Question

Consider the problem regarding the genetics of crossing two types of peas. The Mendelian theory states that the probabilities of the classifications (a) round and yellow, (b) wrinkled and yellow, (c) round and green, and (d) wrinkled and green are 9=16 ; 3=16; 3=16; and 1=16, respectively. Suppose that from 160 independent observations, the observed frequencies of these respective classifications are 85; 35; 27 and 13. Test at the 1% level of significance if these data are consistent with the Mendelian theory and choose the incorrect option from the following statements.

1. x² =2:31

2. The critical region is ( x² > 11:3 )

3. The null hypothesis is not rejected.

4. The test supports the Mendelian theory.

5. The chi–square test is appropriate in this test.

Answer 1

none of the option is incorrect.

here the null hypothesis H0: observed frequency=expected frequency ( follow mendelian theory) and

alternate hypothesis H1: observed frequency expected frequency ( donot follow mendelian theroy)

here we use chi-square test and =sum((O-E)²/E)=2.31 with k-1=4-1=3 df

critical chi-square(0.01, 3)=11.3 is more than calculated chi-square=2.31, so we fail to reject null hypothesis. so test supports the mendelian theroy.

all the 5 options are true, so none of the option is incorrect.

following information has been generated for answering above question

classification	Observed(O)	expected ratio	Expected(E)	(O-E)	(O-E)2/E
a	85	9/16	90	-5	0.28
b	35	3/16	30	5	0.83
c	27	3/16	30	-3	0.30
d	13	1/16	10	3	0.90
total	160	0	160	0	2.31