Question

A team of researchers analyzed the meat from each in a sample of 20 "red snapper" fish fillets purchased from vendors across a region in an effort estimate the true proportion of fillets that are really red snapper, DNA tests revealed that 4 of the 20 fillets (or 20%) were not red snapper but the cheaper look-alike variety of fish. Complete parts a through d a. Identify the parameter of interest to the researchers. The parameter of interest isthe b. Explain why a large-sample confidence interval is inappropriate to apply in this study. Choose the correct answer below V of fish fillets that are actually red snapper. O A. OB. is inappropriate because the sampling distribution is approximately normal. It is inappropriate because either the number of successes in the sample or the number of failures in the sample is greater than or equal to 15 O C. It is inappropriate because the expected probability of success is 0.20. 0 D. It is inappropriate because either the number of successes in the sample or the number of failures in the sam ple is less than 15. C. Construct a 99% confidence interval for the parameter of interest using Wilson's adjustment. The 99% confidence interval is Round to three decimal places as needed.) d. Give a practical interpretation of the confidence interval. With % confidence, the interval found in parte contains the true value of "

Answer 1

Solution:-
a) The parameter of interest is p the true proportion of fish fillets that are actually red snapper.

b. option A.

c. 90% confidence interval : p^ +/- Z*sqrt(pq/(n+4))

p^ = (x+2)/(n+4) = (4+2)/(20+4) = 0.25

=> 0.25 +/- 1.645*sqrt(0.25*0.75/24)

=> 0.105 , 0.395

c. The 995 confidence interval is (0.105,0.395)

d. with 90% confidence, the interval found in part c contains the true value of red snapper.