Exam 11: Asking and Answering Questions About the Difference Between Two Population Proportions

Careful and constant and hygiene is necessary to reduce the chance of transmitting pathogens by healthcare professionals. Despite the importance of hand hygiene, getting good compliance is challenging. One complicating factor is the potential for observer bias. That is, compliance monitors might be fellow workers who might report higher compliance than neutral observers. A study designed to assess this possibility was conducted in a hospital in a large city. Trained observers working "under cover" - monitored hand hygiene compliance of a randomly selected sample of healthcare professionals over a calendar year. Some observers worked in the same hospital as the professional being observed (Unit-based) while others did not (Non- Unit-based). Data from one of the hospital units are presented in the table below. Do these data provide sufficient evidence of the existence of observer bias? Hand hygiene compliance: Unit- and Non-unit-based monitors Observers Unit based Non Unit based Total Compliance 92 188 280 Non-compliance 37 108 145 Total 129 296 425 a) What are the appropriate null and alternative hypotheses? b) Show the necessary calculations to demonstrate it is reasonable to use the large- sample test for a difference in population proportions for these data. c) Test the hypothesis you indicated in part (a), and interpret your result in the context of the study.

The pre-historic development of agriculture is an active area of research among anthropologists. The transition from a hunter-gatherer society to an agricultural society is generally assumed to be signaled by an increase in cavities in teeth. Investigators recently studied teeth unearthed in two societies in Colorado: Basketmakers, societies living in small villages, and Post-Basketmakers, societies living in above-ground architectures such as pueblos. The investigators were interested in whether the shift in shelter was associated with a shift in consumption from hunting (meat) to agriculture (maize). Data on the numbers of individuals with interproximal (between teeth) cavities are shown in the table below. Inter-proximal cavities tend to occur more among populations subsisting primarily on agricultural products. You may assume that it is reasonable to regard these two samples as representative of teeth from these two populations. Population Inter- Proximal Cavities No Inter- proximal Cavities Basketmaker 68 91 Post-Basketmaker 60 39 a) Construct and interpret a 90% confidence interval for the difference in population proportions of individuals with interproximal cavities, Basketmaker - Post- Basketmaker. b) Interpret the 90% confidence level c) Based on your results in parts (a) and (b), would you say that a shift in consumption patterns is a reasonable conclusion on the part of the investigators? Justify your response with statistical evidence from parts (a) and/or (b).