Question

Determine if the following statement is true or false. If you believe that the statement is​ false, briefly explain why you think it is false.

Small​ p-values of the​ chi-squared test of independence indicate that the data have small amounts of dependence.

(a) The statement is true

(b) The statement is false because when the​ p-value of the​ chi-squared test of independence is​ small, the results indicate that the two variables are more dependent.

(c) The statement is false because whether the​ p-value of the​ chi-squared test of independence is small or​ large, it does not indicate whether the data have any dependence.

(d) The statement is false because when the​ p-value of the​ chi-squared test of independence is​ small, the results indicate that the two variables are completely independent.

Answer 1

We know the small p-values corresponds to rejecting the null hypothesis. here the null hypothesis is that the there no dependence in the variables or we can say that the variables are independent.

Here the statement is p-values of the​ chi-squared test of independence indicate that the data have small amounts of dependence. Thus the statement is false as lesser tehn p-value, more is the dependence between the variables. Hence the answer is:

(b) The statement is false because when the​ p-value of the​ chi-squared test of independence is​ small, the results indicate that the two variables are more dependent.