Question

22. In a combined study of northern pike, cutthroat trout, rainbow trout, and lake trout, it was found that 38 out of 836 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.

a.99% of all confidence intervals would include the true catch-and-release mortality rate.

b.99% of the confidence intervals created using this method would include the true catch-and-release mortality rate.     

c.1% of the confidence intervals created using this method would include the true catch-and-release mortality rate.

d.1% of all confidence intervals would include the true catch-and-release mortality rate.

(c) Is the normal approximation to the binomial justified in this problem? Explain.

a.Yes; np > 5 and nq > 5.

b.No; np < 5 and nq > 5.

c.No; np > 5 and nq < 5.

d.Yes; np < 5 and nq < 5.

Answer 1

The statistical software output for this problem is:

On the basis of above output:

a) Point estimate of p = 0.0455

b) 99% confidence interval:

Lower limit = 0.027

Upper limit = 0.064

Explanation: 99% of the confidence intervals created using this method would include the true catch-and-release mortality rate. Option B is correct.

c) Yes; np > 5 and nq > 5