Question

In a random sample of 400 registered voters, 120 indicate they plan to vote for Candidate A. Determine a 95% confidence interval for the proportion of all registered voters who will vote for candidate A. The lower limit of the confidence interval is

Answer 1

95% confidence interval for the proportion of all registered voters who will vote for candidate

(0.255 ,0.344)

The lower limit of the confidence interval is 0.255

Explanation:

Explanation:-

Step1:-

Given data In a random sample of 400 registered voters, 120 indicate they plan to vote for Candidate.

n =400

The proportion of success
`p = (120)/(400)`

on calculation 'p' = 0.3

q =1-p

q = 1- 0.3 =0.7

Step2:-

95% confidence interval for the proportion of all registered voters who will vote for candidate

`(p - z_(\alpha ) \sqrt{(pq)/(n) } , p+z_(\alpha ) \sqrt{(pq)/(n) } )`

we use z- value =1.96 at 95% level of significance.

`(0.3 - 1.96\sqrt{((0.3)(0.7))/(400) } , 0.3+1.96\sqrt{(0.3(0.7))/(400) } )`

on calculation , we get

(0.3 - 0.044 ,0.3+0.044)

(0.255 ,0.344)

conclusion:-95% confidence interval for the proportion of all registered voters who will vote for candidate

(0.255 ,0.344)

The lower limit of the confidence interval is 0.255