Final answer:
The question involves statistical analysis related to error types and hypothesis testing within mathematics. It requires understanding of Type I and Type II errors, which deal with incorrectly rejecting a true null hypothesis or failing to reject a false null hypothesis. Without proper data or context, definitive conclusions cannot be made about the expectations surrounding the receipt of a specific graduation amount.
Step-by-step explanation:
The provided statements revolve around statistical concepts including error types, hypothesis testing, and sample data analysis. These are core topics within the field of statistics, a branch of mathematics. They illustrate understanding of statistical errors, such as Type I and Type II errors, as well as the evaluation of means from different samples to draw conclusions about population parameters.
In the scenario where students expect to receive $12,000 upon graduation, without additional context or data provided, it is impossible to determine the correctness of this expectation. The question likely pertains to probability or expectations in a statistical sense, though without the proper data or context, an answer cannot be ascertained confidently.
Type I error occurs when a false null hypothesis is rejected, as in the case where we conclude that the average tuition cost at private universities is higher than $20,000 when it's actually $20,000 or less. Type II error happens when a true null hypothesis is not rejected, such as when one concludes that the mean starting salary is at least $100,000, when in fact, it's less than $100,000.