(a) From lectures we know (b) Let n Σ(-)² ~ x²(v). What is the value of ? i=1 = n 1 120 1 i=1 n- -Σ(X; - X) ². Determine Var(s), that is, the variance of the sample variance. (c) Assume now that we have observed data ₁,..., ER with sample variance s². Use the result from part (a) to find numbers an and bn, such that [ans, bns] is an exact 95%-confidence interval for ².

A population has a mean µ = 161 and a standard deviation o = 20. Find the mean and standard deviation of the sampling distribution of sample means with sample size n = 56. The mean is = μx (Round to three decimal places as needed.) and the standard deviation is o- = X 3 X

Say you have two sets of data X1, ..., X10 and Y1,..., Y40. All of this data is considered independent. The first set of data are Normally distributed with mean B and variance 10. The second set of data are Normally distributed with mean y and variance 10. We are trying to estimate 0 = X = X; 18 + y. Consider the estimate ô = }X + Ÿ where 3 4 iX + Y where 10 vi=1 1 10 and Y = E Y;? 40 vi=1 40 (a) What is the mean, variance and distribution of 0? (b) What is the probability that 0 is larger than 1 away from 0? (c) What is the bias, variance and MSE of the estimate 0 for estimating 0?

What is the variance and standard deviation for the number of times the SAT is taken? x Frequency (f) fx f*x2= (f*x) x (x) (4) = (3)x(1) 5152727-(2547473)(2547473)/1518859=880035.3688/1518859=0.5794 (1) (2) (3)=(1)x(2) (4)=(3x1)   Population Variance 1 721,769 721,769 721,769   2 601,325 1,202,650 2,405,300   3 166,736 500,208 1,500,624   4 22,299 89,196 356,784   5 6,730 33,650 168,250   Total 1,518,859 2,547,473 5,152,727 880035.3688 0.5794   n=1,518,859 ∑fx = 2,547,473                       The population variance is 0.5794 The Standard Deviation? 0.76  Can you show me the steps to reach the standard deviation of .76 ?