Question

Consider a random sample of size n from a continuous distribution with a median of 0, where the probability of any one observation being positive is 0.5. Disregarding the signs of the observations, rank them from smallest to largest in absolute value, and let

W₅ be the sum of the ranks of the observations with positive signs.
A) True
B) False

Answer 1

The sum of the ranks for positive observations in this random sample will be equal to half the total number of observations.

Step-by-step explanation:

According to the given information, the random sample has a median of 0 and a probability of 0.5 for any observation being positive. We need to rank the sample from smallest to largest in absolute value and calculate the sum of the ranks for positive observations (W₅). Since the probability of positive observations is 0.5, we can expect half of the sample to be positive and half to be negative. Therefore, the sum of the ranks for positive observations (W₅) will be equal to half the total number of observations (n/2). A) True.