Question

A consumer advocacy group published a study of labeling of seafood sold in three U.S. states. The group purchased 203 pieces of seafood from various kinds of food stores and restaurants in the three states and genetically compared the pieces to standard gene fragments that can identify the species. The study found that 13 of the 28 ​"red snapper" packages tested were a different kind of fish. Assume that the study used a simple random sample. Complete parts a through c below.

​a) Are the conditions for creating a confidence interval​ satisfied? Explain.

A. ​No, because the sample is a simple random​ sample, the sample is less than​ 10% of the​ population, and there are at least 10 expected​ "successes" and 10 expected​ "failures."

B. ​Yes, because the sample is a simple random​ sample, the sample is less than​ 10% of the​ population, and there are at least 10 expected​ "successes" and 10 expected​ "failures."

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

D. ​Yes, because the sample is a simple random​ sample, the sample proportion is between​ 10% and​ 90%, and there are at least 20 expected​ "successes" and 20 expected​ "failures."

b) Construct a 95​% confidence interval for the proportion 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 states. Select the correct choice below and fill in the answer boxes within your choice. ​(Round to one decimal place as​ needed)

A.​ Ninety-five percent of the​ time, the true proportion of​ "red snapper" sold in these three states that is falsely labeled is between __ and __.

B.There is a 95% chance that the probability of any given​ "red snapper" sold in these three states being actual red snapper is between __ and __.

C.One is 95% confident that between __ and __ of all​ "red snapper" purchased for the study in these three states was not actually red snapper.

D.One is 95% confident that between __ and __ of all​ "red snapper" sold in food stores and restaurants in these three states is not actually red snapper.

Answer 1

a) = 13/28 = 0.464

n = 28 * 0.464 = 12.992

n(1 - ) = 28 * (1 - 0.464) = 15.008

Option - B) Yes, because the sample is a simple random sample, the sample is less than 10% of the population, and there are at least 10 expected "success" and 10 expected "failures".

b) At 95% confidence level, the critical value is

+/- z_0.025 * sqrt((1 - )/n)

= 0.464 +/- 1.96 * sqrt(0.464(1 - 0.464)/28)

= 0.464 +/- 0.1847

= 0.2793, 0.6487

= 0.279, 0.649

C) Option - D) One is 95% confident that between 0. 279 and 0.649 of all " red snapper" sold in food stores and restaurants in these three states in not actually red snapper.