Question

Recent 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. The Associated Press (San Luis Obispo TelegramTribune, September 13,1995 ) reported that \(71 \%\) supported the \(10-2\) verdict. Suppose that the sample size for this survey was \(n=900\). Compute and interpret a \(99 \%\) confidence interval for the proportion of Californians who favor the \(10-2\) verdict.

Short answer

The 99% confidence interval for the proportion of Californians who favor a 10-2 verdict in criminal cases not involving the death penalty is \(CI = 0.71 ± (2.576 * SE)\), where SE is the standard error calculated from steps above. To get the exact interval, calculate the value of \(SE\) from step 2 and substitute it into the equation.

Step-by-step solution

Calculation of sample proportion

First, we need to calculate the sample proportion (\(p\)). This can be done by dividing the number of favourable responses by the total sample size. Given that the number of favourable responses is \(71\%\) of \(900\), we get \(p = 0.71\)

Calculate the standard error

We now compute the standard error of the sample proportion, using the formula \(SE = \sqrt{p(1-p) / n}\). Plugging in our values, we get \(SE = \sqrt{0.71 * 0.29 / 900}\)

Calculate the confidence interval

The next step is to compute the 99% confidence interval. To do this, we need the z-score for our 99% confidence level, which is 2.576. The confidence interval for a proportion is calculated using the formula: \(CI = p ± (z*SE)\). Therefore we get: \(CI = 0.71 ± (2.576 * SE)\)