Tuberculosis (TB) is an infectious disease caused by the Mycobacterium tuberculosis bacteria. Active TB can be cured by adhering to a treatment regimen of several drugs for 6-9 months. A major barrier to eliminating TB worldwide is failure to adhere to treatment; this is known as defaulting from treatment. A study was conducted in Thailand to identify factors associated with default from treatment. The study results indicate that out of 54 diabetic participants, 0 defaulted from treatment; out of 1,180 non-diabetic participants, 54 defaulted from treatment. Participants were recruited at health centers upon diagnosis of TB.

(a) Create a two-way table presenting the results of this study.

(b) State appropriate hypotheses to test for difference in proportions of treatment default between diabetics and non-diabetics.

(c) Check assumptions. You may use a less stringent version of the success-failure condition: the expected number of successes per group should be greater than or equal to 5 (rather than 10).

(d) Formally test whether the proportion of patients who default from treatment differs between diabetics and non-diabetics. Summarize your findings.