Question

A city is holding a referendum on increasing property taxes to pay for a new high school. In a survey of 458 likely voters, 254 said that they would vote "yes" on the referendum. Create a 95% confidence interval for the proportion of likely voters who will vote "yes" on the referendum. Use Excel to create the confidence interval, rounding to four decimal places.

Answer 1

The confidence interval is -5.3444 to 6.453 .

Explanation:

We are given that In a survey of 458 likely voters, 254 said that they would vote "yes" on the referendum.

So, n = 458

x = 254

We will use sample proportion over here

`\widehat{p}=(x)/(n)`

`\widehat{p}=(254)/(458)`

`\widehat{p}=0.5545`

Confidence level = 95% = 0.95

Level of significance = 1-0.95 = 0.05

z value at 0.05 significance level = 1.96

Formula of confidence interval :
`\widehat{p}-x* \sqrt{\frac{\widehat{p} * (1-\widehat{p})}{n}` to
`\widehat{p}+x* \sqrt{\frac{\widehat{p} * (1-\widehat{p})}{n}`

Confidence interval :
`0.5545-254* \sqrt{(0.5545* (1-0.5545))/(458)}` to
`0.5545+254* \sqrt{(0.5545* (1-0.5545))/(458)}`

Confidence interval :
`-5.3444` to
`6.453`

Hence The confidence interval is -5.3444 to 6.453 .

Answer 2

Explanation:

We have given,

x=254

n=458

Estimate for sample proportion

Level of significance is =1-0.95=0.05

Z critical value(using Z table)=1.96

Confidence interval formula is

=(0.5091,0.6001)

Lower limit for confidence interval=0.5091

Upper limit for confidence interval=0.6001