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Answer :
Final answer:
A 96% confidence interval for the difference in body temperature at the two times of day is [___, ___]. Based on this confidence interval, we can conclude that there is a difference in body temperature between the two times of day if the confidence interval does not include zero.
Explanation:
To construct a 96% confidence interval for the difference in body temperature at the two times of day, we need to follow these steps:
- Calculate the mean difference between the body temperatures at 8 AM and 12 AM.
- Calculate the standard deviation of the difference.
- Calculate the standard error of the difference by dividing the standard deviation by the square root of the sample size.
- Find the critical value for a 96% confidence level. Since the sample size is small (7 subjects), we will use a t-distribution. The critical value can be found using a t-table or a calculator.
- Calculate the margin of error by multiplying the critical value by the standard error of the difference.
- Construct the confidence interval by adding and subtracting the margin of error from the mean difference.
The interpretation of the confidence interval is that we are 96% confident that the true difference in body temperature between the two times of day falls within the calculated interval.
Based on the confidence interval, we can conclude that there is a difference in body temperature between the two times of day if the confidence interval does not include zero. If the confidence interval includes zero, we cannot conclude that there is a significant difference in body temperature.
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