Question

It was found that a machine has produced pipes having a thickness 0.50 mm. To determine whether the machine is in proper working order a sample of 10 pipes is chosen for which the mean thickness is 0.53 mm and S.D. is 0.03 mm. Test the hypothesis that the machine is in proper working order using a level of significance of 0.01.

Answer 1

Given: n= 10, x̄ =0.53, 

μ = 0.50, S = 0.03, α = 0.01 = 1% 

H₀: The machine is in proper working order, 

i.e., H₀: µ = 0.50 

H₁ : The machine is not in proper working order. 

i.e., H₁ : µ ≠ 0.50 {two tailed test}

The test statistic is –

For (n-1) = (10 -1) = 9 d.f at 1% level of significance the two tail critical values are 

k₁ =-3.25 and k₂ = 3.25 

Here t_cal = 3 is in acceptance region. 

∴ H₀ is accepted. 

Conclusion : The machine is in proper working order.