A drug company developed a honey-based liquid medicine designed to calm a childʹs 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 childrenʹs cough diagnosis as either better or worse. The results are shown in the table below:

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

Question

A drug company developed a honey-based liquid medicine designed to calm a childʹs 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 childrenʹs cough diagnosis as either better or worse. The results are shown in the table below:

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

Quizplus · Accepted Answer

The Answer of A drug company developed a honey-based liquid medicine designed to calm a childʹs 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 childrenʹs cough diagnosis as either better or worse. The results are shown in the table below:

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

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