Question

A manufacturer of tyres claims that average life is more than 15000 kms under normal condition. A random sample of 15 tyres was tested and mean and S.D. was found to be 18000 kms and 4000 kms respectively. Test whether the manufacturer’s claim is justified.

Answer 1

Given: μ= 15000 kms, nj = 15, X̄ = 18000, s = 4000, α = 1%

H₀ : Average life of tyres is 15000 kms (i.e. H₀ : μ = 15000)

H₁ : Average life of tyres is more than 15000 kms

(H₁ : μ >15000) {Right/upper tail test)

The t-test statistic is ( Here n < 30 use t -test for mean)

At α = 1 % for (n – 1) = (15 ) = 14 d.f. the upper tail critical value k = 2.62

Here t_>cal > k/t_cal is in rejection region.

∴ H₀ is rejected and H₁ is accepted.

Conclusion : Average life of tyres is more than 15000 kms.