Question

A consumer advocacy group published a study of labeling of seafood sold in three U.S. states. The study found that 15 of the 25 ​"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. ​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. ​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 is less than​ 10% of the​ population, and there are at least 10 expected​ "successes" and 10 expected​ "failures."

D. ​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." ​

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) One is 95% confident that between ________% and ______________% of all red snapper sold in food stores and restaurants in these states is not actually re snapper.

B) 98% of the time, the true proportion of red snapper sold in these three states is falsely labeled is between__________% and ________%.

C) One is 95% confident that between ______% and ________% of all red snapper purchased for the study in these states was not actually red snapper.

D) 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".

Answer 1

a) Sample size is 25 , which is less than 10% of the population . Expected success ,np is 15 and expected failure, n(1-p) is 10 . That is np 10 and n(1-p) 10 .

Answer is

B) Yes , because the sample is 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) The 95% confidence interval for actual proportion is

where

   15/ 25 = 0.6

n= 25

For 95% confidence , from z table we get , zc = 1.96

Therefore , 95% confidence interval for proportion of red snapper that were a different kind of fish

= ( 0.408 , 0.792)

c) Answer is

A) One is 95% confident that between 40.8% and 79.2 % of all red snappers sold in food stores and restaurants in these states is not actually red snappers.

Note : For 95% confidence , from z table we get , zc = 1.96

that is P( -1.96 < z < 1.96) = 0.95