SOLUTION: 35 out of 80 male candidates and 25 out of 60 female candidates who took a recruitment examination were successful. Test at 5% level of significance that the proportion of males wh

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Question 985205: 35 out of 80 male candidates and 25 out of 60 female candidates who took a recruitment examination were successful. Test at 5% level of significance that the proportion of males who were successful in the examination exceeded that of the females.
Answer by stanbon(75887) About Me  (Show Source):
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35 out of 80 male candidates and 25 out of 60 female candidates who took a recruitment examination were successful. Test at 5% level of significance that the proportion of males who were successful in the examination exceeded that of the females.
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Ho: pm - pf <= 0
Ha: pm - pf > 0 (claim)
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sample diff:: (35/80)-(25/60) = 1/48
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test stat:: z(1/48) = (1/48-0)/sqrt[(35/80)(45/80)/80 + (25/60)(35/60)/60]
= (1/48)/sqrt[0.0031+0.0041]
= 0.246
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Conclusion:: Since the test stat is less than 1.96, fail
to reject Ho.
Conclusion:: the test results do NOT support the claim.
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Cheers,
Stan H.
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