Statistical agencies depend on responses to inquiries made to the public, and occasionally conduct experiments to improve contact procedures. Agencies may explicitly seek improved response rates, or may wish to assess whether or not there is significant change in response rates due to an operational improvement. The present work considers statistical experiments to assess household response rates when up to L attempts are made to contact each household. The process can be viewed as a sequence of L binary trials carried out until either the first success is observed, or failures occur in all L trials. Sequential regression models are used to associate the probabilities in such a sequence to covariates of interest. In particular, the continuation-ratio logit (CRL) model facilitates inference on the probability of success at each step of the sequence, given that failures occurred at previous steps. The CRL model is investigated as a basis for sample size determination—one of the major decisions faced by an experimenter. An adequate sample size is sought to attain a desired power for a Wald test of a general linear hypothesis. A motivating application is provided by an actual experiment being considered for nonresponse follow-up in the United States 2020 Decennial Census. The experiment involves assessment of a training module which provides guidance to enumerators interviewing Spanish speaking households. Data analysis and sample size determination based on the CRL model are both addressed in detail. Taking the enumerator training experiment as an illustration, some typical features of an experiment by a statistical agency are also encountered, such as access to a portion of covariate data in advance of the experiment and constraints on the design due to the operation.