Question

High-profile legal cases have many people reevaluating the jury system. Many believe that juries in criminal trials should be able to convict on less than a unanimous vote. To assess support for this idea, investigators asked each individual in a random sample of Californians whether they favored allowing conviction by a 10–2 verdict in criminal cases not involving the death penalty. A newspaper article reported that 79% supported the 10–2 verdict. Suppose that the sample size for this survey was

n = 900.

Compute a 99% confidence interval for the proportion of Californians who favor the 10–2 verdict.

(, )

We are 99% confident that the proportion of all people who favor the 10–2 verdict is within this interval.We are confident that the proportion of all people who favor the 10–2 verdict is within this interval at least 99% of the time.    We are confident that 99% of the proportion of Californians who favor the 10–2 verdict is within this interval.We are 99% confident that the proportion of Californians who favor the 10–2 verdict is within this interval.Interpret the interval.

Answer 1

sample size          n=		900
sample proportion p̂ =x/n=		0.7900
std error se= √(p*(1-p)/n) =		0.0136
for 99 % CI value of z=		2.576
margin of error E=z*std error   =		0.0350
lower bound=p̂ -E                       =		0.7550
Upper bound=p̂ +E                     =		0.8250
from above 99% confidence interval for population proportion =(0.755,0.825)

We are 99% confident that the proportion of Californians who favor the 10–2 verdict is within this interval.Interpret the interval.