For Exercises 11–14, test whether or not the variables are independent.

  1. State the hypotheses.
  2. Verify that the conditions for performing the test for independence are met.
  3. Find and state the rejection rule.
  4. Calculate .
  5. Compare with . State the conclusion and the interpretation.

Question 11.46

11. Exercise 5, level of significance

11.2.11

(a) : Variable and Variable are independent. : Variable and Variable are dependent.

(b)

A1 A2 Total
B1 11 19 30
B2 11 19 30
Total 22 38 60

Since none of the expected frequencies is less than 1 and none of the expected frequencies is less than 5, the conditions for performing the test for independence are met. (c) 3.841. Reject if . (d) 0.2871 (e) Since is not , we do not reject . There is insufficient evidence that variable and variable are dependent.