In a combined study of northern pike, cutthroat trout, rainbow trout, and lake trout, it was found that 40 out of 866 fish died when caught and released using barbless hooks on flies or lures. All hooks were removed from the fish.   (a) Let p represent the proportion of all pike and trout that die (i.e., p is the mortality rate) when caught and released using barbless hooks. Find a point estimate for p. (Round your answer to four decimal places.) (b) Find a 99% confidence interval for p. (Round your answers to three decimal places.) lower limit       upper limit       Give a brief explanation of the meaning of the interval. We are 99% confident that the true catch-and-release mortality rate falls outside this interval.We are 1% confident that the true catch-and-release mortality rate falls above this interval.    We are 99% confident that the true catch-and-release mortality rate falls within this interval.We are 1% confident that the true catch-and-release mortality rate falls within this interval. (c) Is the normal approximation to the binomial justified in this problem? Explain. Yes; np < 5 and nq < 5.

Question

In a combined study of northern pike, cutthroat trout, rainbow trout, and lake trout, it was found that 40 out of 866 fish died when caught and released using barbless hooks on flies or lures. All hooks were removed from the fish.

 
(a) Let p represent the proportion of all pike and trout that die (i.e., p is the mortality rate) when caught and released using barbless hooks. Find a point estimate for p. (Round your answer to four decimal places.)


(b) Find a 99% confidence interval for p. (Round your answers to three decimal places.)
lower limit      
upper limit      

Give a brief explanation of the meaning of the interval.
We are 99% confident that the true catch-and-release mortality rate falls outside this interval.We are 1% confident that the true catch-and-release mortality rate falls above this interval.    We are 99% confident that the true catch-and-release mortality rate falls within this interval.We are 1% confident that the true catch-and-release mortality rate falls within this interval.

(c) Is the normal approximation to the binomial justified in this problem? Explain.
Yes; np < 5 and nq < 5.

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