Question

A company makes wires with mean breaking strength of wires is greater than 50.
They measure and test Hv0 : u =50 versus Hv1 : u > 50

If a type 1 error is made what conclusion will be made regarding breaking strength

Answer 1

In hypothesis testing, a Type I error occurs when the null hypothesis (\(H_0\)) is rejected when it is actually true. In your case:

- Null Hypothesis (\(H_0\)): The mean breaking strength of the wires is equal to 50 (i.e., \( \mu = 50 \)).
- Alternative Hypothesis (\(H_1\)): The mean breaking strength of the wires is greater than 50 (i.e., \( \mu > 50 \)).

If a Type I error is made, it would mean that you reject the null hypothesis and conclude that the mean breaking strength is greater than 50, when in fact, it is not (i.e., it is actually 50 or less).

In summary, if a Type I error occurs, the conclusion regarding the breaking strength would incorrectly state that the wires have a mean breaking strength greater than 50, when this is not true.

Answer 2

What if a type 2 error is made

Answer 3

A Type II error occurs when the null hypothesis (\(H_0\)) is not rejected when it is actually false. In your scenario:

- Null Hypothesis (\(H_0\)): The mean breaking strength of the wires is equal to 50 (i.e., \( \mu = 50 \)).
- Alternative Hypothesis (\(H_1\)): The mean breaking strength of the wires is greater than 50 (i.e., \( \mu > 50 \)).

If a Type II error is made, it would mean that you fail to reject the null hypothesis and conclude that there is not enough evidence to support that the mean breaking strength is greater than 50, when in fact, it is indeed greater than 50.

In summary, if a Type II error occurs, the conclusion regarding the breaking strength would incorrectly state that the wires do not have a mean breaking strength greater than 50, even though they actually do.