Are you really being served red snapper? Refer to the Nature (July 15, 2004) study of fish specimens labeled “red snapper,” presented in Exercise. 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.
Are you really being served red snapper? Red snapper is a rare and expensive reef fish served at upscale restaurants. 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. Researchers at the University of North Carolina used DNA analysis to examine fish specimens labeled “red snapper” that were purchased form vendors across the country (Nature , July 15, 2004). The DNA tests revealed that 77% of the specimens were not red snapper, but the cheaper, look-alike variety of fish.
a. Assuming that the results of the DNA analysis are valid, what is the probability that you are actually served red snapper the next time you order it at a restaurant?
b. If there are five customers at a restaurant, all who have ordered red snapper, what is the probability that at least one customer is actually served red snapper?
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