8. Let X and Y be the means of two independent random samples, each of size n, from respective distributions N (14,02) and N (1,0), where the common variance is known. Find the value of n such that PX-Y- - < M < X + | = 0.90. 5 5 9. Two companies can supply a raw material. The concentration of a particular element in this material is important. The mean concentration for both suppliers is the same, but we suspect the variability in concentration may differ between the two companies. The standard deviation of concentration in a random sample of n = 10 batches produced by company 1 is s = 4.7 grams per liter, while for company 2, a random sample of n = 16 batches yields s = 5.8 grams per liter. Find a 95% confidence interval for the ratio of the two population variances. Provide an interpretation of the interval.