Human blood is grouped into four types: A, B, AB, and 0. The percent of American

ID: 3230140 • Letter: H

Question

Human blood is grouped into four types: A, B, AB, and 0.

The percent of Americans with each type are as follows:

O – 43%

A - 40%

B - 12%

AB – 5%

A recent blood drive found the individuals that donated blood were classified into each of the four categories. Test (using a 5-step hypothesis test) to determine if the proportions of blood types are different from those stated above using = 0.05. Remember, if you reject the null, you need to describe how the distribution is different. INCLUDE A TABLE OF YOUR OBSERVED AND EXPECTED VALUES REMEMBER, that your expected values are a function of (a) sample size and (b) your GIVEN (above) percentages)

Observed Frequencies:

O - 60

A - 65

B - 15

AB - 10

Explanation / Answer

Solution:

Here, we have to use chi square test.

Null hypothesis: H0: Proportions of blood types are not different from stated proportions.

Alternative hypothesis: Ha: Proportions of blood types are different from stated proportions.

The test statistic formula is given as below:

Chi square = [(O – E)^2/E]

Where, O = expected frequencies and E is expected frequencies

The calculation table is given as below:

Group

Percentage

(O - E)

(O - E)^2/E

43%

64.5

-4.5

0.31

40%

0.42

12%

-3

0.50

7.5

2.5

0.83

Total

150

100%

150

2.06

Chi square = [(O – E)^2/E] = 2.06

We are given

Level of significance = = 0.05

Degrees of freedom = n – 1 = 4 – 1 = 3

Chi square critical value = 7.814728

P-value = 0.560047

P-value > = 0.05

So, we do not reject the null hypothesis that Proportions of blood types are not different from stated proportions.