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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?

In Exercises 17-20, refer to the sample of body temperatures (°Fahrenheit) in the table below. (The body temperatures are from a data set in Appendix B.)

| Subject | 1 | 2 | 3 | 4 | 5 |
|---------|------|------|------|------|------|
| 8 AM | 97.0 | 98.5 | 97.6 | 97.7 | 98.7 |
| 12 AM | 97.6 | 97.8 | 98.0 | 98.4 | 98.4 |

Answer :

Final answer:

To determine the statistical significance of the differences between the 8 AM and 12 AM body temperatures, we can use a hypothesis test. If the probability of obtaining the differences by random chance is high, then the differences are not statistically significant.

Explanation:

To determine the statistical significance of the differences between the 8 AM and 12 AM body temperatures, we can use a hypothesis test. The null hypothesis would state that there is no difference between the two sets of temperatures. The alternative hypothesis would state that there is a difference between the two sets of temperatures.

  1. Set the significance level (usually denoted as alpha). This is the threshold at which we would consider the differences statistically significant.
  2. Calculate the test statistic. This depends on the type of hypothesis test being used and the sample data.
  3. Compare the test statistic to the critical value(s) based on the significance level. If the test statistic is greater than the critical value(s), we reject the null hypothesis and conclude that the differences are statistically significant.

In this case, since we are given the probability of obtaining the differences by random chance (64%), we can conclude that the differences are not statistically significant, as the probability is high that the differences can be explained by random results from populations with the same temperatures at both 8 AM and 12 AM.

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