B3.

A researcher is interested in the average age people first develop symptoms of a particular condition they are investigating. They record the ages of first developing symptoms from 30 random people (below) who have been involved in a recent large trial on managing the condition.

25, 19, 60, 76, 52, 42, 56, 99, 61, 42, 70, 23, 23, 19, 18, 54, 72, 18,

42, 33, 42, 19, 41, 24, 67, 70, 23, 21, 30, 22

1. Calculatea95%and99%confidenceintervalfortheaverageageoffirst developing symptoms. Carefully explain the two confidence intervals and why they differ. [8marks]
2. Previous well-established research shows that the average age of first developingsymptomswasaround30.Areyourfindingsconsistentwith this? [6 marks]
3. We are interested in independent and identically distributed (iid) random variables when sampling. What do you understand by an iid and do you think the survey data in this case is iid? [6marks]
4. Acolleaguehasaskedforasmaller confidenceinterval.Howmightthis be achieved? [5marks]