For Exercises 15–18, test whether or not the variables are independent.

  1. State the hypotheses and the rejection rule for the p-value method, and verify that the conditions for performing the test for independence are met.
  2. Find .
  3. Calculate the p-value.
  4. Compare the p-value with . State the conclusion

Question 11.52

17. Exercise 10, level of significance

11.2.17

(a) : Variable and Variable are independent. : Variable and Variable are dependent. Reject if -value .

K1 K2 K3 K4 Total
L1 37.5 72.92 89.58 100 300
L2 23.75 46.18 56.74 63.33 190
L3 28.75 55.90 68.68 76.67 230
Total 90 175 215 240 720

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. (b) (c) -value (d) Since the -value is not , we do not reject . There is insufficient evidence that variable and variable are dependent.