Question

1.Water samples were taken from water used for cooling as it was being discharged from a power plant into a river. It has been determined that as long as the mean temperature of the discharged water is at most 150 F, there will be no negative impact on the river's ecosystem. To investigate whether a plant is in compliance with regulations that prohibit a mean discharge water temperature above 150 F, researchers took 50 water samples at randomly selected times and recorded the temperature of each sample. It is known that the temperature of the discharged water is normally distributed.

a. Determine an appropriate null and alternative hypothesis for this test.

b. In the context of this situation, describe type I and type II errors

c. Which type of error would you consider more serious? Explain, please.

Answer 1

ANSWER :-

(a).

According to given data , the null and alternative hypothesis are written as  

Null hypothesis is H : = 150 F

Alternative hypothesis is H : > 150 F

here consider type I error: it rejects the null hypothesis when it is true.

and type II error : it is fail to rejects the null hypothesis when it is false.

(b).

In the context of this situation, the Type I error and Type II errors are described as below.

Type I Error : dismiss the mean temperature of the released water is at most 150 degree F when it is valid. that implies , the plant isn't in consistence with controls that forbid a mean release water temperature. that is, we reason that the plant isn't in consistence when it is.

Type II Error : neglect to dismiss the mean temperature of the released water is at most 150 degree F when it is false. that implies , the plant is in consistence with controls that deny a mean release water temperature. that is, we reason that the plant is in consistence when it isn't.

(c).

from above outcomes , it is derived that type II mistake is more serious than type I error.