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 38 out of 863 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.

99% 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.    1% of the confidence intervals created using this method would include the true catch-and-release mortality rate.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.

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

Answer 1

a) Point estimate of p is given by

b) 99% confidence interval for p

For 99% confidence , zc =2.58

99% confidence interval is

=

= (0.0260 , 0.062)

lower limit = 0.0260

upper limit = 0.062

Explanation

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

Note : If we create 100 confidence interval for true proportion , 99 of them will include true population proportion that is true catch and release mortality rate .

(c) n=863

p = 0.0440

np = 38

q= 1-p = 0.956

nq= 825

Answer is: Yes , np > 5 and nq>5

Note : Normal approximation to binomial is satisfied if np > 5 , nq >5