1 Two groups of patients, suffering from the same medical condition, took part in a clinical trial of a new drug. One of the groups was given the drug whilst the other group was given a placebo, a drug that has no physical effect on their medical condition.
The table shows the number of patients in each group and whether or not their condition improved.
| \cline { 2 - 3 }
\multicolumn{1}{c|}{} | Placebo | Drug |
| Condition improved | 20 | 46 |
| Condition did not improve | 55 | 29 |
Conduct a \(\chi ^ { 2 }\) test, at the \(5 \%\) level of significance, to determine whether the condition of the patients at the conclusion of the trial is associated with the treatment that they were given.
(10 marks)