(25 marks) A property developer suggested to build a private residential estate by a lake,

in hope for its high return. An environmentalist, however, objected strongly to this project

as the living environment of the fish would be seriously damaged. They finally came to an

agreement depending on a critical value 21000. Denote as the number of fish living in the

lake, and the project should be passed if < 21000 and suspended if > 21000. Unaware

of the exact value of , field investigators took 1000 fish from the lake, marked them, and

returned them. Over the next month, they caught 2000 fish and found that 100 of them

were marked. (Suppose the significance level 0:05)

(a) (10 marks) Conduct the hypothesis test

H0 : 21000 vs HA : > 21000;

and argue whether the project should be passed or suspended