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You test the hypotheses Ho A 1 vs H1 : > # 1 by using the test =1 (|X, 5> Can) Find the smallest threshold Can so...
Using the plug-in method determine A >0 such p (1-p) (1- A),p (1-p)(1+ A)] is a confidence interval for p (1 -p) with asymptotic level 95%. Note that A should only depend on n and p (Enter hatp for p. If applicable, enter Phi(z) for the cdf (z) of a normal variable Z, q(alpha) for the quantile qa for any numerical value a Recall the convention in this course that P (Z< qa) =1-a for Z~ N (0,1).) Using the...
In each of the following questions, you are given an i.i.d. sample and two hypotheses. For any ?∈(0,1), define a test with asymptotic level ?, then give a formula for the asymptotic ?-value of your test. a) b) c) i.id. Xi, , xn Poiss (A) for some unknown λ > 0; V.S x) where Z ~ N (0, 1), and q(alpha) Type barx-n for Xn, lambda-0 for λο. . If applicable, type abs(x) for lxi. Phi(x) for Φ (x) =...
Let X1, ..., X, bei.i.d. random variable with pdf fe defined as follows: fo (2) = 0x0-11(0<x< 1) where 0 is some positive number. Using the MLE Ô, find the shortest confidence interval for 6 with asymptotic level 85% using the plug-in method. To avoid double jeopardy, you may use V for the appropriate estimator of the asymptotic variance V (Ô), and/or I for the Fisher information I (Ô) evaluated at ê, or you may enter your answer without using...
As on the previous page, let Xi,...,Xn be i.i.d. with pdf where >0 2 points possible (graded, results hidden) Assume we do not actually get to observe X, . . . , Xn. to estimate based on this new data. Instead let Yİ , . . . , Y, be our observations where Yi-l (X·S 0.5) . our goals What distribution does Yi follow? First, choose the type of the distribution: Bernoulli Poisson Norma Exponential Second, enter the parameter of...
Bonus (5 points) Suppose that you are testing the following hypotheses: Ho: 4 = 10 and H :> 10. If the null hypothesis is rejected at the 1% level of significance, what statement can you make about the confidence interval on the mean? a) The lower bound of a 95% one-sided confidence interval on the mean exceeds 10. b) 9 <u< 13 c) No statement can be made. d) The lower bound of a 95% one-sided confidence interval on the...
Can anyone help me with this problem? Thank you! 7. Let X1,.. , Xn denote a random sample from (1-9)/0 x; Test Ho: θ Bo versus H1: θ θο. (a) For a sample of size n, find a uniformly most powerful (UMP) size-a test if such exists. (b) Take n-?, θ0-1, and α-.05, and sketch the power function of the UMP test. 7. Let X1,.. , Xn denote a random sample from (1-9)/0 x; Test Ho: θ Bo versus H1:...
Im so sorry for spamming Question 1: Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. Upper H 0 : p equals 0.84 versus Upper H 1 : p not equals 0.84, n equals 500, x equals 410 comma alpha equals 0.05 Is np 0 left parenthesis 1 minus p 0 right parenthesis greater than or equals 10np01−p0≥10? Select the correct choice below and fill in the answer box to complete your choice....