Question

Examine the sample obtained from a normally distributed population.

5.6	10.5	5.4	2.5	4.2	15.5	10.5
8.8	2.7	4.1	4.8	13.1	15.3	14.8

Calculate the probability that a randomly chosen sample would produce a sample variance at least as large as that produced in part a (23.3) if the population variance was equal to 21.

USE EXCEL PLEASE!!!

Answer 1

Let indicate the sample variance.

We want to know the probability that a sample of size n=14, taken from this population, would have sample variance of atleast 23.3. That is

We know that the sample variance has a ch-square distribution with statisics

where is the population variance and with a degrres of freedom (n-1)

We can write the required probability as