Question

A drug company developed a honey-based liquid medicine designed to calm a child's cough at night. To test the drug, 105 children who were ill with an upper respiratory tract infection were randomly selected to participate in a clinical trial. The children were randomly divided into three groups - one group was given a dosage of the honey drug, the second was given a dosage of liquid DM (an over-the-counter cough medicine), and the third (control group) received a liquid placebo (no dosage at all). After administering the medicine to their coughing child, parents rated their children's cough diagnosis as either better or worse. The results are shown in the table below:

Treatment Better Worse Total Control 4 33 37 DM 12 21 33 Honey 24 11 35 Total 40 65 105

In order to determine whether the treatment group is independent of the coughing diagnosis, a two-way chi-square test was conducted.

1. State the alternative and the null hypothesis.

2. Calculate test statistic

3. Determine the chi square critical value.

4.Write the decision rule

5. Decision and Conclusion

Answer 1

We wish to test cle Ho: Treatment group and laughing diagnosis's Hii Teeatment group and coughing diagnose's independent sis ue dependent We have Bettet Worse Total Control 4 33 31 DM 12 21 33 11 35 #Honey 24 Totull 40 65 los Expected Valle (Ei) Rixci N Bettee losse Total! 65*3] - 22.9 37 105 control. 40x37 :14-10 105 Dr 40 x 38 = 12.57 105 65x33 105 20.43 33 35 40x35 = 18.33 10$ Honey Total 65*35-21.67 los 65 40 Squse distance (Oi-E.J2 Ei Better (4-14.10) Control -7.235 14.10 Woese 183-22.9012 --4.455 22.9 [21-20.43)? =0.016 20.43 (12-12.875, 0.026 DM 12.57 2011 –21.679?- 5.154 124-13-3331 = 8:541 13.33 21.67 Honry 7.235+0.026+8.541 +4:455 +0.016+5.254=25.527 Test istatistic X5 I 6000 25-837 (tistical Valce: 230.05. 72 = Xian (furcu) • X1.005,12-1/237) - X 35,2 = 5.99). Decision: Since be X27X2 We Erject Ho at stj.os We con conclude theat Tertment group and Coughing dugnasis oze dependent 25.927> 5.991

PER Console > Chisgeachigg(0.95,2) [1] 5.991465