A simple null hypothesis against a composite alternative

Assignment Help Basic Statistics

Reference no: EM131137829

When we test a simple null hypothesis against a composite alternative, a critical region is said to be unbiased if the corresponding power function takes on its minimum value at the value of the parameter assumed under the null hypothesis. In other words, a critical region is unbiased if the probability of rejecting the null hypothesis is least when the null hypothesis is true. Given a single observation of the random variable X having the density

where -1 θ 1, show that the critical region x α provides an unbiased critical region of size α for testing the null hypothesis θ = 0 against the alternative hypothesis θ 0.

Reference no: EM131137829

Questions Cloud

What effect does this have on the effective annual interest : If the loan in Problem 21 is paid off at the end of the tenth year (at the time of the 120th payment) what effect does this have on the effective annual interest rate?

What is the maximum number of edges in a graph : What is the maximum number of edges in a graph with V vertices and no parallel edges - What is the minimum number of edges in a graph with V vertices, none of which are isolated (have degree 0)?

What is budgeted sales for 2016 : Kramer is developing the 2016 budget. In 2016 the company would like to increase selling prices by 12.5%, and as a result expects a decrease in sales volume of 9%. What is budgeted sales for 2016

What effect do the closing costs have on the effective a i r : The bank charges $500 for closing costs on a $17,000 loan with an annual percentage rate of 11% compounded monthly with a term of five years. The bank will not allow the closing costs to be added to the $17,000 borrowed. What effect do the closing co..

A simple null hypothesis against a composite alternative : When we test a simple null hypothesis against a composite alternative, a critical region is said to be unbiased if the corresponding power function takes on its minimum value at the value of the parameter assumed under the null hypothesis.

Discuss overarching duty of the health care governing board : Discuss the overarching duties of the health care governing board in mitigating the effects of medical non-compliance, as they apply to the rules of practice set forth in the Well Care Hospital governing board's manifesto.

Write a program that takes four command line arguments : Write a program that takes four command line arguments: start, stop, step, and file. The first three arguments are nonnegative integers and the fourth is a string.

Calculate the hydraulic conductivity of this clay : A falling-head permeability test was carried out on a clay soil of diameter 10 cm and length 15 cm. In 1 hour the head in the standpipe of diameter 5 mm dropped from 68 cm to 50.2 cm.

What effect do the closing costs have on the effective a i r : The bank charges $4,000 for closing costs on a $200,000 loan with an annual percentage rate of 8.5% compounded monthly with a term of thirty years. The bank will not allow the closing costs to be added to the $200,000 borrowed. What effect do the clo..

User Account

All Pages