Assume that the paired sample data are simple random samples...

Assume that the paired sample data are simple random samples and that the differences have a distribution that is approximately normal. Does Your Body Temperature Change During the Day? Listed below are body. temperatures (in $^{\text {of }}$ ) of subjects measured at 8: 00 AM and at 12: 00 AM (from University of Maryland physicians listed in Data Set 2 in Appendix B). Construct a $95 \%$ confidence interval estimate of the difference between the 8: 00 AM temperatures and the 12: 00 AM temperatures. Is body temperature basically the same at both times? $8.00 \mathrm{AM} \quad 97.0 \quad 96.2 \quad 97.6 \quad 96.4 \quad 97.8 \quad 99.2$ $12=00 \mathrm{AM} \quad 98.0 \quad 98.6 \quad 98.8 \quad 98.0 \quad 98.6 \quad 97.6$

Assume that the paired sample data are simple random samples and that the differences have a distribution that is approximately normal.
Does Your Body Temperature Change During the Day? Listed below are body. temperatures (in $^{\text {of }}$ ) of subjects measured at 8: 00 AM and at 12: 00 AM (from University of Maryland physicians listed in Data Set 2 in Appendix B). Construct a $95 \%$ confidence interval estimate of the difference between the 8: 00 AM temperatures and the 12: 00 AM temperatures. Is body temperature basically the same at both times?
$8.00 \mathrm{AM} \quad 97.0 \quad 96.2 \quad 97.6 \quad 96.4 \quad 97.8 \quad 99.2$
$12=00 \mathrm{AM} \quad 98.0 \quad 98.6 \quad 98.8 \quad 98.0 \quad 98.6 \quad 97.6$

Key Concepts

Paired Sample Data

Paired sample data refers to observations collected in pairs, where each pair is related or matched in some meaningful way. This design is commonly used in experiments or observational studies when comparing two conditions or measurements taken from the same subjects. The analysis focuses on the differences within each pair, which often helps control for variability among subjects.

Simple Random Sampling

Simple random sampling is a basic sampling technique in which every member of the population has an equal chance of being selected. This method is important for minimizing selection bias and ensuring that the sample is representative of the population, which in turn supports the validity of statistical inference.

Normal Distribution Assumption

Assuming that the differences are approximately normally distributed is a crucial condition for many statistical methods, such as the construction of confidence intervals and hypothesis tests. This assumption justifies the use of the t-distribution for inference on the mean difference, especially when the sample size is small.

Confidence Interval

A confidence interval is a range of values derived from sample data that is likely to contain the true value of an unknown population parameter. In constructing a 95% confidence interval, researchers can be 95% confident that the interval encompasses the true mean difference between the paired measurements.

t-Distribution

The t-distribution is used instead of the normal distribution when the sample size is small and the population variance is unknown. It accounts for extra uncertainty by having heavier tails, making it a crucial tool for constructing confidence intervals and performing hypothesis tests in studies involving paired sample data.

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