Question

Q1: Match the statement to the correct choice. Number of degrees of freedom in the​ chi-squared test of independence in a 4 x 2 table. ​

(a) 0 ​(b) 3 ​(c) 7 ​(d) 8

Q2:

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.

The​ chi-squared test of independence only detects linear association between variables in a contingency table.

A: The statement is true.

B: The statement is false because the test also detects any nonlinear associations between the variables.

C: The statement is false because the test detects any dependence between the​ variables, not linear associations.

D: The statement is false because the test determines if two proportions are​ equal, not if there is a linear association between the variables.

Q3:

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 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.

C: 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.

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 more dependent.

Q4:

Mark the statement below as True or False. If you believe that the statement is​ false, briefly explain why you think it is false.

The sum of the fitted value y^ plus the residual e is equal to the original data value y.

Answer 1

Q1:

Degree of freedom = (r-1) * (c - 1) = (4-1) * (2 - 1) = 3

(b) 3 ​

Q2:

It is a false statement.

C: The statement is false because the test detects any dependence between the​ variables, not linear associations.

Q3:

It is a false statement.

Small​ p-values of the​ chi-squared test of independence indicate that the data have large amounts of 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 more dependent.

Q4:

It is a true statement.  

The sum of the fitted value y^ plus the residual e is equal to the original data value y.