Question:

Part (a):

An automotive expert claims that the large number of self-serve petrol stations has resulted in poor car maintenance, and that the average lyre pressure is at least 28 kilopascals below its manufacturers 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

Is there sufficient evidence, at a significance level of 5%, to support the expert's claim? State any assumptions that need to be made.

Part (b):

In the 2000 federal election, a candidate received 58% of the ballots cast. Four months later, a survey of 700 people revealed that 54% now supported the candidate. Is this sufficient evidence, at a significance level of 5%, to allow us to conclude that the candidate's popularity has decreased? State any assumptions that need to be made.