Statistics

QUESTION 3 (a) Let (Xil, ..., Xin) and (X21. ... X2;) be two independent random samples from n (; of) and a (2: ;) distributions, respectively. Show that a 100 (1 - a)% two-sided confidence interval for = is given by: Fa/2:01-1:03-1 (7) (b) Two chemical companies can supply a raw material. The concentration of a particular ele- ment in this material is important. The mean concentration for both suppliers is the same, but we suspect that the variability in concentration may differ between the two companies. The standard deviation of concentration in a random sample of m = 10 batches produced by company 1 is s1 = 4.7 grams per liter, while for company 2, a random sample of n2 = 16 batches yields s2 = 5.8 grams per liter. (i) Is there sufficient evidence to conclude that the two population variances differ? Test at the 5% level of significance. (10) (i) Determine a 95% confidence interval for and interpret the results. (B) (Clearly show how you compute the critical values.) [25]