Careful and Constant and Hygiene Is Necessary to Reduce the Chance

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? $$\begin{array}{l}\text { Hand hygiene compliance: Unit- and Non-unit-based monitors }\\\begin{array} { | c | c | c | c | } \hline \text { Observers } & \begin{array} { c } \text { Unit } \\\text { based }\end{array} & \begin{array} { c } \text { Non } \\\text { Unit based }\end{array} & \text { Total } \\\hline \text { Compliance } & 92 & 188 & 280 \\\text { Non-compliance } & 37 & 108 & 145 \\\text { Total } & 129 & 296 & 425 \\\hline\end{array}\end{array}$$ 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.