A prison official wants to estimate the proportion of cases of recidivism. Examining the records of...

A prison official wants to estimate the proportion of cases of recidivism. Examining the records of 236 convicts, the official determines that there are 78 cases of recidivism. Find the lower limit of the 80% confidence interval estimate for the population proportion of cases of recidivism. (Round to 3 decimal places.

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Expert Solution

Solution :

Given that,

Point estimate = sample proportion = = x / n = 78 / 236 = 0.331

1 - = 1 - 0.331 = 0.669

Z/2 = 1.28

Margin of error = E = Z / 2 * $\sqrt$ (( * (1 - )) / n)

= 1.28 * ( $\sqrt$ ((0.331 * 0.669) / 236)

Margin of error = E = 0.039

A 80% confidence interval for population proportion p is ,

- E < p < + E

0.331 - 0.039 < p < 0.331 + 0.039

0.292 < p < 0.370

The 80% confidence interval for the population proportion p is : 0.292 , 0.370

orchestra answered 2 years ago

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