1. A certain lake containing the invasive species zebra mussels is considered \"

Question

1. A certain lake containing the invasive species zebra mussels is considered "healthy" if the average number of zebra mussels per acre is less than or equal to 100,000. If the average is larger than 100,000, the lake is considered "infested" and will be treated with pesticide, killing all the aquatic fauna. (a) (2 pts Write down the appropriate null and alternative hypotheses corresponding to the lake being "healthy" or "infested". (c) {2 pts) In the context of the problem, explain the Type I error and the consequences of making this error

Explanation / Answer

let u denotes the actual average number of zebra mussels per acre.

if u<=100,000 then it is categorized as healthy otherwise if u>100,000 it is categorized as infested.

a) so null hypothesis is H0: u<=100,000 and alternative hypthesis is u>100,000

b) the error diagram is as follows

testing conclusion

is lake is healthy

now if the lake is actually healthy and the conclusion is that leake is healthy then there is no error

and also if the lake is actually infested and the conclusion is that the lake is infested then also there is no error

but if lake is actually healthy but the conclusion is that lake is infested then we are making an error. and this error is called type 1 error.
type 1 error is that error when we wrongly reject a true null hypothesis.

if the lake is actually infested and the conclusion is that the lake is healthy then also we are making an error and that is called type 2 error.

type 2 error is that error when we wrongly accept a false null hypothesis.

c) in the context of the problem type 1 error is declaring the lake as infested when the lake is actually healthy.

because here null hypothesis is that the lake is healthy and the lake is actually healthy but we are rejcting H0.

which means we are rejecting a true null hypothesis.

in this problem type 1 error is more serious. because if the lake is declared as infested then it will be treated with pesticides and all the aquatic fauna will die. but since the lake is healthy there is no need to this. so basically by committing type 1 error we are destroying the biosystem of the lake when there is no need to doing it.

d)

in the context of the problem type 2 error is declaring the lake as healthy when the lake is actually infested.

because here null hypothesis is that the lake is healthy but the lake is actually infested but we are accepting H0.

which means we are accepting a false null hypothesis.

then no action will be taken and the lake will remain as infested which will affect the biosystem of the lake

u<=100,000 (lake is healthy) u>100,000(lake is infested)

testing conclusion

is lake is healthy

correct decision error2 testing conclusion is lake is infested error1 correct decision

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.