Question

Water used for cooling from a power plant is discharged into a nearby river. The temperature of the discharged water is recorded at random times. As long as the temperature is below 150o F, the river's ecosystem will be not be damaged. Hint: You want to prove that the ecosystem is safe.

(1 pt.) a) State the null and alternative hypotheses. Write '≤' as '<=' and '≥' as '>='.

(1 pt.) b) In context, explain what the Type I error is.

(1 pt.) c) In context, explain what the Type II error is.

(1 pt.) d) Which error is worse for the ecosystem, a Type I error or a Type II error? Why?

Answer 1

a)

Ho: µ >= 150

H1:µ<150

b)

Type I error is rejecting Ho when it is true

Type I error is concluding that the river's ecosystem will be not be damaged, while in actual, it will be damaged

or

Type I error is concluding that temperature is below 150 while in actual it it greater than equal to 150

c)

Type II error is concluding that temperature is greater than equal to 150, while in actual it below 150

d)

Type I error is worse. because, it will lead to damage of river's ecosystem