Question

Test the hypothesis that a = 5, given that sample standard devrection is 8 for random sample of size 25 from a normal population use a = 0.05.

Answer 1

Given : σ = 5, n = 25, s = 8, α = 0.05

H₀ : σ = 5

H₁ : σ ≠ 5(Two tailed test)

Under H₀, the test statistic is : –

At α = 0.05 for (n – 1) = 25 = 1 

= 24 d.f the two tail critical values

are k₁ = 13.85 and k₂

Here χ²_cal = 64 lies in Rejection region (RR)

∴ H₀ is rejected and H₁ is accepted

conclusion : σ ≠ 5.