Question

Which of the following interpretations of a Chi-square test is CORRECT? (you may use the table below as reference).

a. Assume that a Chi-square test was conducted to test the goodness of fit to a 3:1 ratio and that a Chi-square value of 2.62 was obtained. The null hypothesis should be accepted.

b. With the test of a 3:1 ratio, there are two degrees of freedom.

c. The larger the Chi-square value, the more likely your results are real.

d. Assume that a Chi-square statistic corresponds to a p-value of 0.075. The null hypothesis should be rejected.

e. Assume that a Chi-square test was conducted to test the goodness of fit to a 9:3:3:1 ratio and a Chi-square value of 10.62 was obtained. The null hypothesis should be accepted.

Answer 1

Chi square test is conducted to determine the relation between expected and observed values.

Answer: A)Assume that a Chi-square test was conducted to test the goodness of fit to a 3:1 ratio and that a Chi-square value of 2.62 was obtained. The null hypothesis should be accepted.

Explanation: This is true because on comparison with the goodness of fit table with degree of freedom=1 ( 3:1, 2 trait -1=1), the p value got was nearly 0.10. Thus null hypothesis can be accepted as 0.5 or below is considered as rejection of null hypothesis.

B) With the test of a 3:1 ratio, there is one degree of freedom.

Explanation: As 3:1 has two trait, degree of freedom= 2-1=1.

C) The larger the Chi-square value, the more likely your results are different.

Explanation: Higher chi square value means the p-value is low and thus the difference is more.

D) Assume that a Chi-square statistic corresponds to a p-value of 0.075. The null hypothesis should be accepted.

Explanation: As the p- value is more than 0.05 i.e. they have more than 5% relation, then the difference is less and the rejection of null hypothesis weakens.

E) Assume that a Chi-square test was conducted to test the goodness of fit to a 9:3:3:1 ratio and a Chi-square value of 10.62 was obtained. The null hypothesis should be rejected.

Explanation: The 9:3:3:1 ratio has 3 as degree of freedom and when comparing it gives p value near 0.01. Thus null hypothesis should be rejected.