4
$\begingroup$

It was suggested that this forum may be quite helpful. My most humble apologies if I am somehow not posting in the right place!

My bosses asked me (I am not a statistician) how many letters have to be mailed out in a certain county in order to see if the response rate for the whole list is likely to be at least 10%?

I have no training in statistics and am completely confused at this point. Here are the relevant numbers that should be necessary to arrive at an answer, though:

  • The county has 1,532 locations that could be mailed.
  • My bosses would like to be a minimum of 80% sure.
  • The response rate of the letter is generally 10% anywhere in the United States (I'm not sure if this number is relevant or not).

How many letters must be sent to determine with about 80% confidence that the whole (1,532) list will be as responsive as normal (10%)?

I'd be delighted to to add whatever numbers or answers I might have unintentionally left out.

Improve this question
$\endgroup$
1
  • 1
    $\begingroup$ I suspect that there is a problem with the way the question is asked. Sending more letters will not increase the rate of response, so “how many letters do we have to send to be 80% sure that the response will be 10%” can’t be what is truly sought. As @asdf points out, given an effect size like 5%, we can ask how many letters do we need to send to be 80% sure the answer is 15% rather than the null-hypothetical 10%, based on something like a 95% confidence interval around 10%. ( He says its 150. Sounds plausible to me.) So please verify the exact question you mean to ask. $\endgroup$
    – Peter Leopold
    Commented Mar 2, 2019 at 3:41

1 Answer 1

Reset to default
0
$\begingroup$

Well, it depends on the actual response rate itself. If it is very far from 10%, you will need fewer. If it is 9,99999999%, your grandchildren would be sending letters without still finding a significant difference.

As a reference, if the response rate was close 15%, you would find out after about 150 letters sent

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.