Question

A pollster plans to survey a random sample of voters in a certain city to ask whether they support an increase in property taxes to fund the construction of a new elementary school. A preliminary poll of 40 voters finds that 29 of them support the proposal. (a) Find a 95% confidence lower bound for the proportion of voters who favor the proposal.

Answer 1

0.5867 is the lower bound for the proportion of voters who favor the proposal.

Explanation:

We are given the following in the question:

Sample size, n = 40

Number of voters who support the proposal, x = 29

`\hat{p} = (x)/(n) = (29)/(40) = 0.725`

95% Confidence interval:

`\hat{p}\pm z_(stat)\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}`

`z_(critical)\text{ at}~\alpha_(0.05) = 1.96`

Putting the values, we get:

`0.725\pm 1.96(\sqrt{(0.725(1-0.725))/(40)})\\\\ = 0.725\pm 0.1383\\\\=(0.5867,0.8633)`

0.5867 is the lower bound for the proportion of voters who favor the proposal.