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 standard deviation is 15, the population appears to be skewed

Group of answer choices

T-Distribution

Normal Distribution

neither of the methods studied by us can be used

Answer 1

To determine whether to use the t-distribution or the normal distribution for constructing a confidence interval, consider the following:

1. **Sample Size (n)**: The sample size is 200, which is considered large. In general, for large sample sizes (usually n > 30), the Central Limit Theorem suggests that the sampling distribution of the sample mean will be approximately normal, even if the population distribution is not.

2. **Population Standard Deviation**: In this case, the standard deviation (σ) is provided as 15. Since we have the population standard deviation, we can use the normal distribution for constructing the confidence interval.

3. **Population Shape**: It is mentioned that the population appears to be skewed. While skewness might be a concern with smaller sample sizes, with n = 200, the sampling distribution of the mean will still approximate normality due to the large sample size.

Given these points, the appropriate choice would be:

**Normal Distribution**

Thus, the correct answer from your options is **Normal Distribution**.