Trendy Tyres Ltd. has introduced a new brand of tyres, which in their
advertisements claim to be superior to their only competitor brand, the
Roadmaster Tyres. The brand manager of Roadmaster Tyres disputes this claim
which he says is an advertisement gimmick. The brand manager of the two
companies agree to run a road test for the brands. Ten (10) saloon cars of
uniform weight and identical specifications are to be used for the test. Each car is
fitted with both brands of tyres: One brand at the front and the other brand at the
rear. The cars cover a distance of 5,000 kilometres and the trend wear is recorded
as follows:
Trendy tyres Roadmaster tyres
Centimetres Centimetres
1 1.08 1.12
2 1.06 1.09
3 1.24 1.16
4 1.20 1.24
5 1.17 1.23
6 1.21 1.25
7 1.18 1.20
8 1.10 1.15
9 1.22 1.19
10 1.60 1.13
Required:
(i) Determine whether Trendy Tyres Ltd.’s claim is true using
α
= 0.01. (18
marks)
(ii) What are the assumptions you have made in (i) above? (2
mark