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.

Question

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.