Question

9. Consider the mean of a random sample of size 75, X. If S2 is the sample variance and the population is normally distributed with mean y, what is the distribution of 10. The mean weight of peanuts in a sample of size 16 from a barrel is 0.09 ounces. The standard deviation of the sample is 0.015 ounces. What is a 90% confidence interval for the mean weight of all peanuts in the barrel? Assume peanut weights in the barrel are normally distributed.

Answer 1

DOMS Page No. Date x . Nel, o os we know, Ecx) = oy, m = 75 F = x + x xm Sassuming iid 3 ETD xm* £x) - Ecx = 0 varc = mar (Exi) HG 5 using central limit theorem, for distribution of t X ~ (H, s onxn (M.2 - this shows. distribution is normally distributed of x which

DOMS Page No. Date n = 16 4-o.og o=0.015 Given peanuts are normally distributed Tet x,,82 a. xn are n beatuts weignt which are iid. mean weight = x = Exi ECK = f cx = 0.09. Marca = varcx) soc) -- SDCx) - oois 0.015 - 0.003757 X ~ N(0.09 0.00375) confidence inter real- x + za -0.09 7 zxo.00375 = 0.09 ± 1.645x0.00375 o.og ± 0.00616 8 75 {o.08 3 8 3125, 0.096 168753 1