A random sample of 150 recent donations at a certain blood b

A random sample of 150 recent donations at a certain blood bank reveals that 82 were type A blood. Does this suggest that the actual percentage of type A donations differs from 40%, the percentage of the population having type A blood? Carry out a test of the appropriate hypotheses using a significance level of .01. Would your conclusion have been different if a significance level of .05 had been used?

Solution

POPULATION PROPORTION Z TEST          
          
Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.4
Ha:   p   =/=   0.4
As we see, the hypothesized po =   0.4      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.546666667      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.04      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    3.666666667      
          
As this is a    2   tailed test, then, getting the p value,  
          
p =    0.000122866      

significance level =    0.01      

Comparing p and the significance value, we   REJECT THE NULL HYPOTHESIS.

There is significant evidence that the actual percentage of type A donations differs from 40%.      
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If alpha = 0.05 instead, it will still be the same. Whatever Ho gets rejected at 0.01 will be rejected at any higher alpha, like 0.05.