In some countries, people believe that blood type has a strong impact on personality. For example, Type B blood is thought to be associated with passion and creativity. A statistics student at a large U. S. university decides to test this theory. Reasoning that people involved in the arts should be passionate and creative, she takes a simple random sample of students majoring or minoring in arts at her university and asks them for their blood type. Here are her results: Observed number of performing arts majors with each blood type
Type A Type B Type AB Type 0 Total
50 23 10 67 150
Assume the distribution of blood type among all U. S. residents is as follows:
Type A: 42%; Type B: 10%; Type AB: 4%; Type O: 44%.
(a) The student wants to carry out a test of significance to see if the distribution of blood types among arts majors or minors is different from the U. S. distribution. State the null and alternative hypotheses for this test.
(b) Find the expected counts for each blood type under the assumption that the null hypothesis is true.
(c) Discuss whether the conditions for this test have been met.
(d) Find the value of the test statistic and the P-value of the test, and make the appropriate conclusion. Use α = 0.05.
(e) Based on your answer to (d), which error is it possible that you have made, Type I or Type II? Describe that error in the context of the problem.