Question

You may not be aware but I am a renowned entomologist. As part of my research, I went on an expedition to study the largest species of insect in the world, the giant weta.  

I decide to gather 20 giant weta and construct a 99% confidence interval for the mean length of this species of insect.

Assuming the length of this species is approximately normal with unknown mean and variance, what would be the value of the distribution percentage point that I would use when constructing this interval?

Answer 1

The answer is:

The length of this species is approximately normal with unknown mean and variance, therefore we will be using the t-distribution. The number of degrees of freedom is df=20−1=19, and the significance level is α=0.01.

Based on the provided information, the critical t-value for α=0.01 and df=19 degrees of freedom is

Hence the value of the distribution percentage point that I would use when constructing this interval is 2.861

Additional info:

Therefore, based on the information provided, the 99 % confidence for the population mean μ is computed using the following expression

Let me know in the comments if anything is not clear. I will reply ASAP! Please do upvote if satisfied!