Hp 49g+ User Manual download pdf (Page 602)

100

101

Page 18-35

Procedure for testing hypotheses

The procedure for hypothesis testing involves the following six steps:

1. Declare a null hypothesis, H

. This is the hypothesis to be tested. For

example, H

: µ

-µ

= 0, i.e., we hypothesize that the mean value of

population 1 and the mean value of population 2 are the same. If H

true, any observed difference in means is attributed to errors in random

sampling.

2. Declare an alternate hypothesis, H

. For the example under consideration,

it could be H

: µ

-µ

≠ 0 [Note: this is what we really want to test.]

3. Determine or specify a test statistic, T. In the example under consideration,

T will be based on the difference of observed means, X

-X

4. Use the known (or assumed) distribution of the test statistic, T.

5. Define a rejection region (the critical region, R) for the test statistic based

on a pre-assigned significance level α.

6. Use observed data to determine whether the computed value of the test

statistic is within or outside the critical region. If the test statistic is within

the critical region, then we say that the quantity we are testing is

significant at the 100α percent level.

Notes:

1. For the example under consideration, the alternate hypothesis H

: µ

-µ

≠

0 produces what is called a two-tailed test. If the alternate hypothesis is

: µ

-µ

> 0 or H

: µ

-µ

< 0, then we have a one-tailed test.

2. The probability of rejecting the null hypothesis is equal to the level of

significance, i.e., Pr[T∈R|H

]=α. The notation Pr[A|B] represents the

conditional probability of event A given that event B occurs.

Errors in hypothesis testing

In hypothesis testing we use the terms errors of Type I and Type II to define the

cases in which a true hypothesis is rejected or a false hypothesis is accepted

(not rejected), respectively. Let T = value of test statistic, R = rejection region,

A = acceptance region, thus, R∩A = ∅, and R∪A = Ω, where Ω = the

parameter space for T, and ∅ = the empty set. The probabilities of making

an error of Type I or of Type II are as follows:

1 2 ... 597 598 599 600 601 602 603 604 605 606 607 ... 861 862

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