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 = 200, the population standard deviation is unknown, the population appears to be normally distributed

Group of answer choices

T-Distribution

Normal Distribution

neither of the methods studied by us can be used

Answer 1

In the scenario described:

- The sample size \( n = 200 \) is relatively large.
- The population standard deviation is unknown.
- The population appears to be normally distributed.

Given these points, you should use the **Normal Distribution** for constructing the confidence interval because the sample size is large (typically \( n > 30 \) is considered sufficient), and the Central Limit Theorem suggests that the sampling distribution of the mean will be approximately normal regardless of the population distribution when the sample size is large enough.

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