Question

A consumer advocacy group published a study of labeling of seafood sold in three U.S. states. The study found that 11 of the 22 .red snapper packages tested were a differe kind of fish. Assume that the studv used a simple random sample. Complete parts a through c boiow. a) Are the conditions tor creating a conticence interval satstied? texplain. A. No, bocause the sample is a simple random sample, the sample propertion is between 10% and 90%, and there are at least 20 "successes" and 20 "tailures" B. No, bocause the sample is a simple random sample, the samplo is less than 10% of the population, and there are at least 10 "successes" and 10 "fallures." C. Yes, because the sample is a simple random sample, the samplo proportion is between 10% and 90%, and there are at least 20 "suiccesses" and 20 "ailures." D. Yes, because the sample is a simple random sample, the sample is less than 10∗ of the population, and there are at least 10 "successes" and 10 "Ialures." b) Construct a 95% confidence interval for the proporton of "red snapper" packages that were a different kind of fish. (Round to three decimal places as needed.) c) Explain what the confidence interval from part (b) says about "red snapper" sold in these three statos. Select the cocrect choice below and fill in the answer bexes wthin you choice. (Round to one decimal place as needed.) A. There is a 95% chance that the probability of any glven "red snapper" sold in these three stases being actual rod snapper is besween B. Ninety five percent of the time, the true proportion of "red snopper" sold in these three stales that is falsely labeled is betwean C. One is 95% confident that between % and $ of al "red snapper purchased for the study in these three states was not actualy red snapper D. One is 95% confident that between. \% and W of a1 "red snapper" sold in food stores and restaurints in these three states is not actualy red snapper.

Answer 1

a) No, because the sample is a simple random sample, the sample proportion is between 10% and 90%, and there are at least 20 "successes" and 20 "failures."

b) The 95% confidence interval for the proportion of "red snapper" packages that were a different kind of fish is (0.303, 0.697).

Step-by-step explanation:

a) The conditions for creating a confidence interval are satisfied based on the given information. The sample is a simple random sample, the sample proportion is between 10% and 90%, and there are at least 20 "successes" and 20 "failures," fulfilling the requirements for constructing a valid confidence interval.

b) To construct the 95% confidence interval, we can use the formula for a confidence interval for a proportion:
`\[\text{CI} = \hat{p} \pm z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\] where \(\hat{p}\)` is the sample proportion, z is the Z-score for the desired confidence level, and n is the sample size. Plugging in the values, we get a confidence interval of (0.303, 0.697) for the proportion of "red snapper" packages that were a different kind of fish.

c) The confidence interval (0.303, 0.697) indicates that we are 95% confident that the true proportion of "red snapper" packages mislabeled as a different kind of fish in the population falls within this range. In other words, there is a high degree of certainty that between 30.3% and 69.7% of "red snapper" packages sold in the three states were falsely labeled.