Question

Provided that the population size is significantly greater than the sample size, the spread of the sampling distribution does not depend on the population size.

which of the following is a true statement
a.) the larger the sample, the larger the spread in the sampling distribution
b.) bias has to do with the spread of a sampling distribution
c.) provided that the population size is significantly greater than the sample size, the spread of the sampling distribution does not depend on the population size
d.) sample parameters are used to make inferences about the population statistics
e.) statistics from smaller samples have less variability

Answer 1

The correct response to the student's question is that the spread of the sampling distribution does not depend on the population size when the population is much larger than the sample size. Larger samples result in less variability between samples and more reliable statistics, given the absence of bias in the sampling method.

Step-by-step explanation:

The student's question addresses the concept of sampling distribution and how various factors influence its characteristics. With reference to the key points provided, we can identify that c.) provided that the population size is significantly greater than the sample size, the spread of the sampling distribution does not depend on the population size is the correct statement.

It is essential to understand that a larger sample size generally leads to a reduced spread in the sampling distribution which means lesser variability between sample statistics. This is a core principle of the central limit theorem and is key to producing reliable statistical inferences from sample data to the broader population. Additionally, it's important to remember that while sample statistics are indeed used to make inferences about the population, the quality of those inferences depends on the absence of bias and the representativeness of the sample.