A consumer advocacy group published a study of labeling of seafood sold in three

Question

A consumer advocacy group published a study of labeling of seafood sold in three U.S. states. The group purchased 241 pieces of seafood from various kinds of food stores and restaurants in the three states and genetically compared the pleces to standard gene fragments that can identify the species. The study found that 10 of the 24 "red snapper packages tested were a dMerent 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. O A No, because the sample is a simple random sample, t e sample proportion is between 10% and 90%, and there are at least 20 expected 'successes and 20 expected faires." B. No, because the sample is a simple random sample, the sample is less tar, 10% ofthe population, and there are at least 10 expected "sucesses" and 10 oxpected-alures . C· Yos, because the sample is a simple random sample, te sample s less than 10% of the population·ard tero are at last 10 expected-successes-and 10 expected alves.. D· Yos, because the sample is simple random sample, the sample propofon is between 10% and 90%, and hero are at least 20 expected "successes. and 20 expected alres b)Construct a 96% confiden e interval for the proportion of "red snapper" packages that were a dfferent kind of fish. Round to tree decimal places as needed) c) Explain what the conidence interval from part (b) says about "red snapper sold in hese three states. Select the correct choice below and Sl in the answer boxes within your choice Round to one decimal place as needed. d A. There is a 95% chance that the probablity of any given red snapper sold itese three states being actual red snapper is between 1% and % O BOne is 95% oorfdent that between % and % of all "red snapper" purchased for the study in these three states was not actually red snapper. C. Nine tron pero t of the time, the true proportion of "red snapper sold in these three states that is falsely labeled-between % and %. D One is 95% oorfdent that between l % and % of all red snapper sold in food stores and restaurants in these tree states is not actualy red snapper.

Explanation / Answer

Part a

Correct Answer: C

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

Explanation:

We are given population size = N = 241, 10% of 241 = 24.1

Sample size = n = 24

Sample size < 10% of population size

Also, sample is simple random and there are 10 successes out of 24 and 14 failures out of 24.

Part b

We are given

n = 24, x = 10,

Sample proportion = P = x/n = 10/24 = 0.416666667

Confidence level = 95%

Critical Z value = 1.96 (by using z-table)

Confidence interval = P -/+ Z*sqrt(P*(1 – P)/n)

Confidence interval = 0.416666667 -/+ 1.96*sqrt(0.416666667*( 1 - 0.416666667) / 24)

Confidence interval = 0.416666667 -/+ 1.96*0.1006

Confidence interval = 0.416666667 -/+ 0.1972

Lower limit = 0.416666667 - 0.1972 = 0.219

Upper limit = 0.416666667 + 0.1972 = 0.614

Confidence interval = (0.219, 0.614)

Part c

Correct Answer: D

One is 95% confident that between 21.9% and 61.4% of all ‘red snapper’ sold in food stores and restaurants in these three states is not actually red snapper.

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