Question

2. (a) [5 points] Suppose that we take a random sample of size 12 from a population x for which X is normally distributed with mean m= 17 and the variance is unknown, but with sample variance s = 49. What is the distribution of 2(x - 17), ""?? Justify each part of your answer as well as you can. (b) [5 points) Suppose that we take a random sample of size 36 from a population x with mean w 17 and unknown variance, but the sample variance si-49. What is the distribution of OX-17) ? Justify each part of your answer as well as you can.

Answer 1

for query in above comment

(a Assume txan(m, or o urknown. 3. Jr (-m) ~NCO, 99 ka) (-m) ~NCO, 6%) ? N(o, óa). tere n = 36 70 30) is quite lange, no that we can apply ent. - Jo (Fam) a NCOM) Again for large , as sh in consistent for on we're Vacaqm) Vacancy Joe aam) Suloy Sole-my-$36(4-172 = (x-17) & 4 (8-17) is asymptotically UNCO.).