Answer:
0.5867 is the lower bound for the proportion of voters who favor the proposal.
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 40
Number of voters who support the proposal, x = 29
[tex]\hat{p} = \dfrac{x}{n} = \dfrac{29}{40} = 0.725[/tex]
95% Confidence interval:
[tex]\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.05} = 1.96[/tex]
Putting the values, we get:
[tex]0.725\pm 1.96(\sqrt{\dfrac{0.725(1-0.725)}{40}})\\\\ = 0.725\pm 0.1383\\\\=(0.5867,0.8633)[/tex]
0.5867 is the lower bound for the proportion of voters who favor the proposal.
