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Exercises · Q12

Q.State, with a reason, whether each of the following calls for a one-tailed or a two-tailed test:

(a) a tyre company wants to test whether a new tyre's average life is DIFFERENT FROM the currently advertised 40,000 km;
(b) the same company wants to test whether the new tyre's average life is GREATER THAN 40,000 km (an improvement claim).
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(a) The claim to be tested is whether the average life is different from 40,000 km - this allows for either an increase OR a decrease being of interest, so H1:μ≠40,000H_1: \mu \neq 40{,}000, and the critical region is split across both tails of the distribution. This is a two-tailed test. …

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