For this problem, carry at least four digits after the decimal in your calculati

Question

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding In a combined study of northern pike, cutthroat trout, rainbow trout, and lake trout, it was found that 28 out of 82.1 fish died when caught and released using barbless hooks on files 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. 1% of all confidence intervals would include the true catch and release mortality rate. 99% of the confidence intervals created using this method would include the true catch and release mortality rate. 99% of all confidence intervals would include the true catch and release mortality rate. 1% of the confidence intervals created using this method would include the true catch and release mortality rate. (c) Is the normal approximation to the binomial justified in this problem? Explain, Yes: np > 5 and ng > 5 Yes: np 5. No: np 5.

Explanation / Answer

a)
p = 28 / 821 = 0.0341
Point estimate is 0.0341

b)
For 99% CI z value = 2.576

CI = P + / - z * sqrt(p(1-p)/n)
= 0.0341 + / - 2.576 * sqrt ( 0.0341 * 0.9658 / 821)
= (-0.092 , 0.161)

c) np = 821 * 0.0341 = 27.99
nq = 821 * 0.9658 = 792.92

Yes , because np > 5 and nq >5

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