1. ## Difficult Statistics questions

Hello, I am having quite a bit of difficulty with the following questions:

I am not sure how the letters will produce poor samples for certain inquiries. Also, I am not sure about question #2 at all. If anyone can point me in the right direction I would greatly appreciate it.

Ishihara

2. ## Re: Difficult Statistics questions

Hey ishihara.

Hint: What happens when more than one persons have the same last letter at the start of their last name? How would this bias the sample?

Also you need to specify what you are estimating and what kinds of inferences and/or hypotheses you are making. Are you for example converting A-Z to numbers 1-26 and treating these as a uniform discrete distribution?

3. ## Re: Difficult Statistics questions

I think I understand your hint: If two people have the same letter at the beginning of their last name, we have a higher likelihood for bias.

So if we have a total of N people we are selecting from, certain letters may be more common as a first letter of the last name ("S" vs. "Q").

I know that $Bias = E[\hat{t}] - t$, but I'm not sure how to demonstrate that it is affected.

In terms of variance, I also believe this is affected. There are a large variation of last names, but like you stated before, you can select the same last name more than once.

4. ## Re: Difficult Statistics questions

What specific parameter are you estimating? This is the first step you need to answer before moving on to bias and variance.