Question

A school administrator wants to know the average age of the 25,000 kindergartners in her state at the beginning of the school year. She randomly selects 1,000 kindergarteners in the state, assuring that the group accurately represents all kindergartners in the state, and finds the average age to be 5 years 10 months.

What assumption can she make regarding the approximate average age of all kindergartners in the state?
A. No assumptions can be made regarding the average age of kindergartners in the state because the sample is biased.
B. The approximate average age of kindergartners in the state is less than 5 years 10 months.
C. The approximate average age of kindergartners in the state is greater than 5 years 10 months.
D. The approximate average age of the kindergartners in the state is 5 years 10 months.

Answer 1

The correct answer is D, which states that the estimated average age of all kindergartners is 5 years 10 months, based on a representative and random sample. This is an example of statistical inference.

Step-by-step explanation:

The question asks about the assumptions that can be made about the average age of 25,000 kindergartners based on a sample of 1,000 kindergartners. Given that the sample is random and representative, the best assumption to make is that the average age of all kindergartners in the state is approximately the same as that of the sample. This is a fundamental concept in statistics known as statistical inference, where we use information from a sample to infer characteristics about the larger population.

Therefore, the correct choice is D: The approximate average age of the kindergartners in the state is 5 years 10 months. We can assume this because if the sampling method is truly random and accurately reflects the larger population, then this sample mean is a good estimate of the population mean. However, it is important to note that there will always be some level of uncertainty when using a sample to estimate population parameters.