Question

A normal variate has standard deviation 2.6. Twenty sample observations of the variate have standard deviation 2. Test at 1% level of significance that population standard deviation is less than 2.6.

Answer 1

Given: σ₀ = 2.6, 

n = 20, S = 2, a=1%

H₀: σ₀ =2.6(Standard deviation is 2.6) 

H₁ : σ₀ < 2.6 (Standard deviation less than 2.6) {Lower tailed test}

Under H₀, the test statistic is :

= \(\frac{20 \times2^2}{(2.6)^2}\)

χ²_cal = 11.8343 

For (n- 1) = (20 – 1) = 19 d.f the lower tail critical value at 5% level of significance is K₁ – 10.12; 

Here χ²_cal > K₁ 

∴ H₀ is accepted. 

Conclusion: Standard deviation is 2.6.