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:

$\hat p \pm Z*\sqrt{\frac{\hat p\times(1-\hat p)}{n} }$

$=0.5546\pm1.96*\sqrt{\frac{0.5546\times(1-0.5546)}{458} }$

$=0.5546\pm1.96*\sqrt{\frac{0.5546\times(0.4454)}{458} }$

$=0.5546\pm1.96*\sqrt{\frac{0.2470}{458} }$

$=0.5546\pm1.96*\sqrt{0.00053934}$

$=(0.5091,0.6001)$

Lower limit for confidence interval=0.5091

             

Upper limit for confidence interval=0.6001

Step-by-step 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

$\hat p \pm Z*\sqrt{\frac{\hat p\times(1-\hat p)}{n} }$

$=0.5546\pm1.96*\sqrt{\frac{0.5546\times(1-0.5546)}{458} }$

$=0.5546\pm1.96*\sqrt{\frac{0.5546\times(0.4454)}{458} }$

$=0.5546\pm1.96*\sqrt{\frac{0.2470}{458} }$

$=0.5546\pm1.96*\sqrt{0.00053934}$

$=(0.5091,0.6001)$

Lower limit for confidence interval=0.5091

             

Upper limit for confidence interval=0.6001