58 Are you really being served red snapper? Nature (July 15, 2004) conducted a study of fish specimens labeled “red snapper.” Recall that federal law prohibits restaurants from serving a cheaper look-alike variety of fish (e.g., vermillion snapper or lane snapper) to customers who order red snapper. In an effort to estimate the true proportion of fillets that are really red snapper, a team of University of North Carolina (UNC) researchers analyzed the meat from each in a sample of 22 “red snapper” fish fillets purchased from vendors across the United States. DNA tests revealed that 17 of the 22 fillets (or 77%) were not red snapper, but the cheaper look-alike variety of fish.

a. Identify the parameter of interest to the UNC researchers.

b. Explain why a large-sample confidence interval is inappropriate to apply in this study.

c. Use Wilson’s adjustment to construct a 95% confidence interval for the parameter of interest.

d. Give a practical interpretation of the confidence interval.