Subjects in a test were given a new drug or a placebo, and then their reactions (headache or no headache)were recorded. The results are given in the table below.
$\begin{array}{r|rr}
& \text { Drug } & \text { Placebo } \
\hline \text { Headaches } & 19 & 7 \
\text { No headaches } & 73 & 95
\end{array}$

A) $\mathrm { H } _ { 0 }$ : The drug and the occurrence of headaches are independent.
$\mathrm { H } _ { \mathrm { a } }$ : There is a relationship between the drug and the occurrence of headaches.
B) $\mathrm { H } _ { 0 }$ : The drug and the occurrence of headaches are independent.
$\mathrm { H } _ { \mathrm { a } }$ : There is no relationship between the drug and the occurrence of headaches.
C) $\mathrm { H } _ { 0 }$ : There is a relationship between the drug and the occurrence of headaches.
$\mathrm { H } _ { \mathrm { a } }$ : The drug and the occurrence of headaches are not independent.
D) $\mathrm { H } _ { 0 }$ : There is a relationship between the drug and the occurrence of headaches.
$\mathrm { H } _ { \mathrm { a } }$ : The drug and the occurrence of headaches are independent.

Question

Subjects in a test were given a new drug or a placebo, and then their reactions (headache or no headache)were recorded. The results are given in the table below.
 $\begin{array}{r|rr} 
& \text { Drug } & \text { Placebo } \
\hline \text { Headaches } & 19 & 7 \
\text { No headaches } & 73 & 95
\end{array}$

A) $\mathrm { H } _ { 0 }$ : The drug and the occurrence of headaches are independent.
$\mathrm { H } _ { \mathrm { a } }$ : There is a relationship between the drug and the occurrence of headaches.
B) $\mathrm { H } _ { 0 }$ : The drug and the occurrence of headaches are independent.
$\mathrm { H } _ { \mathrm { a } }$ : There is no relationship between the drug and the occurrence of headaches.
C) $\mathrm { H } _ { 0 }$ : There is a relationship between the drug and the occurrence of headaches.
$\mathrm { H } _ { \mathrm { a } }$ : The drug and the occurrence of headaches are not independent.
D) $\mathrm { H } _ { 0 }$ : There is a relationship between the drug and the occurrence of headaches.
$\mathrm { H } _ { \mathrm { a } }$ : The drug and the occurrence of headaches are independent.

Quizplus · Accepted Answer

In hypothesis testing, the null hypothesis ($H_0$) typically represents the default or no-effect hypothesis, which in this context would be that the drug and the occurrence of headaches are independent. The alternative hypothesis ($H_a$) represents the hypothesis that there is some effect or relationship, in this case, that there is a relationship between the drug and the occurrence of headaches.

Subjects in a Test Were Given a New Drug or a Placebo