Let Y, represent the th normal population with unknown mean , and unknown variance of for i=1,2. Consider independent random samples, Ya, Ya..Yin, of size ni, from the ith population with sample mean Y, and sample variance S?=(-² (g) For non-zero constants a,'s, what is the distribution of U₂ = a₁Y₁-0₂₂? State all the relevant parameters of the distribution. (h) Find the standard error of U₂ in part (g), assuming that of = o² = 0². (i) Discuss how the distribution of Y₁-₂ can be used to test the equality of the two population means, µ and p2, when o=o=o² is known. (j) Define appropriate rejection regions, in terms of Y₁-₂, for testing Ho: #₁ = ₂ against a two-sided alternative hypothesis at the a level of significance.

tion 15 of 25 Birth weights at a local hospital have a Normal distribution, with a mean of 110 oz and a standard deviation of 15 oz. The proportion of infants with birth weights above 125 oz is: O 0.500. 0.159. O 0.341. 0.841. terms of use contact us help aboutus prvacy poly 452 PM 10/14/2020 真 a 2. prt sc insert 110

Assume a normally distributed population with a mean = 90 and standarddeviation = 12. Be sure to sketch the curves, include formulas & round appropriately.  If you select one person at random from this population (M = 90, SD = 12)and find his/her score on this variable to be 68 would you be surprised/consider this score extreme (yes/no)? Why/why not? Be sure to show your work when justifying the answer.

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?