The following are the four Important Properties of a Test of Hypothesis. Kindly explain each further for better understanding. The type I error and type II errors are related. A decrease in the probability of one generally results in an increase in the probability of the other. The size of the critical region, and therefore the probability of committing a type I error, can always be reduced by adjusting the critical value(s). An increase in the sample size n will reduce α and β simultaneously. If the null hypothesis is false, β is a maximum when the true value of a 3parameter approaches the hypothesized value. The greater the distance between the true value and the hypothesized value, the smaller β will be.

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6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The following are the four Important Properties of a Test of Hypothesis. Kindly explain each further for better understanding.

The type I error and type II errors are related. A decrease in the probability of one generally results in an increase in the probability of the other.
The size of the critical region, and therefore the probability of committing a type I error, can always be reduced by adjusting the critical value(s).
An increase in the sample size n will reduce α and β simultaneously.
If the null hypothesis is false, β is a maximum when the true value of a 3parameter approaches the hypothesized value. The greater the distance between the true value and the hypothesized value, the smaller β will be.

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If the null hypothesis is false, β is a maximum when the true value of a parameter approaches the hypothesized value. The greater the distance between the true value and the hypothesized value, the smaller β will be.

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