A random sample of (150) recent donations at a certain bloodbank reveals that (8

Question

A random sample of (150) recent donations at a certain bloodbank reveals that (82) were type a blood.

Does this suggest that the actual percentage of type a donationdifference from 40% the percentage of the population having type ablood?

Carry out a test of the appropriate using a significance levelof (0.1).

Would your conclusion have been different if a significancelevel of (0.05) had been used?

Explanation / Answer

n=150 phat=82/150 =0.55 =0.1, Z(0.05)=1.645 (check normal table) =0.05, Z(0.025)=1.96 (check normal table) The test hypothesis is Ho:p=0.4 Ha:p not equal 0.4 The test statistic is Z=(phat - p)/p*(1-p)/n =(0.55-0.4)/sqrt(0.4*0.6/150) = 3.75 Since Z=3.75 > 1.645, we reject Ho. Thus, this suggests that theactual percentage of type a donation difference from 40% thepercentage of the population having type a blood. Since Z=3.75 > 1.96, we reject Ho. Thus, there has been nodifferent if a significance level of (0.05) had been used.

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