Water pipe to be used in a certain application is required to have a mean breaking strength of more than 2000 pounds per foot. A test is made of Hv0 : u =2000 versus Hv1 : u>2000. There are two possible errors. Identify them.

Question

a) The true mean is greater than 2000, but the pipe is not used. This is a type [blank] error

Answer 1

a) The true mean is greater than 2000, but the pipe is not used. This is a type II error.

In statistical hypothesis testing, a type II error occurs when the null hypothesis (in this case, that the mean breaking strength is 2000 or less) is not rejected when, in fact, it is false (the true mean is greater than 2000).

The alternative (type I) error would be rejecting the null hypothesis when it is actually true.

Answer 2

(b) The true mean is 2000 or less, but the pipe is used. This is a type [blank] error

Answer 3

b) The true mean is 2000 or less, but the pipe is used. This is a type I error.

In this case, a type I error occurs when the null hypothesis (that the mean breaking strength is 2000 or less) is rejected when it is actually true. This means that the pipe would be used despite it not meeting the safety requirement, leading to potential failure in the application.