4.5.11. Let Y₁ < Y2 < Y3 < Y4 be the order statistics of a random sample of sizen = 4 from a distribution with pdf f(x; 0) = 1/0, 0 < x < 0, zero elsewhere, where0 <0. The hypothesis Ho: 0 = 1 is rejected and H₁0 > 1 is accepted if theobserved Y4 > c.(a) Find the constant c so that the significance level is a = 0.05.(b) Determine the power function of the test.

Answered: Image /qna-images/answer/730fb252-1ad2-4579-b410-7f4fa240ae61.jpg

Answered: 4.5.11. Let Y₁ < Y2 < Y3 < Y4 be the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Say that we have a null hypothesis that X1,..., X16 that are Normally distributed with mean 0 and variance 1. Call the sample mean X. Consider the test where p-value = 20 (4 X) - 24 (4|X) – 1 We will reject this if p-value < a. a) Show that the type I error rate of this test is a. b) Say that X1,..., X16 that are Normally distributed with mean 1 and variance 1. What is the type II error rate of this test when a = 0.05? •..
Let X1, X2, *. Xn be a random sample of size n from norm population with mean and unknown a. Let X and s be the sample mean and sample standard deviation. Then for any 0
Use the t-distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from random samples, and if the sample sizes are small, assume the underlying distributions are relatively normal. Test Ho : HA = Ha VS H. : HA # Hg using the fact that Group A has 8 cases with a mean of 125 and a standard deviation of 18 while Group B has 15 cases with a mean of 118 and a standard deviation of 14. (a) Give the test statistic and thep-value. Round your answer for the test statistic to two decimal places and your answer for the p- value to three decimal places. test statistic = p-value = eTextbook and Media (b) What is the conclusion of the test? Test at a 10% level. O Reject Ho. O Do not reject Ho. eTextbook and Media
6). A random sample of 90 observations produced a mean of x¯=21 from a population with a normal distribution and a standard deviation σ=4.1.
A company is doing a hypothesis test on the variation of quality from two suppliers. Both distributions are normal, and the populations are independent. use a = 0.01 2 H0:01 HA: 01 > 2 2 02² 10₂² The standard deviation of the first sample is 2.2077 5.1485 is the standard deviation of the second sample. The test statistic is =
H. Let X1,..., X, be a random sample from some distribution with unknown u. It's known that X 100 and X = 1783. %3D %3D (40) Supposen = 144 and o? = 12. The value of a, corresponding to the confidence interval [0.7, 1.3] is (a) 0.212 (b) 0.122 (c) 0.050 (d) 0.298
6.1
11. Consider a random sample Y₁, Y2, ..., Yn from a normal population Y~N(μ, o²) where the population variance and mean are unknown. We want to construct a Σ(X-X)² Show 100(1 a)% confidence interval for the population variance if g² whether or not is a pivotal quantity and construct a 100(1-a) confidence interval.
A researcher suspects that the mean birth weights of babies whose mothers did not see a doctor before delivery is less than 3000 grams. The researcher states the hypotheses as H:x = 3000 grams H, x 3000 grams; He:x< 3000 grams, where x = the mean birth weights of the sample of babies whose mothers did not see a doctor before delivery. Ho: x < 3000 grams; H,:x = 3000 grams, where x = the mean birth weights of the sample of babies whose mothers did not see a doctor before delivery. Ho: = 3000 grams; H # 3000 grams, where = the true mean birth weights of all babies whose mothers did not see a doctor before delivery. Ho: i = 3000 grams; H:< 3000 grams, where = the true mean birth weights of all babies whose mothers did not see a doctor before delivery. O Ho : š == 3000 grams; H. x 3000 grams, where x = the mean birth weights of the sample of babies whose mothers did not see a doctor before delivery.
question 12.12 using the numbers from 12.11.
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3.An insurance company employs agents on a commission basis. It claims that in their first year, agents will earn a mean of at least 40.000TL and that the population standard deviation is no more than 6.00OTL. A random sample of 9 agents are found for commissions in the first year and has values as follows: 9. 9. X; = 333000 ve (Xi – x)2 = 312000 i=1 i=1 Where x; are the values for each agent and the distribution is normal. a.Test at the 0.05 significance level the null hypothesis that the population mean is at least 40.000TL and interpret the result b.Test at 0.10 significance level the null hypothesis that the population standard deviation is at most 6.000TL and interpret the result.

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