Suppose that in a simple random sample of 30 chicken carcasses from the ACME chicken plant (which has 10,000 chickens), 5 test positive for salmonella and 25 test negative for salmonella. Provide a...

Suppose that in a simple random sample of 30 chicken carcasses from the ACME chicken plant (which has 10,000 chickens), 5 test positive for salmonella and 25 test negative for salmonella. Provide a point estimate and 95% CIs for the prevalence of salmonella among chicken carcasses from the ACME plant, assuming the test is 100% accurate.

For the confidence interval, use a two-sided interval and report results from both the “exact method” and the “normal-theory method” (large sample approximation), then comment on whether the normal-theory method is reasonable based on comparison with results from the exact method.