Question

A random sample of 150 recent donations at a certain blood bank reveals that 73 were typa A blood. Does this suggest that the actual percentage of type A blood donations differs from 40% (the percentage of the population having type A blood)? Carry out a test of hypotheses showing the following steps:

a) write symbolically the null and alternative hypothesis that would be appropriate for this test.

b) if you are given a significance level of .05 state the rejection region that would be used.

c) use the data given above to calculate the value of the test statistic. show the setup of the formula used in this calculation

d) what decision should be made regarding the null hypothesis, and why?

Answer 1

a)

H0: p = 0.40

Ha: p 0.40

b)

z critical values at 0.05 level = -1.96 , 1.96

Rejection region = Reject H0 if z < -1.96 or z > 1.96

c)

Sample proportion = 73 / 150 = 0.4867

Test statistics

z = - p / sqrt( p ( 1 - p) / n)

= 0.4867 - 0.40 / sqrt( 0.40 * 0.60 / 150)

= 2.17

d)

Since test statistics falls in rejection region, we have sufficient evidence to reject H0.

We conclude at 0.05 level that we have enough evidence to support the claim.