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 voters.

(0.076, 0.140)

Step-by-step explanation:

Confidence interval for population proportion (p) is given by :-

, where = sample proportion.

n= sample size.

= significance level .

= critical z-value (Two tailed)

As per given , we have

sample size : n= 500

The number of Independents.:  x= 54

Sample proportion of Independents

Significance level 98% confidence level :

By using z-table , Critical value :

The 98% confidence interval for the true percentage of Independents among Haywards 50,000 registered voters will be :-

Hence, the 98% confidence interval for the true percentage of Independents among Haywards 50,000 registered voters.= (0.076, 0.140)