What resolution came about in response to the debate over legislative representation?

pepin the short[a] (german: pippin der kurze, french: pépin le bref, c. 714 – 24 september 768) was the king of the franks from 751 until his death. he was the first of the carolingians to become king.[b][2]

the younger son of the frankish prince charles martel and his wife rotrude, pepin's upbringing was distinguished by the ecclesiastical education he had received from the monks of st. denis. succeeding his father as the mayor of the palace in 741, pepin reigned over francia jointly with his elder brother carloman. pepin ruled in neustria, burgundy, and provence, while his brother carloman established himself in austrasia, alemannia and thuringia. the brothers were active in suppressing revolts led by the bavarians, aquitanians, saxons, and the alemanni in the early years of their reign. in 743, they ended the frankish interregnum by choosing childeric iii, who was to be the last merovingian monarch, as figurehead king of the franks.

a hypothesis is an expected answer to a question, usually based on some theory or prior research. hypothesis testing is a method of determining the viability of a hypothesis. let’s use the us presidential election as an example. there are many hypotheses (questions) about how people feel or whom they will vote for. the only way to know the 100% “truth” about the answers to these questions is to ask every single possible voter – something that is impossible, expensive, time consuming etc. instead, we take samples and use statistics to make “best guesses” about the answer to a particular hypothesis. we never know for sure if our conclusion is right at the time we accept/reject it, but these techniques, when used appropriately can get us close to the truth most of the time (which is a lot better than guessing, flipping coins or throwing darts to get answers).

the tricky part about hypothesis testing is that we have to think somewhat backwards about it – we have to test what is known as the “null hypothesis”. as an example, the hypothesis might be “obama is more popular than romney” while the null hypothesis is “there is no difference in popularity between obama and romney”. we focus on the null hypothesis because it tells us exactly what the expected value of our tests should be (obama popularity = romney popularity) and we can collect data and see if it comes out that way (see next section on “significance”). if it does, then we “accept the null hypothesis” and reject our original hypothesis. if the null hypothesis is disproven, we look at the data to see if our original hypothesis holds (obama> romney).