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

Answer:

The confidence interval is -5.3444 to 6.453 .

Step-by-step 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

$\widehat{p}=\frac{x}{n}$

$\widehat{p}=\frac{254}{458}$

$\widehat{p}=0.5545$

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 : $\widehat{p}-x\times \sqrt{\frac{\widehat{p} \times (1-\widehat{p})}{n}$ to $\widehat{p}+x\times \sqrt{\frac{\widehat{p} \times (1-\widehat{p})}{n}$

Confidence interval : $0.5545-254\times \sqrt{\frac{0.5545\times (1-0.5545)}{458}}$ to $0.5545+254\times \sqrt{\frac{0.5545\times (1-0.5545)}{458}}$

Confidence interval : $-5.3444$ to $6.453$

Hence The confidence interval is -5.3444 to 6.453 .

Answer 2

Answer:

Step-by-step 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