The National Basketball Association had 47 black top executi

The National Basketball Association had 47 black top executives (presidents or vice presidents) among its 374 senior managers. Meanwhile Major League Baseball had only 14 blacks among its 302 top administrators. Test at the .01 significance level if this reveals the NBA has significantly more black participation in higher levels of management. Hint: For the calculations, assume the NBA as the first sample.

Compute the value of the test statistic. (Do not round the intermediate values. Round your answer to 3 decimal places.)

Test at the .01 significance level if this reveals the NBA has significantly more black participation in higher levels of management.

Solution

(1) Given a=0.01, the critical value is Z(0.01) = 2.33 (from standard normal table)

Reject H₀ if z >2.33

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(2)

p1=47/374 = 0.1256684

p2=14/302= 0.04635762

the test statistic:

Z=(p1-p2)/sqrt(p1*(1-p1)/n1+p2*(1-p2)/n2)

=(0.1256684-0.04635762)/sqrt(0.1256684*(1-0.1256684)/374+0.04635762*(1-0.04635762)/302)

=3.780

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(3)Reject the null.

The NBA has significantly more black participation.