Question

A company manufactures car tyres. Their average life is 40,000 km and standard deviations 5,000 km. A change in the production process is believed to result in a better product. A test sample of 100 new tyres has mean life of 41,000 km. Can you conclude at 1% L.O.S. that the new product gives better result?

Answer 1

Given: µ = 40,000, σ = 5,000, n = 100, x̄ =41,000, α = 1% .
H₀ : Mean lif eof tyres is 40,000 kms (i.e., µ = 40,000)
H₁ : Mean life of tyres is mroe than 40,000 kms (better result) (i.e., µ > 40,000) {upper tail test)

Under H₀ the test statistics is:

At α = 1% the lower tail critical value k = 2.33
Here z_cal lies in acceptance region (A.R) H₀ is accepted
∴ H_o is accepted.
Conclusion: Mean life of tyres is 40,000 kms.