The treadwear index provided on car tyres helps prospective buyers make their purchasing decisions by

The treadwear index provided on car tyres helps prospective buyers make their purchasing decisions byindicating a tyre's resistance to tread wear. A tyre with a treadwear grade of 200 should last twice as

indicating a tyre's resistance to tread wear. A tyre with a treadwear grade of 200 should last twice aslong, on average, as a tyre with a grade of 100. A consumer advocacy organisation wishes to test the

long, on average, as a tyre with a grade of 100. A consumer advocacy organisation wishes to test thevalidity of a popular branded tyre that claims a treadwear grade of 200. A random sample of 23 tyres

validity of a popular branded tyre that claims a treadwear grade of 200. A random sample of 23 tyresindicates a sample mean treadwear index of 192.8 and a sample standard deviation of 21.8.

indicates a sample mean treadwear index of 192.8 and a sample standard deviation of 21.8.

(a) Using 0.05 level of significance, is their evidence to conclude that the tyres are not meeting the

(a) Using 0.05 level of significance, is their evidence to conclude that the tyres are not meeting theexpectation of lasting twice as long as a tyre graded at 100? Show all your workings

expectation of lasting twice as long as a tyre graded at 100? Show all your workings

(b) What assumptions are made in order to conduct the hypothesis test in (a)?