In a combined study of northern pike, cutthroat trout, rainbow trout, and lake t
ID: 3182940 • Letter: I
Question
In a combined study of northern pike, cutthroat trout, rainbow trout, and lake trout, it was found that 32 out of 845 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. (Use 4 decimal places.)
(b) Find a 90% confidence interval for p. (Use 4 decimal places.)
Give a brief explanation of the meaning of the interval.
90% of the confidence intervals created using this method would include the true catch-and-release mortality rate.
90% of the all confidence intervals would include the true catch-and-release mortality rate.
10% of the all confidence intervals would include the true catch-and-release mortality rate.
10% of the confidence intervals created using this method would include the true catch-and-release mortality rate.
lower limit upper limitExplanation / Answer
a.
No. of success(x)=32
Sample Size(n)=845
Sample proportion = x/n =0.038
b.
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Confidence Interval = [ 0.038 ±Z a/2 ( Sqrt ( 0.038*0.962) /845)]
= [ 0.038 - 1.645* Sqrt(0) , 0.038 + 1.65* Sqrt(0) ]
= [ 0.027,0.049]
c.
90% of the all confidence intervals would include the true catch-and-release mortality rate.