^1/2  

0.36 +/- 1.96(0.024)

0.36 +/- 0.04704

0.36 - 0.04704, 0.36 + 0.04704

0.31296 , 0.40704

confidence interval is  [0.31296 , 0.40704 ]

lower limit = 0.31296

upper limit = 0.40704