Question

The Chi-square test is often used to test if different ratios are the same, for example to see if a trait is controlled by one or many genes. Here we would like you to see if there the ratio is equal to the 3:1 ratio which would mean the trait is controlled by a single gene, for the gene shrunken2 which makes corn sweet. 4. Class Expected Frequency Round 290 300 Shrunken2 110 100 a. What is the null hypothesis? b. What is the alternative hypothesis? C. What is the p-value? d. Is this trait controlled by a single gene?

Answer 1

Solution:

Part a

The null hypothesis is given as below:

Null hypothesis: H₀: Ratio is equal to 3:1. (Trait is controlled by a single gene.)

Part b

The alternative hypothesis is given as below:

Alternative hypothesis: H_a: Ratio is not equal to 3:1. (Trait is not controlled by a single gene.)

Part c

Here, we have to use Chi square test for goodness of fit.

We assume 5% level of significance for this test. (? = 0.05)

Total number of categories = n = 2

Degrees of freedom = n – 1 = 2 – 1 = 1

Test statistic formula is given as below:

Chi square = ?[(O – E)^2/E]

Where O is observed frequencies and E is expected frequencies.

Calculation table is given as below:

Class	O	E	(O - E)^2	(O - E)^2/E
Round	290	300	100	0.333333333
Shrunken2	110	100	100	1
Total				1.333333333

Chi square = ?[(O – E)^2/E] = 1.333333333

DF = 1

P-value = 0.248213251

(By using Chi square table/Excel)

Part d

Here, P-value > ? = 0.05, so we do not reject the null hypothesis that Trait is controlled by a single gene.

There is sufficient evidence to conclude that trait is controlled by a single gene.