Question

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 population having type A blood? Carry out a test of appropriate hypotheses using a significance level of 0.01. Would your conclusion have been different if a significance level of 0.05 has been used?

Answer 1

Answer:

We  reject H₀   Porcentage of type A blood  donations differs from 40% (porcentage of population having type A blood)

Step-by-step explanation:

We are going to develop a proportion test.

Information we have:

Proportion   P₀   =  40 %      P₀   =  0,4  (porcentage of population having type A blood)

Sample size    n   =   150

Sample  mean   P  =  82/ 150      P  = 0,5466

As  P₀  =   0,4      Q₀  =  0,6     P₀*Q₀   =  0,24

1.-Test Hypothesis:

H₀    null hypothesis                            P₀   =   0.4

Hₐ   alternative hypothesis                 P₀   ≠   0.4

2.- signficance level

     a  )   α  =  0.01    we have a two tail-test      α/2    =   0.005  

     b  )   α  =  0.05                                               α/2    =   0.025

Then  from t-student table we get t(c)   n  = 150    df =  149

     a  )   α/2    =   0.005             t(c)    =  2.581

     b  )   α/2    =   0.025             t(c)    =  1.962

3.-Compute t(s)

t(s)   =   (  P  -  P₀ )  / √P₀Q₀/n  

Plugging  in known values  

t(s)   =[ ( 0.5466 -  0,4  )*√150 ] / √0.24

t(s)   = 0,1466 * 12.25 / 0.4899

t(s)   =  3.6657

Compare t(s)  and  t(c)

t(s)  >  t(c)       3.6657  >  2.581      

Then  t(s) is out of the acceptance region  we reject  H₀.

Simple inspection led us see that for

α/2    =   0.025             t(c)    =  1.962

The situation is the same