Regression analysis, Module 1, “Statistical models”
(The attached PDF file has better formatting.)
Homework assignment: probabilities
Fox uses the data in Table 1.1 on page 5 to infer that judges grant leave at different rates.
A. If all judges grant leave in 25% of cases, and the differences among judges are random fluctuations, what is the probability a judge (Desjardins) grants leave in 49% or more of cases?
B. If all judges grant leave in 25% of cases, and the differences among judges are random fluctuations, what is the probability that a judge (Pratte) grants leave in 9% or fewer of cases?
Write an algebraic expression for the solution. You need not compute a numerical solution.
Note: Judge Desjardins heard 47 cases and granted leave in 49% × 47 = 23 cases.
Write the expression for 23 successes in 47 cases with a probability of 25%.
This is a binomial probability with ð = 25%.
Write the summation for 23 through 47 successes. You need not evaluate the sum.
The sum goes from 23 successes to 47 successes.
Judge Pratte heard 57 cases and granted leave in 9% × 57 = 5 cases.
Write the expression for 5 successes in 57 cases with a probability of 25%.
Write the summation for 0 through 5 successes. You need not evaluate the sum.
The sum goes from 0 successes to 5 successes.
Note: The PMF of the binomial distribution is
where n is the number of trials and p is the probability of success on each trial.
You do not have to compute any figures for this homework assignment.