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. P0 ( Home team win) = 0.5

as per question we have to find probability that home team would win 65% or more of its games in a simple random sample of 80 games that mean home team have to win minimum 52 game

so P ( Homw team win game >= 52; 80; 0.5) = Binomidist (X >=52; 80; 0.5) = 0.00484

we can calculate it by normal aprroximation of binomial

where mean = np = 80 * 0.5 = 40 and

Standard Deviation () = sqrt ( np( 1- p) ) = sqrt ( 80 * 0.5 * 0.5) = 4.47

Z - value = ( 52 - 40 ) / 4.47 = 2.6845

so NormP (X >=52; 40; 4.47) = 1 - 0.9963 = 0.0037 ( approximate to the above bionomial result)

b. Null Hypothesis : Ho : phome Game win = 0.5

Alternative Hypothesis H1 : phome game win > 0.5

The given sample imformation P - value is less than the usual significance levels of 0.05 and 0.01. The given statistic is stastically significant and we can reject the null Hypothesis here

So, the given stastics tell us that given sample information does provide strong evidence that the home team wins more than half of its games in the long run.

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