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 11.48

13. Exercise 9, level of significance

11.2.13

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

(b)

I1 I2 I3 Total
J1 99.2788 93.6058 102.1154 295
J2 55.5288 52.3558 57.1154 165
J3 20.1923 19.0385 20.7692 60
Total 174.9999 165.0001 180 520

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) 13.277. Reject if . (d) 4.000 (e) Since is not , we do not reject . There is insufficient evidence that variable and variable are dependent.