Question

Recidivism occurs when a person continues to commit criminal behavior even after having been punished. A prison official wants to estimate the proportion of cases of recidivism. Examining the records of 250 convicts, the official determines that there are 65 cases of recidivism. Construct a 99% confidence interval for the proportion of cases of recidivism.A. (0.331, 0.567)B. (0.188, 0.332)D. (0.289, 0.431)E. (0.069, 0.111)

Answer 1

Option (C) [0.2574 , 0.2626]

Explanation:

Of 250 convicts, there are 65 cases of recidivism.

- Construct a 99% confidence interval for the proportion of cases of recidivism.

This calls for first finding the proportion of cases of recidivism. This will be 65/250 = 0.26

You are 100% confident that the proportion of cases of recidivism is 0.26

You will be 99% confident that the recidivism cases are between:

99% of 0.26 = 0.2574

1% of 0.26 = 0.0026

[0.26 - 0.0026] , [0.26 + 0.0026] = [0.2574 , 0.2626]

This should be OPTION C, as that option is missing in the list of options.