Final answer:
Without specific dataset information, determining the exact number of observations lost by removing schools where teacher benefits are less than 1% of salary is not possible. However, changing teacher benefit criteria significantly affects the dataset and the ensuing statistical analysis.
Step-by-step explanation:
To address the question of redoing example 4.10 by dropping schools where teacher benefits are less than 1% of salary, we would need more specific information regarding the size of the dataset to accurately determine how many observations are lost. However, the concept behind this adjustment is that we are refining our sample to include only those schools where teacher benefits represent a significant portion of the total compensation which likely are more representative of the average school. Without additional context or data provided by the student, we unfortunately cannot give a precise answer to part (i) of the question.
Regarding the teacher salaries and their distribution patterns, we know that changes to salaries or sample sizes can affect the distribution curve. For example, if every teacher received a $3,000 raise, the distribution of salaries would shift to the right, indicating a higher average salary among teachers. Also, sampling a larger number of teachers, such as 70 instead of 10, would make the distribution curve more symmetric and normal due to the central limit theorem. The provided statistical analysis, including conducting hypothesis tests or determining the probability of certain outcomes given a sample, is a basic principle used throughout statistics to help make decisions or predictions based on sampled data. These methodologies are commonly applied in various fields including education analytics, business decisions, and scientific research.