A Drug Company Developed a Honey-Based Liquid Medicine Designed to Calm

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:
$\begin{array}{l}\begin{array}{lccc}&\text { Diagnosis }\\\text { Treatment } & \text { Better } & \text { Worse } & \text { Total } \\\text { Control } & 4 & 33 & 37 \\\text { DM } & 12 & 21 & 33 \\\text { Honey } & 24 & 11 & 35 \\\text { Total } & 40 & 65 & 105\end{array}\end{array}$

In order to determine whether the treatment group is independent of the coughing diagnosis, a two-way chi-square test was conducted. Use the chi-square distribution to determine the rejection region for this test when testing at $\alpha = 0.025$ .

A) Reject $\mathrm { H } _ { 0 }$ if $\chi ^ { 2 } > 5.99147$
B) Reject $\mathrm { H } _ { 0 }$ if $\chi ^ { 2 } > 7.81473$
C) Reject $\mathrm { H } _ { 0 }$ if $\chi ^ { 2 } > 7.37776$
D) Reject $\mathrm { H } _ { 0 }$ if $\chi ^ { 2 } > 9.34840$