Consider the question of whether the home team wins more than half of its games

Question

Consider the question of whether the home team wins more than half of its games in the National Basketball Association. Suppose that you study a simple random sample of 80 professional basketball games and find that 52 of them are won by the home team.

a. Assuming that there is no home court advantage and that the home team therefore wins 50% of its games in the long run, determine the probability that the home team would win 65% or more of its games in a simple random sample of 80 games.

b. Does the sample information (that 52 of a random sample of 80 games are won by the home team) provide strong evidence that the home team wins more than half of its games in the long run? Explain.

Explanation / Answer

a) Z=(X-mean)/standard dev
compute Z=(.65-.50)/sqrt[.50(1-.50)/80]
=2.68,
[Where mean=0.5 and standard dev= sqrt (p*(1-p)/n)[p is the probability of success]]
which from the normal table... 0.9963

bans) yes beacuse due to probability is nearly equal to 1 and the standard devauation mean is half of it

b)

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