Confidence Intervals with Two Samples
Figure 7.1 Fires burning on the Hawaiian islands in 2023.
Chapter Objectives
By the end of this chapter, the student should be able to:
- Distinguish between independent and paired/dependent samples
- Construct confidence intervals for the difference between two population means or proportions
- Describe the pooled standard deviation and the known standard deviation methods
We have already seen the usefulness of Confidence Intervals when we are trying to estimate a population parameter (mean or proportion). Often times we want to compare a parameter from two different populations. To do this, we can create a confidence interval to estimate the difference between the two parameters.
For example, medical researchers may want to know whether a new treatment for colon cancer is effective. They can assign a group of patients to receive the new treatment and another group of patients to receive the old treatment. The researchers might then look at the difference in the proportion of patients in each group who went into remission.
As another example, the data below lists the sea surface high temperature recorded each month of the years 1960 and 2020.
| 2020 | 1960 | |
| January | 0.672 | -0.016 |
| February | 0.6215 | -0.0385 |
| March | 0.6505 | -0.0055 |
| April | 0.6475 | -0.0315 |
| May | 0.671 | 0.022 |
| June | 0.737 | -0.037 |
| July | 0.718 | 0.061 |
| August | 0.776 | 0.05 |
| September | 0.726 | 0.0785 |
| October | 0.705 | -0.0245 |
| November | 0.6875 | -0.0195 |
| December | 0.7415 | 0.016 |
Source: Our World In Data
We can use a confidence interval to look for a difference between the average high temperatures.
In this chapter, we will become familiar with the techniques of constructing confidence intervals that look for differences in population parameters such as those in this introduction.
