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1. • Probability of an event occurring is low

     
     • When the probability of an event occurring is low, and it happens, it is called a rare event. Rare events are important to consider in hypothesis testing because they can inform your willingness not to reject or to reject a null hypothesis.
     philschatz.com/statistics-book/contents/m47044.html

     Rare Events, the Sample, Decision and Conclusion · Statistics

2. stats.libretexts.org › Bookshelves › Introductory9.5: Rare Events, the Sample, Decision and Conclusion

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   Apr 2, 2023 · When the probability of an event occurring is low, and it happens, it is called a rare event. Rare events are important to consider in hypothesis testing because they can inform your willingness not to reject or to reject a null hypothesis.

3. ecampusontario.pressbooks.pub › introstats › chapter8.5 Rare Events, the Sample, Decision, and Conclusion

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   A rare event is an event that is unlikely to occur. The probability of a rare event happening is very small. In a hypothesis test, we want to determine if the collected sample is a rare event.

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5. pressbooks.ccconline.org › accintrostats › chapterChapter 10.5: Rare Events, the Sample, Decision and ...

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   When the probability of an event occurring is low, and it happens, it is called a rare event. Rare events are important to consider in hypothesis testing because they can inform your willingness not to reject or to reject a null hypothesis.

6. openstax.org › books › introductory-statistics-2e9.4 Rare Events, the Sample, Decision and Conclusion - OpenStax

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   Rare Events. Suppose you make an assumption about a property of the population (this assumption is the null hypothesis). Then you gather sample data randomly. If the sample has properties that would be very unlikely to occur if the assumption is true, then you would conclude that your assumption about the population is probably incorrect.

7. pressbooks-dev.oer.hawaii.edu › introductoryRare Events, the Sample, Decision and Conclusion - UH Pressbooks

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   A “rare event” has occurred (Didi getting the 💲100 bill) so Ali doubts the assumption about only one 💲100 bill being in the basket. Using the Sample to Test the Null Hypothesis. Use the sample data to calculate the actual probability of getting the test result, called the p-value.

8. openstax.org › books › statistics9.4 Rare Events, the Sample, and the Decision and Conclusion

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   Rare Events. The thinking process in hypothesis testing can be summarized as follows: You want to test whether or not a particular property of the population is true. You make an assumption about the true population mean for numerical data or the true population proportion for categorical data. This assumption is the null hypothesis.

9. People also ask

   What is a rare event in a hypothesis test?

   • A rare event is something we consider to be unlikely to happen (i.e. the probability of that event happening is very small). This is what we are looking for in a hypothesis test. We want to determine if the sample collected for the test is a rare event (unlikely to happen) under the assumption the null hypothesis is true.

   8.5 Rare Events, the Sample, Decision, and Conclusion

   ecampusontario.pressbooks.pub/introstats/chapter/8-5-rare-events-the-sample-decision-and-conclusion/

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   How do you determine if a sample is a rare event?

   • To determine if the sample is a rare event, we calculate the probability of the sample occurring, assuming that the null hypothesis is true. If the probability of the sample occurring is small, then the sample is a “rare event” and unlikely to occur under the assumption the null hypothesis is true.

   8.5 Rare Events, the Sample, Decision, and Conclusion

   ecampusontario.pressbooks.pub/introstats/chapter/8-5-rare-events-the-sample-decision-and-conclusion/

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   What is the probability of a rare event happening?

   • The probability of a rare event happening is very small. In a hypothesis test, we want to determine if the collected sample is a rare event. The p -value is the probability of getting the sample. In a hypothesis test, the significance level is the cut-off value for likely versus unlikely.

   8.5 Rare Events, the Sample, Decision, and Conclusion

   ecampusontario.pressbooks.pub/introstats/chapter/8-5-rare-events-the-sample-decision-and-conclusion/

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   What is a rare event?

   • This page titled 9.5: Rare Events, the Sample, Decision and Conclusion is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform. When the probability of an event occurring is low, and it happens, it is called a rare event.

   9.5: Rare Events, the Sample, Decision and Conclusion

   stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_1e_(OpenStax)/09:_Hypothesis_Testing_with_One_Sample/9.05:_Rare_Events_the_Sample_Decision_and_Conclusion

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   What is a null hypothesis?

   • Suppose you make an assumption about a property of the population (this assumption is the null hypothesis). Then you gather sample data randomly. If the sample has properties that would be very unlikely to occur if the assumption is true, then you would conclude that your assumption about the population is probably incorrect.

   9.5: Rare Events, the Sample, Decision and Conclusion

   stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_1e_(OpenStax)/09:_Hypothesis_Testing_with_One_Sample/9.05:_Rare_Events_the_Sample_Decision_and_Conclusion

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   How does the hypothesis test work?

   • The hypothesis test works by asking the question how unlikely the sample mean would be if the null hypothesis were true. The graph shows how far out the sample mean is on the normal curve. The p -value is the probability that, if we were to take other samples, any other sample mean would fall at least as far out as 17 cm.

   9.5: Rare Events, the Sample, Decision and Conclusion

   stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_1e_(OpenStax)/09:_Hypothesis_Testing_with_One_Sample/9.05:_Rare_Events_the_Sample_Decision_and_Conclusion

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10. louis.pressbooks.pub › introductorystatistics8.4 Rare Events, the Sample, Decision, and Conclusion

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    Identify rare events. Conduct and interpret hypothesis tests. Describe a decision and conclusion. Establishing the type of distribution, sample size, and known or unknown standard deviation can help you figure out how to go about a hypothesis test. However, there are several other factors you should consider when working out a hypothesis test.