Search for question

16 teams each, for a total of 64 teams (not counting the somewhat recently added play-in

games). Within each bracket, teams are "seeded" from 1 to 16, with the number-1 seed being

the team judged to be the strongest in a bracket, and the 16-seed being the weakest team.

The winners of each of the four brackets go on to meet in the tournament semi-final (the "final

four"). There have been 37 tournaments since 1985 (2020 was cancelled due to COVID-19),

for a total of 37(4) = 148 number-1 seeds. Of these, 60 have advanced to the final-four.

a) Let p represent the true probability that a randomly chosen number-1 seed will advance

to the final-four, and assume that different number-1 seeds advance or don't advance

independently (even within the same tournament, the four number-1 seeds play in inde-

pendent brackets). Let the random variable X represent the number of number-1 seeds

out of 148 that advance to the final four. What is the distribution of X? For what

values of p would the distribution of p = X/148 be approximately Normal?

b) Find a 95% confidence interval for p from part a, based on the observed outcome x = 60.

Compute both using the "large sample" margin of error and the "conservative" margin

of error.