In a combined study of northern pike, cutthroat trout, rainbow trout, and lake t
ID: 3151353 • Letter: I
Question
In a combined study of northern pike, cutthroat trout, rainbow trout, and lake trout, it was found that 24 out of 827 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 forp. (Use 4 decimal places.)
(b) Find a 98% confidence interval for p. (Use 4 decimal places.)
Give a brief explanation of the meaning of the interval.
98% of the confidence intervals created using this method would include the true catch-and-release mortality rate.98% of the all confidence intervals would include the true catch-and-release mortality rate. 2% of the all confidence intervals would include the true catch-and-release mortality rate.2% of the confidence intervals created using this method would include the true catch-and-release mortality rate.
lower limit upper limitExplanation / Answer
a)
Note that
p^ = point estimate of the population proportion = x / n = 24/827 = 0.029020556 [ANSWER]
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b)
Also, we get the standard error of p, sp:
sp = sqrt[p^ (1 - p^) / n] = 0.005837207
Now, for the critical z,
alpha/2 = 0.01
Thus, z(alpha/2) = 2.326347874
Thus,
Margin of error = z(alpha/2)*sp = 0.013579375
lower bound = p^ - z(alpha/2) * sp = 0.015441181
upper bound = p^ + z(alpha/2) * sp = 0.042599931
Thus, the confidence interval is
( 0.015441181 , 0.042599931 ) [ANSWER]
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c)
OPTION A: 98% of the confidence intervals created using this method would include the true catch-and-release mortality rate. [ANSWER]