Final answer:
The purpose statement 'To tell my audience about the life of Florence Nightingale' is indicative of an informative speech, which is designed to provide educational content to the audience without trying to persuade or entertain.
Step-by-step explanation:
The specific purpose statement 'To tell my audience about the life of Florence Nightingale' is characteristic of an informative speech. An informative speech aims to explain, describe, or demonstrate particular facts or subjects to an audience. The objective is to provide comprehensive information without seeking to persuade or entertain necessarily. In contrast, a persuasive speech would attempt to sway the audience's opinions or behaviors, an entertaining speech would seek to amuse, and a demonstrative speech would show the audience how to do something step by step. In this case, the primary focus is to educate the audience about Florence Nightingale's life without necessarily aiming to persuade or entertain them.