(2) A single observation of a random variable having a geometric distribution isused to test the null hypothesis p = po against the alternative H₁ p = P₁ < Po.:Use the Neyman-Pearson lemma to find the best critical region of size a.(a) Use the Neyman-Pearson lemma to find the best critical region of size a.(b) If po = 0.2, p₁ = 0.15, and a = 0.1, calculate the constant in part (a).

The Neyman-Pearson lemma states that the best critical region of size a for testing a simple null…

Answered: (2) A single observation of a random…

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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Assume the MR model: Y = 3 + 4x1 + 5x2 + epsilon, with sigma = 5 Select the Excel command that will find P(Y < 18) when X₁ = 2 and X₂ = 1. (Note: epsilon is the random error term and sigma is the population standard deviation)
[Bayes' Theorem, Discrete Random Variables] It is known that 90% of new cars produced by a certain company have on average À malfunctions per 1 km of covered distance. Besides this, it is known that remaining 10% of new cars were produced with a defect which increases the average malfunction rate to 2λ. The two types of cars are indistinguishable otherwise. When (a) Suppose that only a single malfunction has occured with a randomly selected car over 1,000 km of distance. What is the probability that the car is from the defective group, and how does it depend on λ? (b) For a randomly selected car, find a minimum distance covered with no malfunctions for the probability that the car is from the non-defective group is 95% or above (express the result as a function of X).
A random sample X1,X2,...,Xn is drawn from the normal distribution. i. Suppose μ is a known parameter. Find the maximum likelihood estimator for σ. ii. Find the bias and variance of the obtained estimator
Two independent random variables, X and Y, are both uniformly distributed on [0, 1]. The random variable Z is defined by Z = (X-H)² + (Y - My) ², E[X] and y E[Y]. Determine the expected value of Z. where (a) (b) = Determine the variance of Z.
A snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.34. A dietician is asked to test this claim and finds that a random sample of 16 servings has a variance of 1.22. At α=0.05, is there enough evidence to reject the manufacturer's claim? Assume the population is normally distributed. Complete parts (a) through (e) below.
Test the claim about the difference between two population means mu 1μ1 and mu 2μ2 at the level of significance alphaα. Assume the samples are random and independent, and the populations are normally distributed. Claim: mu 1μ1equals=mu 2μ2; alphaαequals=0.01 Population statistics: sigma 1σ1equals=3.3, sigma 2σ2equals=1.5 Sample statistics: x overbar 1x1equals=17, n1equals=29, x overbar 2x2equals=19, n2equals=28 Determine the alternative hypothesis. Upper H Subscript aHa: mu 1μ1 ▼ not equals≠ greater than or equals≥ less than or equals≤ greater than> less than< mu 2μ2 Determine the standardized test statistic. zequals=nothing (Round to two decimal places as needed.) Determine the P-value. P-valueequals=nothing (Round to three decimal places as needed.) What is the proper decision? A. Reject Upper H 0H0. There is enough evidence at the 1% level of significance to reject the claim. B. Fail to reject Upper H 0H0. There is not…
c,d,e
In a survey of 240 males ages 20 to 24, 38% were neither in school nor working. In a survey of 210 females ages 20 to 24, 42% were neither in school nor working. These samples are random and independent. At α=0.06, can you support the claim that the proportion of males ages 20 to 24 who were neither in school nor working is less than the proportion of females ages 20 to 24 who were neither in school nor working? Find Z-test statistc

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