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Chapter 8: Problem 19

In problem \(8.15\) the nutritionist was interested in knowing if the rate of vegetarianism in American adults has increased. She carried out a hypothesis test and found that the observed value of the test statistic was \(2.77 .\) We can calculate that the p-value associated with this is \(0.0028\), which is very close to 0\. Explain the meaning of the p-value in this context. Based on this result, should the nutritionist believe the null hypothesis is true?

Short Answer

Expert verified
The p-value of \(0.0028\) is interpreted as only a \(0.28\%\) chance that the observed test statistic or an extreme value could have occurred by chance if there was no increase in the rate of vegetarianism. Since this p-value is considerably less than the commonly used significance level of \(0.05\), we have sufficient evidence to reject the null hypothesis meaning that it is very likely vegetarianism rate has increased.

Step by step solution

01

Understanding the p-value

First, let's understand the concept of p-value. A p-value is a measure of how extreme the data are. In hypothesis testing, p-value helps to decide whether to reject the null hypothesis. A smaller p-value means that there is stronger evidence in favor of the alternative hypothesis.
02

Interpreting the p-value

In this scenario, the p-value of \(0.0028\) can be interpreted as there being a \(0.28\%\) likelihood that the observed test statistic of \(2.77\) (or a higher magnitude) would have arisen by chance if indeed there hasn't been any increase in the rate of vegetarianism among American adults.
03

Decision about the Null Hypothesis

Typically, a p-value less than \(0.05\) is considered statistically significant, i.e., there are very unlikely these observations happened by chance, which means we can reject the null hypothesis. Here, the p-value of \(0.0028\) is much smaller than \(0.05\). Hence, there is strong evidence against the null hypothesis.

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Most popular questions from this chapter

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