Question

Suppose we hypothesize that x exponential(8) and aim to test this hypothesis by choosing an acceptance region x>c for some constant c. What does this acceptance region imply?

A) X is greater than a specific constant c with a probability of 8%.
B) X is less than a specific constant c with a probability of 8%.
C) X follows an exponential distribution with a mean of 8.
D) X is greater than a specific constant c with a probability of 92%.

Answer 1

The acceptance region x>c for the hypothesis x exponential(8) implies that X is greater than a specific constant c with a probability of 8%.

Step-by-step explanation:

The acceptance region x>c for the hypothesis x exponential(8) implies that X is greater than a specific constant c with a probability of 8%.

To understand this, let's consider an example. Suppose we choose c=10. If X is greater than 10, it falls within the acceptance region and supports the hypothesis. The probability of X being greater than 10 is 8% for the exponential(8) distribution.

Therefore, the correct answer is A) X is greater than a specific constant c with a probability of 8%.