The biologist is studying Black Carp invasiveness in Lake Ontario next. He doesn't have time to sample the fish himself, so instead he instead asks a fisherman who has been fishing off of one of Toronto's piers all morning about his catch. The fisherman responds that, of the 75 fish he has caught, 47 have been Black Carp. What is the lower bound of a 99% confidence interval for the true proportion of fish that are Black Carp in Lake Ontario

The 99% confidence interval for the true proportion of fish that are Black carp in Lake Ontario

(0.4828 , 0.7704)

Step-by-step explanation:

Step(i):-

Given that the fisherman responds that, of the 75 fish he has caught, 47 have been Black carp

Sample proportion =

We have to find the 99% confidence interval for the true proportion of fish that are Black carp in Lake Ontario

Step(ii):-

solution:-

Given that the level of significance = 0.01

Z-score = 2.576

The 99% confidence interval for the true proportion of fish that are Black carp in Lake Ontario

After calculation, we get

(0.6266 - 0.1438 , 0.6266 +0.1438)

(0.4828 , 0.7704)

Final -

The 99% confidence interval for the true proportion of fish that are Black carp in Lake Ontario

(0.4828 , 0.7704)