Question

A team of researchers analyzed the meat from each in a sample of 22 "red snappee fish fillets purchased from vendors across a region in an efort estimate the true proportion of fillets that are really red snapper DNA tests revealed that 5 of the 22 fillets (or 23%) were rot red snapper but the cheaper lokalike variety of fish. Complete parts a trough a Identify the parameter of interest to the researchers The parameter of interest is the 7of fish fillets that are actually red snapper b. Explain why a large-sample confidence interval is inappropriate to apply in this study Choose the correct answer below O A. It is inappropriate because the sampling distribution is approximately hormal O B. It is inappropriate because ether the number of successes in the sample or the number of talures in the sample is greater than or equal to 15 O c. It is inappropriate because ether ข, number of successes in the sample or the number of falures n the sample is less than 15. O D. In is inappropriate because the expected probability of success is 0.23 e. Construct a 90% confdence interval for the parameter of interest using Wason's adusmere

Answer 1

the parameter of interest is p the proportion of fish fillets that are actually red snappers

b)

it is inappropriate because either the number of success in the sample or the number of failures in the sample is less than 15

c)

$P = \frac{X+1/2z^2}{n+z^2}$
P = 0.23 (given) , X = 5 and n = 22
alpha = 1 - 0.9 = 0.1
Z (0.1/2) = 1.64

P = (5+1/2(1.64)^2)/ (22+(1.64)^2) = 6.724 / 24.6896 = 0.272

$\\ I: 0.272 &plus;/-1.64* \sqrt \frac{0.272*(1-0.272)}{22} \\ I:\:0.272&plus;/-0.156\\ \\ \mathbf{0.116<p<0.428}$