4) Let X have the p.m.f.f(x; 8) = 6" (1 – 0)'-², x = 0, 1.We test Ho : 0 = 0.5 vs. H. : 0 < 0.5 by taking a random sampleX1, X2, ..., X, of size n = 5 and rejecting Ho if Y = EX; is observedto be less than or equal to a constant c.a) Show that this is a uniformly most powerful test.b) Find the significance level when c = 1.c) Find the significance level when c= 0.

Answered: Image /qna-images/answer/a7aa6368-3c65-4193-8d02-7d2fdc8d51d3.jpg

Answered: 4) Let X have the p.m.f. f(r; 8) = 0"…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

Suppose that the finite population being studied has N elements from which a sample of size n is drawn using SRSWOR to estimate the population total LOOK AT THE IMAGE ATTACHED
9.3 Let Y₁, Y₂,..., Y, denote a random sample from the uniform distribution on the interval (0, 0+1). Let 0 =Y-; and O=Y). a Show that both ₁ and ₂ are unbiased estimators of 0. b Find the efficiency of 8₁ relative to ₂. n n+1
4.65 Let X1, X2, ..., Xn be a random sample from a N(u, 16) population, where u is an unknown parameter. Test Ho : u = 10 versus H1 : u+10 at a = 0.05 using the test statistic X. (a) Find the decision rule for the test. (b) Draw the power curves for n =9 and n= 100 on the same set of axes.
10. Let X1,..., X„ be an iid sample from f(x | 0) = 0x°-1, positive. Find the MLE and MOM estimators for 0. 0 < I < 1, where the parameter 0 is
Need help with parts C & D The proportion of Americans who have frequent migraines is 15.2% according to the CDC. An acupuncturist claims that her treatment can reduce this figure significantly. A random sample of 191 Americans is administered the acupuncturists treatment and 25 report experiencing migraines.a. State Hypotheses to the scenario using the correct symbols. b. What is the sample proportion? (Round to 2 decimal places) ˆpp^= c. Suppose the P-value is calculated to be 0.0318What would your decision be for this test using α=α= 0.025? fail to reject the null accept the null reject the null d. Write a conclusion in terms of the acupuncturist's claim. Use the model provided by the instructor. Assume no errors were made.
3. Let X1,X2, ..,X, be a random sample form a normal distribution with E(X;) = µ;and Var(X;) = o². Assume s? = E(X;_ X)²/n and s3 = (n/(n – 1))s?. Questions: a. Compare between the estimators si and s?. b. Which one you preferred? What is (are) your reason(s). 4. Let X1,X2, . X, be a random sample form a uniform distribution, f(X)e = 0*(1– e)!-*; 0 < x < 1. Assume T1 = X1 and T, = (-)Ex;. %3D a. Check the unbiasedness property for T1 and T,. b. Find the MSE of T, and T,. Can you preferer one of them? Discuss your reasons. с. 5. Suppose that X, X2,. , X, are an iid sample from the distribution given below, f(X)e = (1/2)(1+ X8); -1< X <1. Show that 3x is a consistent estimator of e.
11. A hypothesis test is conducted with H0 : µ = 46 vs. Ha: µ ≠ 46. The hypothesis test sample finds x̅ = 47.2, s = 5, and n = 81. The tail area in this test is P =
7. (4 pts) if fx(x) = 2x for 0 ≤ x ≤ 1 and Y = 10 – X², then find Fx (x) (remember to give the sample space).
5. Let X₁ and X₂ be iid Poisson() random variables with pmf p(x) = H'e exp{p(e-1)), for tER. Let Y=X₁+X₂. a. b. What is the distribution of Y? What are E[Y] and Var[Y]? for x 0,1,2,..., and mgf 9 X!
5. Let X1,X,.., X, is the random samples from U (0,0). Three estimators for parameter 0 are given as, Ô, = 2X , n+1 -Y. Ô, = Y, + Y, п a. Show that estimators are unbiased. b. Find the efficiency of the 1st estimator to the 2nd estimator. c. Check that if the 3rd estimator is consistent. d. Which estimator has the minimum variance?
3. A box should contain exactly 64 matches. 100 boxes were checked and gave the sample mean ī = 65 and sample standard deviation sioo = 25. the sample mean ī = 66 and sample standard deviation sio0 = 25. In each case verify the hypothesis H(m = 64). [Ans. D = (-0, -2, 32) U (2.32, 0)] (a) 2 ¢ D hence we fail to reject ; (b)4 E D hence we reject the hypothesis]

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS