Question

In a combined study of northern pike, cutthroat trout, rainbow trout, and lake trout, it was found that 36 out of 830 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.)

lower limit

upper limit

Give a brief explanation of the meaning of the interval.

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.

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.

Answer 1

Solution :

Given that,

n = 830

x = 36

a) Point estimate = sample proportion = = x / n = 36 / 830 = 0.0434

1 - = 1 - 0.0434 = 0.9566

b) At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_0.05 = 1.645

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

= 1.645 (((0.0434 * 0.9566 ) / 830 )

= 0.0116

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.0434 - 0.0116 < p < 0.0434 + 0.0116

( 0.0318 < p < 0.0550 )

lower limit = 0.0318

upper limit = 0.0550

90% of the confidence intervals created using this method would include the true catch-and-release mortality rate.