Question

A team of researchers analyzed the meat from each in a sample of 27 ​"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 6 of 27 the fillets​ (or ​22%) were not red snapper but the cheaper​look-alike variety of fish.

a. Identity the parameter ot interest to the researchers. The parameter of interest is the of fish fillets that are actually red snapper.
b. Explain why a large-sample confidence interval is inappropr
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.)

Answer 1

The parameter of interest is the true proportion of red snapper among the fillets. A large-sample confidence interval is inappropriate due to the small sample size and the proportion not being close to 50%. Wilson's adjustment is used instead to create a 99% confidence interval, but specific calculations are not provided.

Step-by-step explanation:

The parameter of interest to the researchers is the true proportion of fish fillets that are actually red snapper. Since the sample size is relatively small (27 fillets), and the sample proportion (22%) is not very close to 50%, the use of a large-sample confidence interval is inappropriate. Instead, Wilson's adjustment will be used to create a more accurate 99% confidence interval. Wilson's formula takes into account the sample size and the observed proportion to adjust the confidence interval in situations where standard large-sample intervals may not perform well.

To construct the 99% confidence interval using Wilson's adjustment, one needs to follow specific statistical procedures which include incorporating the number of successes, the total number of trials, and the desired level of confidence. The calculations will provide the lower and upper bounds that estimate the range within which the true proportion of actual red snapper fillets is likely to fall.

Unfortunately, without performing the necessary calculations, which require more detailed statistics formulas and potentially software, the exact confidence interval cannot be provided here.