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Chapter 7: Q6E (page 397)

We reject the null hypothesis when the test statistic falls in the rejection region, but we do not accept the null hypothesis when the test statistic does not fall in the rejection region. Why?

Short Answer

Expert verified

The simple justification for this is that the absence of evidence supporting the falsity of a statement does not provide enough to support its truthfulness.

Step by step solution

01

Given information

The statement is given that "We reject the null hypothesis when the test statistic falls in the rejection region, but we do not accept the null hypothesis when the test statistic does not fall in the rejection region".

02

Explaining the given statement

The null hypothesis is an assertion assumed to be true until proven otherwise by facts. When a test fails to reject the null hypothesis, it is important to remember that this does not prove it.

The simple justification for this is that the absence of evidence supporting the falsity of a statement does not provide enough to support its truthfulness. For example, there are frequently many null hypotheses for the mean's true value that can't reject for a given collection of data. Hence, we reject the null hypothesis when the test statistic falls in the rejection region, but we do not accept the null hypothesis when the test statistic does not fall in the rejection region.

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Most popular questions from this chapter

Salaries of postgraduates. The Economics of Education Review (Vol. 21, 2002) published a paper on the relationship between education level and earnings. The data for the research was obtained from the National Adult Literacy Survey of more than 25,000 respondents. The survey revealed that males with a postgraduate degree have a mean salary of \(61,340 (with standard error \(Sx\) = \)2,185), while females with a postgraduate degree have a mean of \(32,227 (with standard error \(Sx\) = \)932).

  1. The article reports that a 95% confidence interval for \[{\bf{\mu }}M\] , the population mean salary of all males with post-graduate degrees, is (\(57,050, \)65,631). Based on this interval, is there evidence to say that \[{\bf{\mu }}M\] differs from \(60,000? Explain.
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a. What is the null hypothesis, H0?

b. What is the alternative hypothesis,Ha?

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