Question

An automatic machine fills tea in sealed tins with a mean weight of tea as 1 kg and S.D 1 gram. A random sample of 50 tins was examined and it was found that their mean weight was 999.5 grams. Is the machine working properly?

Answer 1

Given 

Sample size n = 50

Sample mean \(\overline{x}\) = 999.5 grams 

Population mean µ = 1000 grams 

Population SD σ = 1 gram 

H₀ : µ = 1 kg 

H₁ : µ ≠ 1 kg 

Test statistic : 

Z = (999.5 - 1000)/(1/√50) = -3.54

The table value of Z_α/2  at 1% level = 2.58. Since |Z| > , Z_α/2 H₀ is rejected. Therefore the machine is not working properly.