The need for inference does not only apply regarding one population. Another common need is to compare some numerical trait of two populations. Let's return to the example about the gasoline additive at the beginning of Chapter 10, but with a slight modification. Now, in the experiment, some cars are driven with the gasoline additive and others are driven without the additive. To determine if the gasoline additive is any good, the mean miles per gallon of the cars using it and of the cars driving without it will be compared. As another example, suppose a professor has two groups taking business statistics. Both groups have similar qualifications for the course and simply take the same class at different times of the day. The professor gives each group a different version of an exam. Are mean exam scores of the two groups different? If so, this would be a problem to the professor, it would not be fair to give exams of differing difficulty to these two groups.
Our main tools for statistical inference will still be confidence intervals and hypothesis testing. Although it may seem that statistical inference is only slightly more complicated, there are several things that require consideration.
- Are the samples independent or dependent?
- Are the standard deviations known? If not, are the standard deviations unknown but can be assumed to be equal or are they unknown and cannot be assumed to be equal? ...