The University of California, Berkeley (Cal) and Stanford University are athleti

Question

The University of California, Berkeley (Cal) and Stanford University are athletic archrivals in the Pacific 10 conference. Stanford fans claim Stanford's basketball team is better than Cal's team; Cal fans challenge this assertion. In 2004, Stanford University's basketball team went nearly undefeated within the Pac 10. Stanford's record, and those of Cal and the other eight teams in the conference, are listed in In all, there were 89 games played among the Pac 10 teams in the season. Stanford won 17 of the 18 games it played; Cal won 9 of 18. We would like to use these data to test the Stanford fans' claim that Stanford's team is better than Cal's. That is, we would like to determine whether the difference between the two teams' performance reasonably could be attributed to chance, if the Stanford and Cal teams in fact have equal skill.

The sample percentage of games won by Stanford is .94

What is the Bootstrap estimate of the standard error of the sample percentage of games won by stanford?

Explanation / Answer

null hypothesis H0:  P1=P2

Alternative hypothesis H1:  P1 P2

Sample 1 =x1/n1 = 17/18= 0.9444

Sample 2 x2/n2 = 9/18= 0.5

pi= (17+9)/(18+18) = 0.7222

Variance= pi*(1-pi)*(1/n1+1/n2)

(0.722222)(0.277778)(1/18+1/18) =0.0222908

Standard error of (p1^-p2^) = 0.149301
z = (p1^-p2^) / sqrt[pi*(1-pi)*(1/n1+1/n2)]
Z = 0.444444 / 0.149301 = 2.976834

P-value = P( |Z| > 2.9768) = 2 * P( Z > 2.9768) = 0.0014*2 = 0.002

there is evidence of a difference in the proportion of games won by the two teams

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