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 26 out of 842 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.

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.

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.

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

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

Answer #1

a)

sample proportion, = 0.0309

b)

sample size, n = 842

Standard error, SE = sqrt(pcap * (1 - pcap)/n)

SE = sqrt(0.0309 * (1 - 0.0309)/842) = 0.00596

Given CI level is 99%, hence α = 1 - 0.99 = 0.01

α/2 = 0.01/2 = 0.005, Zc = Z(α/2) = 2.576

Margin of Error, ME = zc * SE

ME = 2.576 * 0.00596

ME = 0.0154

CI = (pcap - z*SE, pcap + z*SE)

CI = (0.0309 - 2.576 * 0.00596 , 0.0309 + 2.576 * 0.00596)

CI = (0.016 , 0.046)

lower limit = 0.016

upper limit = 0.046

c)

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

d)

Yes; np > 5 and nq > 5

For this problem, carry at least four digits after the decimal
in your calculations. Answers may vary slightly due to
rounding.
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rounding.
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when caught and released using barbless hooks on flies or lures.
All hooks were removed from the fish.
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