STAT 8320 Homework Solution: Hypothesis Testing and Normal Distributions, Assignments of Statistics

Download STAT 8320 Homework Solution: Hypothesis Testing and Normal Distributions and more Assignments Statistics in PDF only on Docsity! STAT 8320 HW #1 (Solution) 1.(a) y3 ∼ N1(5, 9) (b) 2y1 − 5y2 + 3y3 ∼ N1(32, 257) (c)   y2 3y1 + y2 − 2y3   ∼ N2     −3 −10   ,   16 0 0 56     (d)   y4 y1 + y4   ∼ N2     −8 −7   ,   25 19 19 17     ⇒ y1|y1 + y4 ∼ N(−7917 , 6417) (e) (i) and (iii) are independent, while (ii) is not. 2. (a) k2 . = −2.156 the p-value < 0.05, so we reject H0 for MVN. (b) The data does not appear normal because the points do not follow a straight line. (It is ok if you say the data appears normal, but the reason should be consistent to the result you got.) (c) F . = 3.166 > f(5,25) = 2.6, so we reject H0. i.e. µ 6= (515, 145, 30, 35, 345). (d) The confidence intervals are (514.7, 519.9), (143, 146.6), (28.95, 31.25), (34.9, 37.3), (343.7, 347.7) for y1, y2, y3, y4, y5 respectively. (e) The mles for mean and variance are 245.12 and 11.31 respectively. 3. (a) MC−1 .= 7.957 < χ2.95,10 = 18.307. So we can not reject H0. The two variance-covariance matrices are equal. (b) F = 11.756 > f(.95,4,19) = 2.9. So we reject H0. The two means are different. (c) Calculate either F or the confidence interval. The confidence interval is (-11.9, 40.7) contains 0. So we can not reject H0. There is sufficient evidence to show that there is no difference between the initial cholesterol means for the two groups. (d) F = 11.16 > f(2,21) = 3.47. So we reject H0. The two medications are not parallel for 2, 4 and 6 months. 1