Question

Let 𝑋1,𝑋2,...,𝑋𝑛 be a random sample from a normal distribution with known

mean 𝜇. Using a distribution of 𝑈=∑ (𝑋𝑖−𝜇)2

𝜎2

𝑛𝑖=1 , Mr Mbalula showed that a

100(1−𝛼)% two sided confidence interval for 𝜎2 is give by

[∑ (𝑋𝑖 −𝜇)2𝑛𝑖=1

𝜒𝛼

2,𝑛

2 ;∑ (𝑋𝑖 −𝜇)2𝑛𝑖=1

𝜒1−𝛼

2,𝑛

2 ].

Prove whether or not Mr Mbalula is correct.