Final answer:
To answer the student's question, the population mean is calculated, then compared to the sample mean. The t-distribution is commonly used when the population standard deviation is unknown and sample size is small, while the normal distribution is used when the population standard deviation is known or for large samples.
Step-by-step explanation:
The subject at hand involves the statistical concept of comparing a sample mean to a population mean and determining the appropriate statistical distribution to perform a hypothesis test. Given the population dataset, we first need to calculate the population mean. After calculating the population mean, we can then compare it to the sample mean given in the question to find out by how much the sample mean exceeds the population mean.
In statistical analyses, when the population standard deviation is unknown and the sample size is small, the t-distribution is typically used; however, if the population standard deviation is known or the sample size is large, the normal distribution may be appropriate. In scenarios where the Central Limit Theorem (CLT) applies, the distribution of sample means will approximate a normal distribution regardless of the original population distribution, as long as the sample size is sufficiently large (typically n ≥ 30).