Boneitis is in the news again: several cases have been reportedin Miami, and more are soon to follow. In order to receive aid fromthe state government, the city of Miami has to provide a smallamount of evidence that the prevalence of the disease (i.e., theproportion of Miami residents who have boneitis) is greater than20%. City ocials took a random sample of 200 residents and foundthat 33.0% had been diagnosed with boneitis.
(a) (4 points) Perform a z-test at the 0.01 significance levelto determine if this sample provides evidence that the prevalenceof boneitis in Miami is greater than 20%. Be sure to state the nulland alternative hypotheses, any calculator functions you use(including inputs and relevant outputs), and clearly state yourconclusion in context.
(b) (3 points) Construct a 95% plus-two confidence interval forpˆ, the sample proportion of Miami residents with boneitis. Showyour work, including any calculator functions you use, and be sureto round interval bounds properly.
