Introduction to Probability and Statistics
Introduction to Probability and Statistics
14th Edition
ISBN: 9781133103752
Author: Mendenhall, William
Publisher: Cengage Learning
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Chapter 15.2, Problem 15.3E

a.

To determine

Explain the null and alternative hypothesis to be tested.

b.

To determine

Find the rank of combined sample from smallest to largest.

c.

To determine

Find the rejection region of the test for the given value of α .

d.

To determine

Check the data provide sufficient evidence to indicate that population one is shifted to the left of population two.

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Suppose a linear model y=β0+β1xy=β0+β1x is fit to a sample data set, and a test of the null hypothesis H0:β1=0H0:β1=0 against an alternative hypothesis HA:β1≠0HA:β1≠0 is performed; a PP-value of 0.4203 is obtained. Which of the following scatter plots depicts the data set on which this model was fit and the hypothesis test was performed?
Let X1,...,Xn be iid exponential(θ) random variables. Derive the LRT of H0 : θ = θ0 versus Ha : θ 6= θ0. Determine an approximate critical value for a size-α test using the large sample approximation.
Consider the following two formulations of the bivariate PRF, where ui and εi are both mean-0 stochastic disturbances (i.e random errors): yi = β0 + β1xi + u yi = α0 + α1(xi − x¯) + ϵ a) Write the OLS estimators of β1 and α1. Are the two estimators the same? b) What is the advantage, if any, of the second model over the first?

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