Question

A sample of 21 first year night-school students' ages is obtained in order to estimate the mean age of night school students. The study yielded the sample mean of x = 24.5 years. Assume that the age of the night-school students is normally distributed with the standard deviation of 16.7. (a) Which approximation is more appropriate in this problem? 1) Normal approximation 2) T-distribution approximation

Answer 1

The T-distribution approximation is more appropriate for the given problem since the sample size is below 30 and the population standard deviation is known.

The correct answer is option 2

Step-by-step explanation:

When determining an appropriate approximation to estimate the mean age of night school students based on the sample data provided, we need to consider the sample size and the population standard deviation.

Since the sample size is 21, which is less than 30, and the population standard deviation is known (16.7 years), the T-distribution approximation is more appropriate for this problem.

This is because the T-distribution is better suited for small sample sizes and when the population standard deviation is known. It becomes similar to the normal distribution as the sample size increases.

The normal approximation is typically used when the sample size is large (n > 30) and the population standard deviation is known, which is not the case here.

The correct answer is option 2