Question: Equation 7.5 states that \(\frac{\left( N-1 \right){{s}^{2}}}{{{\sigma }^{2}}}\) is distributed as a Chi-Square variable if each score in the sample is randomly drawn from an independently and normally distributed population of scores.

(a) Suppose we draw many samples of size N from a normally distributed population. We calculate the ratio \(\frac{\left( N-1 \right){{s}^{2}}}{{{\sigma }^{2}}}\) for each sample. If N = 6,

(i) What is the probability that the ratio is less than 9.236?

(ii) What is the probability that ratio lies between 1.145 and 6.626?

(b) The population sampled in part (a) has a variance of 10, in what proportion of samples will s² be less than 8.703?