An automotive expert claims that the conversion of petrol stations to self-serve petrol stations has resulted in poor car maintenance, and that the average tyre pressure is at least 28 kilopascals below its manufacturer's specification. As a quick test, 10 tyres are examined, and the number of kilopascals by which each tyre is below specification is recorded. The resulting data (in kilopascals) are as follows:

48

62

14

0

34

41

21

34

55

62

(a) Is there sufficient evidence, with a = 0.05, to support the expert's claim?

(b) Did you use any assumption in answering (a)? Investigate the validity of that assumption.

What formulas would need to be used?