7. Suppose X,Y "Unif( 0, 0+1). Suppose the scientists wish to test Ho : 0 =...
please do NOT repeat the previous answer .Consider a random sample from a uniform distribution, X, Unif (0,10) a. Derive a test of Ho :0-2 versus H, 03. Suppose that you observe the following data: 6.20, 4.88, 4.30, 6.56, 4.96, 5.04, 3.02,9.06, 6.33, 6.98, 7.15, 3.81. Run the test that you derived in part (a) at the 0.05 level of significance. b. What is the power of this test? c. .Consider a random sample from a uniform distribution, X, Unif...
Suppose that we wish to test the null hypothesis Ho that the proportion p of ledger sheets with errors is equal to .05 versus the alternative Ha , that the proportion is larger than .05, by using the following scheme. Two ledger sheets are selected at random. If both are error free, we reject Ho. If one or more contains an error, we look at a third sheet. If the third sheet is error free, we reject Ho. In all...
07 (15) Suppose that we wish to test the null hypothesis Ho that the proportion p of ledger sheets with errors is equal to .05 versus the alternative Ha , that the proportion is larger than .05, by using the following scheme. Two ledger sheets are selected at random. If both are error free, we reject Ho. If one or more contains an error, we look at a third sheet. If the third sheet is error free, we reject Ho....
N(0,02). We wish to use a 1. [18 marks] Suppose X hypothesis single value X = x to test the null Ho : 0 = 1 against the alternative hypothesis H1 0 2 Denote by C aat the critical region of a test at the significance level of : α-0.05. (f [2 marks] Show that the test is also the uniformly most powerful (UMP) test when the alternative hypothesis is replaced with H1 0 > 1 (g) [2 marks Show...
(b) Find the pr Problem 2. Let x,, ,X, be We wish to test Ho versus Hi: ba a random sample from a population with parameter with density H: 0. Consider a test which rejects Ho when Xa>e, where a test x,.-min(X, , ,x, ) . Find the value of c so that significance level of that test is 0.05, if n -100
2. (7 pts) Given the pdf f(x,0)- statistic Ymaz to test Ho : θ, θ > 0, .Take a sample of size 3 from this pdf. Use the 4,0 y 5 versus HA : θ > 5. (a) What is the decision rule when a 0.05. (b) Suppose θ-7, what is the Type II error for the test in part (a). 2. (7 pts) Given the pdf f(x,0)- statistic Ymaz to test Ho : θ, θ > 0, .Take a...
Let X have the pdf defined for 0<x<2. Let Y~Unif(0,1). Suppose X and Y are independent. Find the distribution of X-Y. fx() =
1(a) Let Xi, X2, the random interval (ay,, b%) around 9, where Y, = max(Xi,X2 ,X), a and b are constants such that 1 S a <b. Find the confidence level of this interval. Xi, X, want to test H0: θ-ya versus H1: θ> %. Suppose we set our decision rule as reject Ho , X, be a random sample from the Uniform (0, θ) distribution. Consider (b) ,X5 is a random sample from the Bernoulli (0) distribution, 0 <...
Consider X1,X2, , Xn be an iid random sample fron Unif(0.0). Let θ = (끄+1) Y where Y = max(X1, x. . . . , X.). It can be easily shown that the cdf of Y is h(y) = Prp.SH-()" 1. Prove that Y is a biased estimator of θ and write down the expression of the bias 2. Prove that θ is an unbiased estimator of θ. 3. Determine and write down the cdf of 0 4. Discuss why...
4. Exercise Let X, Y be RVs. Denote E[X] = Hy and E[Y] =py. Suppose we want to test the null hypothesis Ho : Mx = uy against the alternative hypothesis Hi : 4x > uy. Suppose we have i.i.d. pairs (X1,Yı),...,(Xn, Yn) from the joint distribution of (X,Y). Further assume that we know the X - Y follows a normal distribution. (i) Show that exactly) T:= (X-Y)-(ux-uy) - tn-1), Sin (3) where s2 = n-1 [?-,((X; – Y;) –...