Question

Your blood belongs to one of four genetically determined types: O, A, B, or AB. A bulletin issued by a large blood bank claims that these four blood types are distributed in the U.S. population according to the following proportions: 0.44 are type O, 0.41 are type A, 0.10 are type B, and 0.05 are type AB. Let’s treat this claim as a null hypothesis to be test with a random sample of 100 students from a large university. The data collection results of each blood type from the university showed 38 for O and A, 20 for B, and 4 for AB.

A) What is the statistical hypothesis? (Ho and Ha)

B) Find an expected frequency for each expected proportion.

C) Solve for chi-square test statistic.

D) Find the degrees of freedom.

E) Identify the chi-square value from the table.

F) What is the conclusion?

Answer 1

a) As we are testing here whether four blood types are distributed in the U.S. population according to the following proportions: 0.44 are type O, 0.41 are type A, 0.10 are type B, and 0.05 are type AB, therefore the null and the alternative hypothesis here are given as:

H0: The four blood types are distributed in the U.S. population according to the following proportions: 0.44 are type O, 0.41 are type A, 0.10 are type B, and 0.05 are type AB

Ha: The four blood types are not distributed in the U.S. population according to the given set of proportions

b) Total Frequency = 38 + 38 + 20 + 4 = 100

The expected frequencies for each category here are computed as:
E(O) = 0.44*100 = 44
E(A) = 0.41*100 = 41
E(B) = 0.1*100 = 10
E(AB) = 0.05*100 = 5

These are the required expected frequencies here.

c) The chi square test statistic here is computed as:

Therefore 11.2377 is the required chi square test statistic here.

d) The degrees of freedom here is computed as:
df = number of categories - 1

= 3

Therefore 3 is the required number of degrees here.

e) For 0.05 level of significance, and 3 degrees of freedom, we get from the chi square distribution tables here as:

Therefore 7.82 is the chi square critical value here.

f) As the test statistic value here is 11.2377 > 7.82, therefore the test is not significant here and we cannot reject the null hypothesis here. Therefore we dont have sufficient evidence here to reject the null hypothesis that The four blood types are distributed in the U.S. population according to the following proportions: 0.44 are type O, 0.41 are type A, 0.10 are type B, and 0.05 are type AB