6 It has been suggested that people who suffer anxiety when they are about to undergo surgery can have their anxiety reduced by listening to relaxation tapes. A study was carried out on 18 experimental subjects who listened to relaxation tapes, and 13 control subjects who listened to neutral tapes. After listening to the tapes, the subjects were given a test which produced an anxiety score, \(X\). Higher scores indicated higher anxiety. The results are summarised in the table.

1. Use a two-sample \(t\)-test, at the \(5 \%\) significance level, to test whether anxiety is reduced by listening to relaxation tapes. State two necessary assumptions for the validity of your test.
2. State why a test using a normal distribution would not have been appropriate.