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 30 out of 857 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.)

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.

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

lower limit     upper limit     For thls problem, carry at least four diglts after the decimal In your calculations. Answers may vary slightly due to rounding Tn a combined study of northern pike, cutthroat trout, rainhow trout, and lake trout, it was found that 30 out of 857 tish died when caught and released using barhless hooks on flies or lures. All hooks were removed from the fish. a Let represent the proportion o al pike and trout that die Le places.) p is the mortality rate when caught and released using ba bless hooks Find a point estimate or Round ouran e our decimal (b) Find a 99% confidence interval for p. (Round your answers to three decimal places.) lower llmit 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. O 99% of all confidence intervals would include the true catch-and-release mortality rate. O 1% of uhe confidence intervals created using this method would include lhe true catch-and-release mortality rate. (c) Is the normal approximation to the binomial ustified in this problem? Explain. No; np 5. Yes; np 5 and nq > 5.

Explanation / Answer

The statistical software output for this problem is:

One sample proportion summary confidence interval:
p : Proportion of successes
Method: Standard-Wald

99% confidence interval results:

a) Point estimate of p = 0.0350

b) 99% confidence interval:

(0.019, 0.051)

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

c) Yes; np > 5 and nq > 5.

Proportion Count Total Sample Prop. Std. Err. L. Limit U. Limit p 30 857 0.035005834 0.0062783012 0.018834002 0.051177667

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