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 72% 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.

(________,________)

Interpret the interval.

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

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = 72% = 0.72

1 - = 1 - 0.72 = 0.28

n = 900

At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z _0.005 = 2.576

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 2.576 (((0.72 * 0.28) / 900 )

= 0.039

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.72 - 0.039 < p < 0.72 + 0.039

(0.681 < p < 0.759)

( 0.681, 0.759 )

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