two sample t test - comparing rates

Hi

I have been asked to evaluate the below results from a fundraising campaign, and conclude whether there are any differences between the TEST and CONTROL groups. Specifically, i need to decide whether the response rate and income per £ invested are significantly higher in the TEST group.

I would be grateful for any help with this, i think i may have the answer for the response rate test. I believe this would involve a two sample t test using Mailing volume as the 'n1' and 'n2', and estimating the sample standard deviation as SQRT(p*(1-p)) where p is the observed response rate in both samples, given that these are bernoulli trials. I would be grateful if anyone could confirm this approach, and how i could carry out a similar analysis for income per £ invested (which doesnt constitute a bernoulli trial).

Many thanks
Colin

CONTROL VS TEST	Mailing Volume	Responses	Income	Cost	response rate	income per £ invested
TEST	2140	211	£8,845	£1,070	0.099	8.27
CONTROL	576	32	£1,489	£288	0.056	5.17

Follow this example.


Hypothesis Test: Difference in Proportions


Make the response rate for the test group and the response rate for the control group

Use the case where

Thanks for this very quick response. But if i need to estimate the standard deviation would it not be a t-test (as opposed to analysis using the Normal Distribution)? Im fine with the logic other than that.

Also, can you advise how i might compare 'income per £ invested' in the same way?

I really appreciate the help here

Bests,
Colin