Question

Researchers at a hospital lab are studying the relationship between blood type and a type of surgical procedure. Typically, they hypothesize that distribution of blood type of people undergoing surgery should be similar to that of the population it serves. The distribution of the population that the hospital services is: 44% type O, 45% Type A, 8% Type B and 3% Type AB. They have blood type data on 187 patients who underwent the surgery at that hospital as follows:

Blood Type	number of patients
O	67
A	83
B	29
AB	8

Is their hypothesis correct? Use α =0.05.

Answer 1

(1) The Hypothesis

H0: The population is distributed as follows O = 44%, A = 45%, B = 8% and AB = 3%

Ha: The distribution differs from that stated in the null hypothesis.

(2) The Test Statistic:

Each Expected value = (% / 100) * N. N = 187

	Observed	Expected %	Expected	(O-E)2	(O-E)2/E
O	67	44	82.28	233.4784	2.838
A	83	45	84.15	1.3225	0.000
Brown	29	8	14.96	197.1216	13.000
AB	8	3	5.61	5.7121	1.000
Total	187.00	100.00	187.00		16.838

Test = 16.84

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(3) The Critical value at = 0.05, df = n – 1 = 3, critical = 7.82

(4) The p value Foe Test = 1.84, for df = n – 1 = 3, p value = 0.001

(4) The Decision Rule: If test is > critical, then Reject H0.

If p value is < , Then Reject H0.

(5) The Decision:    Since test (16.84) is > critical (7.82), We Reject H0.

Since p value (0.001) is < (0.05), We Reject H0.

(6) The Conclusion: There is sufficient evidence at the 95% significance level to conclude that the blood type of people undergoing surgery is different from the population that the hospital services.