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

`\hat p \pm Z*\sqrt{(\hat p*(1-\hat p))/(n) }`

`=0.5546\pm1.96*\sqrt{(0.5546*(1-0.5546))/(458) }`

`=0.5546\pm1.96*\sqrt{(0.5546*(0.4454))/(458) }`

`=0.5546\pm1.96*\sqrt{(0.2470)/(458) }`

`=0.5546\pm1.96*√(0.00053934)`

`=(0.5091,0.6001)`

Lower limit for confidence interval=0.5091

Upper limit for confidence interval=0.6001

Explanation:

We have given,

x=254

n=458

Estimate for sample proportion=
`\bar p = 0.5546`

Level of significance is =1-0.95=0.05

Z critical value(using Z table)=1.96

Confidence interval formula is

`\hat p \pm Z*\sqrt{(\hat p*(1-\hat p))/(n) }`

`=0.5546\pm1.96*\sqrt{(0.5546*(1-0.5546))/(458) }`

`=0.5546\pm1.96*\sqrt{(0.5546*(0.4454))/(458) }`

`=0.5546\pm1.96*\sqrt{(0.2470)/(458) }`

`=0.5546\pm1.96*√(0.00053934)`

`=(0.5091,0.6001)`

Lower limit for confidence interval=0.5091

Upper limit for confidence interval=0.6001