Consider an unbalanced study with six subjects,

identified as A, B, C, D, E and G. In the actual

study,

? Subjects A and B are assigned to the first

treatment, and the other subjects are assigned to the second treatment.

? There are exactly two successes, obtained

by A and C.

This information is needed for parts (a)-(c) below.

(a) Compute the observed value of the test

statistic.

(b) Assume that the Skeptic is correct. Determine the observed value of the test statistic for the assignment that places D and E

on the first treatment, and the remaining

subjects on the second treatment.

(c) We have obtained the sampling distribution of the test statistic on the assumption

that the Skeptic is correct. It also is possible to obtain a sampling distribution of the

test statistic if the Skeptic is wrong provided we specify exactly how the Skeptic

is in error. These new sampling distributions are used in the study of statistical

power which is briefly described in Chapter 7 of the text. Assume that the Skeptic

is correct about subjects A and G, but incorrect about subjects B, C, D and E.

For the assignment that puts D and G on

the first treatment, and the other subjects

on the second treatment, determine the response for each of the six subjects.

8. A comparative study is performed; you are

given the following information.

? The total number of subjects equals 33.

? The observed value of the test statistic is

greater than 0.

I used the website to obtain the exact P-value for

Fisher's test for each of the three possible alternatives. These three P-values are below along

with three bogus P-values

Consider a multivariate random variable (X1 , X2, X3) with parameters 71 0 3 72 0.5 73 -0.2, and N = 30 Calculate the following () EX Number (b) var( X ) Number (c) cov( X1, X2) = NumberA six-sided die is rolled, and the following results are obtained: Value Frequency 10 11 13 22 (a) Which is the correct null hypothesis to test if the die is fair? O HO : T = (1/6, 1/6, 1/6, 1/6, 1/6, 1/6) O Ho : n # (1/6, 1/6, 1/6, 1/6, 1/6, 1/6) O Ho : 71 + 72 + 73 + 74 + 75 +76=1 O Ho : y1 + 92 + 93 + 94 + 95 + 96 = n (b) Calculate the value of the test statistic: Number (c) What distribution should you use to calculate the P-value? O standard normal O multinomial O Chi-squared O T-distributionQUESTION 17 For multivariate statistical techniques, when there is multivariate analysis of variance and covariance and canonical correlation, and multiple discriminant analysis can be used. more than one dependent variable one dependent variable variable interdependence interobject similarityLet (Yl, Y2, ..., YK) ~ Multinomial(n, 71, 72, ..., Wk), then (a) Calculate the moment generating function (This will be a multivariate MGF). 3 Marks] (b) Show that E(Y;) = naj [2 Marks] (c) Show that Var(Y;) = na; (1 -nj) [4 Marks (d) Show that Cov(Y;, Y;) = -main; [6 Marks] Hint: You can use the Multivariate MGF. Recall if Y = (Y1, Y2, ..., Y-) be a multivariate random variable. Then the MGF is defined as, MY(1, ..., the) = E(exp(ti Yit ... + YA)) Now use partial derivative on t; or to, b; to achieve the results