The town of hayward (ca) has about 50,000 registered voters. a political research firm takes a simple random sample of 500 of these voters. in the sample, the breakdown by party affiliation is 115 republicans, 331 democrats, and 54 independents. calculate a 98% confidence interval for the true percentage of independents among haywards 50,000 registered vote.

(0.0757;0.1403)

Step-by-step explanation:

1) Data given and notation

Republicans =115

Democrats=331

Independents=54

Total= n= 115+331+54=500

Confidence=0.98=98%

2) Formula to use

The population proportion have the following distribution

The confidence interval for the population proportion is given by this formula

We have the proportion of independents calculated

We can calculate

And we can find , with this value we can find the critical value using the normal distribution table, excel or a calculator.

On this case

3) Calculating the interval

And now we can calculate the interval:

So the 98% confidence interval for this case would be:

(0.0757;0.1403)