Suppose we randomly sample 400 nucleotides from the human genome. (Consider only a single strand.) Does the occurrence of adenine, thiamine, cytosine and guanine (A, C, T and G) in this sample suggest that nucleotides in the human genome follow a uniform distribution?
Use a χ2 test with a significance level of α=0.01 to test the following hypotheses:
- H0:pA=pC=pT=pG=0.25. (pAis the proportion of adenine in the human genome.)
- HA:At least one ofpA,pC,pT,pGis not0.25.
The data obtained was:
|
A
|
C
|
T
|
G
|
|
Count
|
90
|
110
|
85
|
115
|
(a) Calculate the value of the appropriate test statistic.
(b) State the critical value for this test, and your statistical decision. Are your results valid?
Note: Even if A, C, T and G follow a uniform distribution in the human genome that does not mean that nucleotides occur randomly! Even with a uniform distribution, certain patterns can (and do) occur.