Final answer:
Using a 0.05 significance level and comparing α to the p-value of 0.1959, we do not reject the null hypothesis, indicating insufficient evidence to support the claim that the mean magnitude of earthquakes is greater than 1. Richter scale data are quantitative as they represent continuous numerical values. The 0.05 significance level is widely used to limit the Type I error rate in hypothesis testing.
Step-by-step explanation:
The student is asked to test the claim that the population of earthquakes has a mean magnitude greater than 1.00 using a significance level of 0.05. Upon comparing the alpha (α) value of 0.05 to the p-value of 0.1959, we find that α is less than the p-value (α < p-value), which leads us to not reject the null hypothesis (H₀). The conclusion is that, at a 5 percent level of significance, there is insufficient evidence to conclude that the mean magnitude of earthquakes is greater than 1.00, based on the provided data.
Richter scale magnitudes are examples of numerical data that quantify the energy produced by earthquakes. These magnitudes take on continuous numerical values and therefore represent quantitative data. When conducting statistical analysis, these magnitudes can be subjected to various hypothesis tests or correlation assessments depending on the research question.
In the broader context of the examples provided, the use of a 0.05 significance level is common in statistical hypothesis testing to determine if there is enough evidence to support a certain claim about a population. This alpha level sets the threshold for the probability of incorrectly rejecting a true null hypothesis, known as the Type I error rate.