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 20 out of 860 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

Answer 1

Solution :

Given that,

n = 860

x = 20

a)

Point estimate = sample proportion = = x / n = 20/860 = 0.023

1 - = 1-0.023 = 0.977

At 99% confidence level

= 1-0.99% =1-0.99 =0.01

/2 =0.01/ 2= 0.005

Z/2 = Z_{0.005 = 2.576}

Z/2 = 2.576

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 2.576 * ((0.023*(0.977) /860 )

= 0.013

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.023-0.013 < p < 0.023+0.013

(0.010,0.036)

Lower limit = 0.010

Upper limit = 0.036