A car manufacturer claims that the front tyres on a particular model of car have an average life span of 20000 miles. Following comments from customers, the sales manager wishes to test if the hife span of the tyres is greater than 20000 miles.
(a) Explain why the sales manager should carry out a 1-tail test. State hypotheses for the test, defining any symbols you use.
The sales manager contacts customers and gathers details about the life spans of a random sample of 50 of these tyres. The life spans, $x$ thousand miles, are summarised below.
$\Sigma(x-20)=9.4 \quad \Sigma(x-20)^2=38.76$
(b) Calculate unbiased estimates of the population mean and variance of the life spans of the tyres.
(c) Test, at the $5 \%$ level of significance, whether the mean life span of front tyres is more than 20000 miles.
(d) Explain why this test would be inappropriate if the sales manager had taken a random sample of 15 tyres.