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Ch. 1 - Introduction to Statistics
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 1 - Introduction to StatisticsProblem 1.1.24
Chapter 1, Problem 1.1.24

In Exercises 21–24, refer to the sample of body temperatures (degrees Fahrenheit) in the table below. (The body temperatures are from Data Set 5 in Appendix B.)
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Conclusion If we analyze the listed body temperatures with suitable methods of statistics, we conclude that when the differences are found between the 8 AM body temperatures and the 12 AM body temperatures, there is a 64% chance that the differences can be explained by random results obtained from populations that have the same 8 AM and 12 AM body temperatures. What should we conclude about the statistical significance of those differences?

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1
Understand the concept of statistical significance: Statistical significance is a determination that a relationship between variables is caused by something other than chance. In this context, it refers to whether the differences in body temperatures at 8 AM and 12 AM are due to random variation or a true underlying effect.
Identify the given probability: The problem states that there is a 64% chance that the differences can be explained by random results. This probability is often referred to as the p-value in hypothesis testing.
Interpret the p-value: A p-value is a measure of the probability that an observed difference could have occurred just by random chance. In general, a p-value less than 0.05 (5%) is considered statistically significant, meaning the observed effect is unlikely to be due to chance.
Compare the p-value to the significance level: In this problem, the p-value is 0.64 (64%), which is much higher than the common significance level of 0.05. This suggests that the differences in body temperatures are likely due to random variation rather than a true effect.
Draw a conclusion: Since the p-value is greater than the typical significance level, we conclude that the differences in body temperatures at 8 AM and 12 AM are not statistically significant. This means there is not enough evidence to suggest a true difference in body temperatures at these times.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Statistical Significance

Statistical significance refers to the likelihood that a result or relationship is caused by something other than mere random chance. In hypothesis testing, a result is considered statistically significant if the p-value is less than a predetermined significance level, often 0.05. This means that the observed effect is unlikely to have occurred under the null hypothesis.
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P-value

The p-value is a measure used in statistical hypothesis testing to determine the strength of the evidence against the null hypothesis. It represents the probability of obtaining test results at least as extreme as the observed results, assuming that the null hypothesis is true. A lower p-value indicates stronger evidence against the null hypothesis, suggesting that the observed data is unlikely to occur by random chance alone.
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Random Variation

Random variation refers to the natural fluctuations in data that arise from random processes. In the context of statistical analysis, it is important to distinguish between variations caused by random chance and those caused by actual differences or effects. Understanding random variation helps in determining whether observed differences in data are statistically significant or simply due to random noise.
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Related Practice
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Textbook Question

In Exercises 21–24, refer to the sample of body temperatures (degrees Fahrenheit) in the table below. (The body temperatures are from Data Set 5 in Appendix B.)

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Context of the Data Refer to the table of body temperatures. Is there some meaningful way in which each body temperature recorded at 8 AM is matched with the 12 AM temperature?

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Textbook Question

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