Question

which type of error? 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 $h_0: \mu = 2000$ versus $h_1: \mu > 2000$. there are two possible errors. identify them.
part: 0 / 2
part 1 of 2
(a) the true mean is greater than 2000, but the pipe is not used.
this is a type select error.
i ii

Explanation:

Step 1: Recall Type I and Type II Errors

Type I error: Reject \( H_0 \) when \( H_0 \) is true.
Type II error: Fail to reject \( H_0 \) when \( H_0 \) is false.

Step 2: Analyze the Scenario

Here, \( H_0: \mu = 2000 \), \( H_1: \mu > 2000 \). The true mean \( \mu > 2000 \) (so \( H_0 \) is false), but we fail to reject \( H_0 \) (pipe not used, implying we didn't conclude \( \mu > 2000 \)).

Step 3: Identify the Error Type

Failing to reject a false \( H_0 \) is a Type II error.

Answer:

Type II