Just E please 1. A random sample of n = 20 products are taken from the production lines of a factory. LetIIDXi Bernoulli(p) be the indicator of whether the i-th product defective for i = 1,..., 20,where р denotes the proportion of defective products in the population. It is desirable to testwhether the the proportion of defective products is below 30%.(a) State the null hypothesis Ho and the alternative hypothesis Ha.(b) Describe the events of Type I error and Type II error in the procedure of making statisticaldecisions.20i=1(c) Let T = 2₁X; denote the number of defective items in the sample. Suppose that weΣdecide to reject Ho if T ≤ 4. Let (p) denote the corresponding power function, i.e.,T(P) = Pr (T≤4|p).Determine the value of (p) at the points p = 0, 0.1, 0.2, 0.3,...,0.9, and 1.0 and sketchthe power function. (Hint: Use the statistical table for Binomial distribution.)(d) What is the size of the test procedure in part (c), i.e., the maximum probability of makingType I error?(e) What is the power of the test procedure in part (c) when p = 0.1? (Hint: Both part (d)and part (e) can be obtained immediately from the power function (p).)

The defective no. of items in the sample are denoted as: T=∑i=120Xi. It is specified that H0 is…

Answered: 1. A random sample of n = 20 products…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.2: The Least Square Line

Problem 4E

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Suppose Y₁, Y2,…, Yn is an iid sample from a beta (a, ß) distribution with a = ß = 0, 0 > 0 a. Use the Factorization Theorem to show that n T = []Y;(1 — Y;) i=1 is a sufficient statistic. b. The sample variance n 1 = ΣΥ; - Y)2 n 1 i=1 is an unbiased estimator of the population variance 1 4(20 + 1)* Is S² the MVUE of o2? Explain.
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