Since the sample size in Problem 2.1 is not very large, it is better to use exact tests.

(a) Apply exact tests to test the hypothesis in (2.48) for the data in Problem 2.1 and compare your results with those derived from asymptotic tests.

(b) Change \(H_{a}: p>0.3\) in (2.48) to \(H_{a}: p

(c) Change \(H_{a}: p>0.3\) in (2.48) to \(H_{a}: p eq 0.3\) and repeat (a).

Provide the steps that lead to your answers in (a)-(c).

Transcribed Image Text:

2.1 A random sample of 16 subjects was taken from a target population to study the prevalence of a disease p. It turned out that six of them were diseased. (a) Estimate the disease prevalence p. (b) Use the asymptotic procedure to test . Ho p=0.3 VS. Ha p>0.3. : (c) Change Ha p>0.3 in (2.48) to Ha: p <0.3 and repeat (b). (d) Change Ha p > 0.3 in (2.48) to Ha p0.3 and repeat (b). (2.48)