In Exercises 21–24, refer to the sample of body temperatures (...

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.)

[IMAGE]

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?

Accepted Answer

All right, hello, everyone. So this question says, if we analyze the recorded blood sugar levels of 5 individuals using suitable statistical methods, we conclude that when the differences are found, Between the 7 a.m. and 9 p.m. blood sugar levels, there is a 58% chance that these differences can be explained by random results obtained from populations that have the same 7 a.m. and 9 p.m. blood sugar levels. The data is presented in the following table. And so the question is, what conclusions should we draw regarding regarding the statistical significance of the observed differences in blood sugar levels? And here we have 4 different answer choices labeled A through D. OK, so first, what is that 58% chance referring to? Well, going back to the stem of the question, it says that there's a 58% chance that the differences in blood sugar levels between 7 a.m. and 9 p.m. are a result of random chance, as opposed to a true relationship between those two values. This probability, right, this probability that the differences observed are the result of chance refers to the p-value. Which can be obtained by statistical tests such as the paired T test. So, as mentioned before, the P value represents the likelihood that the observed differences between values measured are because of random chance, as opposed to a true effect. Now, recall that in order for something to be considered statistically significant, the P value. Generally speaking, should be less than or equal to 0.05, which corresponds to 5%. Now, it just so happens in this case that the P value is actually 58%, which is far higher than our threshold of 0.05 or 5%. So therefore We don't have enough evidence to say that the differences in blood sugar levels measured between 7 a.m. and 9 p.m. are statistically significant. Instead, those differences are likely the result of random variation as opposed to a true effect or a real relationship between those two values. This would mean that option A is the correct answer. Because the differences in blood sugar levels are not statistically significant because 58% is greater than the usual significance level of 5%. And there you have it. So with that being said, thank you so very much for watching, and I hope you found this helpful.

��app

Key Concepts

Statistical Significance

P-value

Random Variation

Watch next