Question

Rubber rabbitbrush plants display heritable variation in plant height and insect-induced gall formation. In a field study, researchers investigated the relationship between plant height and gall number for the rubber rabbitbrush plants in a natural population. The researchers used the data they collected to perform a chi-square test of independence. The null hypothesis for the chi-square test was that plant height and gall number are independent. The data for the chi-square test are presented in Table 1.

Table 1. Data for the chi-square test of independence

Height Category (cm)(cm)	Number of Plants with Ten or Fewer Galls	Number of Plants with More than Ten Galls
0–30	34	6
31–60	22	16
61–90	14	21
91–120	10	27

The researchers calculated a chi-square value of 29.25. If there are three degrees of freedom and the significance level is p=0.05p=0.05, which of the following statements best completes the chi-square test?

• The critical value is 0.05, and the null hypothesis cannot be rejected because the calculated chi-square value is greater than the critical value.

  A

• The critical value is 0.05, and the null hypothesis can be rejected because the calculated chi-square value is greater than the critical value.

  B

• The critical value is 7.82, and the null hypothesis cannot be rejected because the calculated chi-square value is greater than the critical value.

  C

• The critical value is 7.82, and the null hypothesis can be rejected because the calculated chi-square value is greater than the critical value.

Answer 1

Right answer is C.

Calculated chi square value is 29.25.

The degree of freedom is 3. The significant level is 0.05

The chi square value from table at degree of freedom =3 and at p=0.05 is 7.815

As our chi square experimental value is more than chi square value from table. That's why null hypothesis is rejected.