Question

A study of 938 decision (to grant parole or not) made by a parole board produced the provided computer output. Assuming these cases are representative of all cases that may come before the board, what can be concluded?

z-Interval for proportion With 99.00 confidence, 0.54498422

A. We are 99% confident that the proportion of paroles granted by the board in the sample is between 54.5% and 59.6%.


B. The probability that any given parole request will be granted by the board is between 54.5% and 59.6%.


C. There is a 99% probability that any given parole request will be granted by the board.


D. We are 99% confident that the proportion of paroles granted by the board is between 54.5% and 59.6%.

Answer 1

The correct answer is: option D). We are 99% confident that the proportion of paroles granted by the board is between 54.5% and 59.6%.

Step-by-step explanation:

The correct conclusion from the computer output indicating a 99% confidence interval for the proportion of parole decisions is option D.

It states that we are 99% confident that the true proportion of paroles granted by the board for all cases is between 54.5% and 59.6%. This interval is derived from the sample provided and is used to estimate the true parameter of the entire population of parole decisions.

It is important to note that this does not mean that there is a 99% probability of any given parole request being granted. Rather, it indicates our confidence level in the interval estimate for the proportion of grants as a characteristic of the population, not the determinacy of individual outcomes.