Question

A random sample of 130 recent donations at a certain blood bank reveals that 48 were type A blood. Does this suggest that the actual percentage of Type A donations differs from 39%, the percentage of the population having Type A blood? [Answer the questions, where appropriate, using 4 digits after decimal.]

What are the appropriate hypotheses to test?

The test-statistic formula is:

Rejection region: We reject H₀ at 1% level of significance if:
z < −2.356.
z > 2.356.
|z| > 2.576.
z > 2.326.
|z| > 2.614.
z < −2.326.

What is the value of the test-statistic?

What is the p-value of the test?

For a significance level of 1%, the data would lead to
not rejection of the null hypothesis.
not enough information to reach a decision.
rejection of the null hypothesis.

Answer 1

H0:  p = 0.39

Ha:  p 0.39

Sample proportion = 48 / 130 = 0.3692

Test statistics

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

z critical value at 0.01 significance level = -2.576 , 2.576

Rejection rule = | z | > 2.576  

z = ( 0.3692 - 0.39) / sqr [ 0.39 ( 1 - 0.39) / 130]

= -0.49

p-value = 2 * P(Z < z)

= 2 * P(Z < -0.49)

= 2 * 0.3121

= 0.6242

Since p-value > 0.01 level,

The data would lead to not rejcetion of null hypothesis.