Question

3. You are conducting a randomized experiment on telepathy in which your experimental subjects have to take a test. A medium, i.e. a person with supernatural abilities, claims that she is able to influence other peoples' thoughts and feelings only through extra-sensory perception. You split your N experimental subjects into two groups of m and n individu- als, respectively. For the first m individuals (Ťtreatment groupŤ), the medium is sitting in a room next door with the solutions manual to the test, thinking about the test-taker in order to help him/her on the test. The second group of n individuals (ŤcontrolsŤ) takes the test under normal conditions. In order not to boost the confidence of either group, participants in neither group are told whether they are helped by the medium. You observe the samples X1,..., Xm of scores for the group which received help from the medium, and Y1,..., Yn are the scores of the control group. You know before and that X; ~ N(jx,o?) and Y; ~ N(fly,o?) 1 1. What is the variance of Xm-Yn 2. For a given total number of experimental subjects N=m+n, which value of m mini- mizes the variance of the difference Xm-Yn 3. You want to conduct a test of Ho : lx = Hy against Ha:lx # Hy with size a = 0.05. Suppose o2 = 4, m= 20 and n=8, and you find that Xm-Yn= 1.74. Do you reject the null hypothesis?

Answer 1

n = Nom, Also, Xi and X; ~N 14:02) and Yi mat (My 102) where i=1,2... 2. j 7,2.. in x are independent, - var variance of fm-in = vas (m) + vastin) (xmŷn) OP 62 n 22 when man that is Elo variance 2 of the difference min is minimum. e xm- 9n) + I 82 * 25 n 3 Hypothesis, Ho: Mx = My against Hai Max # My Giveni x 20.05) 02 12 4. m=20 and n=8," xm- qn = 1,74 Test statistic, Xm-9 1.74 Vor ( 1 + r) A ( 3 + 2 2.0797 P-value = 2ė (2 > 2.0797) = 0,0376 The prevalue is less than 2=0.05. Hence, reject the null hypothens,