![4. An exponential random variable X has p.d.f (x,07/», x>0, c.df. F(x:0) 1-exp(-x/8) for x > 0, and mean θ. A single observation of an exponential random variable X is used to test H0 : θ-2 against H1 : θ-5. The null hypothesis is accepted if and only if the observed value of the random variable is less than 3. (a) What is the probability of committing a Type I error? (b) What is the probability of committing a Type II error? (c) What is the power of the test? 13] C11 C2] (d) Find a test of these hypotheses that has significance level 0.05](http://img.homeworklib.com/questions/f79af7f0-71b2-11ea-b74c-8559a55885c8.png?x-oss-process=image/resize,w_560)
Homework Answers
Add Answer to:
4. An exponential random variable X has p.d.f (x,07/», x>0, c.df. F(x:0) 1-exp(-x/8) for x >...
A random variable, X, has uniform distribution on the interval [0,θ] where θ is unknown. A...
A random variable, X, has uniform distribution on the interval [0,θ] where θ is unknown. A hypothesis test is as follows: H0: θ = 2 H1: θ ≠ 2 It has been decided to reject H0 if the observed value of x is x ≤ 0.1 or x ≥ 1.9. Part a: Find the probability of committing a Type I error. Part b: Suppose the true value of θ is 3. Find the probability of committing a Type II error....
2. Let X1,.n be a random sample from the density 0 otherwise Suppose n = 2m+...
2. Let X1,.n be a random sample from the density 0 otherwise Suppose n = 2m+ 1 for some integer m. Let Y be the sample median and Z = max(Xi) be the sample maximum (a) Apply the usual formula for the density of an order statistic to show the density of Y is (b) Note that a beta random variable X has density f(x) = TaT(可 with mean μ = α/(a + β) and variance σ2 = αβ/((a +s+...
5. For X follows Exp(6) (exponential distribution with parameter θ), a hypothesis test rejects th...
5. For X follows Exp(6) (exponential distribution with parameter θ), a hypothesis test rejects the null hypothesis Ho : θ-1 when X k versus H1 : θ > 1. (a) Show that for any k greater than -log(0.05), the test has the probability of type I error less than 0.05 (b) Show that the power of the test at θ-10 is larger when k-1 than k-2. (c) Let k-_ log(0.05), calculate the power function in terms of θ when θ...
5. A bowl contains ten marbles of which 0 are white while the others are black....
5. A bowl contains ten marbles of which 0 are white while the others are black. In order to test the null hypothesis H0 : θ-1 against H1: θ > 1, five of the marbles are randomly drawn with replacement and the null hypothesis is rejected if at least two of the five drawn are white. (a) What is the probability of committing a Type I error? (21 (b) What is the probability of committing a Type II error when...
A random sample of size 295 has x=104. The significance level ? is set at 0.05....
A random sample of size 295 has x=104. The significance level ? is set at 0.05. The P-value for testing H0: ?=100 against Ha: ??100 is 0.057. Identify all the incorrect statements below regarding this P-value of 0.057. (Select all that apply.) The probability of Type I error equals 0.057. If H0 is true, the probability obtaining a sample mean that would show at least as much evidence against H0 as the observed sample mean is 0.057. The probability that...
Fx(x; θ)=1/ θ for 0<x< θ. We want to test H0: θ=1 and H1 : θ>1. To do...
Fx(x; θ)=1/ θ for 0<x< θ. We want to test H0: θ=1 and H1 : θ>1. To do this, we take a single observation X1 of X and we reject H0 if X1> 0.9 . 1. what is the probabilty of Type I error? (false positive, probability = α) 2. what is the value of ß ( type 2 erros ) if θ=1.5? error type ressources: https://en.wikipedia.org/wiki/Type_I_and_type_II_errors
1. Let Y1, . . . ,Y,, be a random sample from a population with density...
1. Let Y1, . . . ,Y,, be a random sample from a population with density function 0, otherwise (a) Find the method of moments estimator of θ (b) Show that Yan.-max(Yi, . . . ,%) is sufficient for 02] (Hint: Recall the indicator function given by I(A)1 if A is true and 0 otherwise.) (c) Determine the density function of Yn) and hence find a function of Ym) that is an unbiased estimator of θ (d) Find c so...
Suppose a single measurement is taken from a distribution with pdf f(x)=?e−?x, x>0. The hypotheses are...
Suppose a single measurement is taken from a distribution with pdf f(x)=?e−?x, x>0. The hypotheses are H0∶?=1 versus HA∶?<1, and the null hypothesis is rejected if x ≥ 3.2. a) Calculate the probability of committing a type I error. b) Calculate the probability of committing a type II error if, in fact, ? = 1∕5.
A random sample of size n -8 is drawn from uniform pdf f(x,θ)- , 0-XS θ for the purpose of testing Ho : θ-2 against H, : θ < 2 at α : 0.10 level of significance. Suppose the decision rule is to be...
A random sample of size n -8 is drawn from uniform pdf f(x,θ)- , 0-XS θ for the purpose of testing Ho : θ-2 against H, : θ < 2 at α : 0.10 level of significance. Suppose the decision rule is to be based on Xmax, the largest order statistic. What would be the probability of committing a Type II error when θ 1.7.
A random sample of size n -8 is drawn from uniform pdf f(x,θ)- , 0-XS...
This file contains independent observations on a random variable X. It is known that a2-1.4246. a...
Mean = -0.92809
This file contains independent observations on a random variable X. It is known that a2-1.4246. a. Test Ho : E(X) 1.6 against H1 : E(X)>1.6 using a significance level of 1%. In your answer, you should state the null and alternative hypotheses, the significance level, the PDF of the test statistic under the null hypothesis, the value of the test statistic, and your conclusion. b. Do you need to make any assumptions in order for your test...
2. Let X1,.n be a random sample from the density 0 otherwise Suppose n = 2m+ 1 for some integer m. Let Y be the sample median and Z = max(Xi) be the sample maximum (a) Apply the usual formula for the density of an order statistic to show the density of Y is (b) Note that a beta random variable X has density f(x) = TaT(可 with mean μ = α/(a + β) and variance σ2 = αβ/((a +s+...
5. For X follows Exp(6) (exponential distribution with parameter θ), a hypothesis test rejects the null hypothesis Ho : θ-1 when X k versus H1 : θ > 1. (a) Show that for any k greater than -log(0.05), the test has the probability of type I error less than 0.05 (b) Show that the power of the test at θ-10 is larger when k-1 than k-2. (c) Let k-_ log(0.05), calculate the power function in terms of θ when θ...
5. A bowl contains ten marbles of which 0 are white while the others are black. In order to test the null hypothesis H0 : θ-1 against H1: θ > 1, five of the marbles are randomly drawn with replacement and the null hypothesis is rejected if at least two of the five drawn are white. (a) What is the probability of committing a Type I error? (21 (b) What is the probability of committing a Type II error when...
1. Let Y1, . . . ,Y,, be a random sample from a population with density function 0, otherwise (a) Find the method of moments estimator of θ (b) Show that Yan.-max(Yi, . . . ,%) is sufficient for 02] (Hint: Recall the indicator function given by I(A)1 if A is true and 0 otherwise.) (c) Determine the density function of Yn) and hence find a function of Ym) that is an unbiased estimator of θ (d) Find c so...
A random sample of size n -8 is drawn from uniform pdf f(x,θ)- , 0-XS θ for the purpose of testing Ho : θ-2 against H, : θ < 2 at α : 0.10 level of significance. Suppose the decision rule is to be based on Xmax, the largest order statistic. What would be the probability of committing a Type II error when θ 1.7.
A random sample of size n -8 is drawn from uniform pdf f(x,θ)- , 0-XS...
Mean = -0.92809
This file contains independent observations on a random variable X. It is known that a2-1.4246. a. Test Ho : E(X) 1.6 against H1 : E(X)>1.6 using a significance level of 1%. In your answer, you should state the null and alternative hypotheses, the significance level, the PDF of the test statistic under the null hypothesis, the value of the test statistic, and your conclusion. b. Do you need to make any assumptions in order for your test...
Most questions answered within 3 hours.
-
3) What are the typical social structures in a global city?
asked 57 minutes ago -
Luther Corporation
Consolidated Balance Sheet
December 31, 2019 and 2018 (in $ millions)
Assets
2019
2018...
asked 59 minutes ago -
(Expected rate of return and risk) Carter Inc. is evaluating a
security. Calculate the investment’s expected...
asked 3 hours ago -
What specific indicators can point to lack of progress for
African Americans in American society?
asked 4 hours ago -
1-The Electrons in a beam are moving at 2.7×108 m/s in an
electric field of 15000...
asked 4 hours ago -
A gas tank is a vertical cylinder. It has a radius of 1m, a
height of...
asked 5 hours ago -
Accent Software faces the following conditions. All of these
support Accent’s use of a market-penetration pricing...
asked 6 hours ago -
A mathematically inclined friend emails you the following
instructions: "Meet me in the cafeteria the first...
asked 6 hours ago -
A monopoly sells in two countries . The demand curves in the two
countries are p1...
asked 7 hours ago -
A .15kg rubber ball is bounced off a wall. Before hitting the
wall, the ball moves...
asked 8 hours ago -
A manufacturing company preparing to build a new plant is
considering three potential locations for it....
asked 8 hours ago -
B. If compound Y has approximately the same values of solubility
in toluene as compound X,...
asked 8 hours ago