Question

Acompany developed a honey based liquid medicine designed to calm achats cough at night. To test the drug. 105 children who wore it with an upper respiratory tract infection were randomly selected to medicine), and the third control group) received aliquid placebo ho dosage). After administering the medicine to their coughing child, petrated their children's cough diagnosis as either better or worse. The results we shown in the table below Diagnosis Treatment Better Wome Total Control 4 33 DM 12 21 33 Honey 24 11 35 Total 305 In order to determine whether the treatment group is independent of the coughing diagnosis a two way che test was conducted Calculate the value of the test statistic for the desired wysis OY.972 OX-2551 Ox? - 1579

Answer 1

Test statistic: x² I (0-E) E Where, O =Observed counts. E = Expected counts The formula for calculating the expected counts is, Row total x column total E Grand total The below table describes the computation of chi square test statistic:

Control Observed Expected O-E (O - EP/E DM Observed Expected O-E (0 - E)/E Honary Observed Expected O-E (0-E) /E Total Observed Expected O-E (0 - E)/E Better 4 14.10 -10.10 7.23 12 12.57 -0.57 0.03 24 13.33 10.67 8.53 40 40.00 0.00 15.79 Worse 33 22.90 10.10 4.45 21 20.43 0.57 0.02 11 21.67 -10.67 5.25 65 65.00 0.00 9.72 Total 37 37.00 0.00 11.68 33 33.00 0.00 0.04 35 35.00 0.00 13.78 105 105.00 0.00 25.51 Therefore, the chi-square test statistic is x = 25.51 The correct answer is option (3)