Question

Assume that we want to construct a confidence interval. Determine whether you should use the t-distribution or the normal distribution to find it, based on the following information. In this problem, let n be the sample size.

n = 25, the population standard deviation is known, the population appears to be very skewed

Group of answer choices

neither of the methods studied by us can be used

Normal Distribution

t-distribution

Answer 1

Based on the provided information, we have a sample size of \(n = 25\), the population standard deviation is known, and the population is noted to be very skewed.

When constructing a confidence interval:

- If the population standard deviation is known, we typically use the normal distribution (Z-distribution), regardless of the sample size or skewness of the population.
- If the population standard deviation is unknown and the sample size is small (usually \(n < 30\)), we often use the t-distribution, and in cases where the population is skewed, this is particularly important.
- However, when the population standard deviation is known, we proceed with the normal distribution even if the population is skewed.

Given these points, since the population standard deviation is known and your sample size is 25 (which is considered small), you will use the **Normal Distribution**.

So, the correct choice is: **Normal Distribution**.