1 A community baseball league claims that it fairly divided

1. A community baseball league claims that it fairly divided players between two teams. One of the coaches wished to test this claim by having the teams play 40 games against each other. Of the games, Team A won 25 of them. For the test conducted, the hypotheses are: H0: p = 0.5 and HA: p 0.5. At a level of significance of 0.02, what is the conclusion of this test? If the league actually hasn\'t divided the teams fairly, what type of error is committed here?

Please show steps, that\'s what I\'m most interested in.

Solution

Ho: p=0.5 (i.e. null hypothesis)

Ha: p not equal to 0.5 (i.e. alternative hypothesis)

The test statistic is

Z=(phat-p)/sqrt(p*(1-p)/n)

=(25/40-0.5)/sqrt(0.5*0.5/40)

=1.58

It is a two-tailed test.

Given a=0.02, the critical values are Z(0.01) =-2.33 or 2.33 (from standard normal table)

The rejection regions are if Z<-2.33 or Z>2.33, we reject the null hypothesis.

Since Z=1.58 is between -2.33 and 2.33, we do not reject the null hypothesis.

So we can not conclude that it fairly divided players between two teams.

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Type II error: We do not reject the nulll hypothesis when it is false.