Question 4

The treadwear index provided on car tyres helps prospective buyers make their purchasing decisions by indicating a tyre’s resistance to tread wear. A tyre with a treadwear grade of 200 should last twice as long, on average, as a tyre with a grade of 100. A consumer advocacy organisation wishes to test the validity of a popular branded tyre that claims a treadwear grade of 200. A random sample of 19 tyres indicates a sample mean treadwear index of 190.4 and a sample standard deviation of 20.3.  

(a) Using 0.05 level of significance, is there evidence to conclude that the tyres are not meeting the expectation of lasting at least 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)?