Final answer:
The statement "Manchester has a high rainfall yesterday with 16.5 inches falling" is a fact because it can be objectively proven or disproven using evidence and measurement.
Step-by-step explanation:
The statement "Manchester has a high rainfall yesterday with 16.5 inches falling" is a fact because it can be objectively proven or disproven using evidence and measurement. In this case, the fact can be confirmed or refuted by checking the weather records for Manchester from the previous day. Rainfall amounts are measured using rain gauges, which provide accurate data on the amount of precipitation that fell within a specific time period.
In the context of analyzing weather and climate data, statistics play a crucial role. For example, using statistical methods, we can determine if the mean amount of rainfall in a certain area during a specific period is significantly different from a known average, as in the question regarding the mean summer rainfall for the northeastern United States. Such statistical hypothesis testing can be performed using a specified significance level, noted as alpha (α), where a common choice for α is 0.05 or 0.01. These values represent the probability of rejecting the null hypothesis when it is actually true, a concept known as the Type I error rate.