Thank you for visiting Does your body temperature change during the day Listed below are body temperatures in F of subjects measured at 8 00 am and at 12. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
The 95% confidence interval is approximately (-1.8871, 1.5537), suggesting no significant difference in body temperature.
To calculate the 95% confidence interval estimate of the difference between the 8:00 am temperatures and the 12:00 am temperatures, we need to follow a few steps:
- Calculate the difference between each pair of temperatures:
8:00 am - 12:00 am
97.0 - 98.0 = -1.0
96.2 - 98.6 = -2.4
97.6 - 98.8 = -1.2
96.4 - 98.0 = -1.6
97.8 - 98.6 = -0.8
99.2 - 97.6 = 1.6
- Calculate the sample mean of the differences:
(-1.0 - 2.4 - 1.2 - 1.6 - 0.8 + 1.6) / 6 = -0.1667
- Calculate the sample standard deviation of the differences:
First, find the sum of squared differences from the mean:
[tex]((-1.0 + 0.1667)^2 + (-2.4 + 0.1667)^2 + (-1.2 + 0.1667)^2 + (-1.6 + 0.1667)^2 + (-0.8 + 0.1667)^2 + (1.6 + 0.1667)^2)[/tex] = 14.8002
Next, divide the sum by (n-1), where n is the number of differences:
14.8002 / (6-1) = 2.9600
Finally, take the square root to get the sample standard deviation:
sqrt(2.9600) ≈ 1.7204
- Calculate the margin of error (E):
The margin of error can be calculated using the formula:
E = t * (s / sqrt(n))
where t is the critical value from the t-distribution for a 95% confidence interval, s is the sample standard deviation, and n is the number of differences.
For a 95% confidence interval with 5 degrees of freedom (n-1), the critical value is approximately 2.571.
E = 2.571 * (1.7204 / sqrt(6)) ≈ 1.7204
- Construct the confidence interval:
The confidence interval estimate is given by:
(mean of the differences) ± (margin of error)
-0.1667 ± 1.7204
(-1.8871, 1.5537)
Therefore, the 95% confidence interval estimate of the difference between the 8:00 am temperatures and the 12:00 am temperatures is approximately (-1.8871, 1.5537).
Since this interval includes zero, we cannot conclude with 95% confidence that the body temperature is significantly different at both times.
However, it's important to note that this analysis is based on a small sample size and may not be representative of the population.
Learn more about Confidence interval
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Thank you for reading the article Does your body temperature change during the day Listed below are body temperatures in F of subjects measured at 8 00 am and at 12. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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