Question

A sample of 400 students is found to have a mean height of 171.38 cms can it be regarded as a sample from a large population with mean height 171.17 cms and S.D 3.30 cms?

Answer 1

Sample size n = 400 

Sample mean \(\overline{x}\) = 171.38 cm 

Population mean µ = 171.17 cm 

Population SD σ = 3.30 cm

H₀ : µ = 171.17 cm 

H₁ : µ ≠ 171.17 cm

Test statistic:

The table value of Z_α/2 at a 5% level is 1.96. Since Z < Z_α/2, H₀ is accepted. Therefore the given sample can be regarded as one from the population with mean 171.17 cm.