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Chapter 10: Problem 12

In a hypothesis test, what does it mean to say that the null hypothesis was not rejected?

Short Answer

Expert verified
When the null hypothesis is not rejected in a hypothesis test, it means that the data does not provide enough evidence to refute the null hypothesis. That is, there's no significant difference between the observed data and what is expected under the null hypothesis. However, this does not prove that the null hypothesis is true.

Step by step solution

01

Understanding Null Hypothesis

A null hypothesis is a general statement or default position that there is no relationship between two measured phenomena, or no association among groups. In simpler terms, it's the hypothesis that suggests nothing special is happening.
02

Understanding Hypothesis Testing

Hypothesis testing is a statistical method that is used in making statistical decisions using experimental data. It is basically an assumption that we make about the population parameter.
03

Interpreting Not Rejecting the Null Hypothesis

When we say that the null hypothesis is not rejected, it means that the experimental data are not significantly different from what is expected under the null hypothesis. In other words, the evidence obtained is not enough to believe that the situation has changed or that something special is going on. We continue to believe in the null hypothesis. However, it is important to note that this does not prove that the null hypothesis is true. It only indicates that the current data does not provide strong enough evidence to reject it.

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Most popular questions from this chapter

The report "2007 Electronic Monitoring and Surveillance Survey: Many Companies Monitoring, Recording, Videotaping-and Firing-Employees" (American Management Association, 2007) summarized a survey of 304 U.S. businesses. Of these companies, 201 indicated that they monitor employees' web site visits. Assume that it is reasonable to regard this sample as representative of businesses in the United States. a. Is there sufficient evidence to conclude that more than \(75 \%\) of U.S. businesses monitor employees' web site visits? Test the appropriate hypotheses using a significance level of 0.01 . b. Is there sufficient evidence to conclude that a majority of U.S. businesses monitor employees' web site visits? Test the appropriate hypotheses using a significance level of 0.01 .

Do state laws that allow private citizens to carry concealed weapons result in a reduced crime rate? The author of a study carried out by the Brookings Institution is reported as saying, "The strongest thing I could say is that I don't see any strong evidence that they are reducing crime" (San Luis Obispo Tribune, January 23,2003 ). a. Is this conclusion consistent with testing \(H_{0}:\) concealed weapons laws reduce crime versus \(H_{a}:\) concealed weapons laws do not reduce crime or with testing \(H_{0}:\) concealed weapons laws do not reduce crime versus \(H_{a}:\) concealed weapons laws reduce crime Explain. b. Does the stated conclusion indicate that the null hypothesis was rejected or not rejected? Explain.

Explain why a \(P\) -value of 0.0002 would be interpreted as strong evidence against the null hypothesis.

Explain why you would not reject the null hypothesis if the \(P\) -value were 0.37 .

One type of error in a hypothesis test is failing to reject a false null hypothesis. What is the other type of error that might occur when a hypothesis test is carried out?
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