Question

A regular type of laminate is currently being used by a manufacturer of circuit boards. A special laminate has been developed to reduce warpage. The regular laminate will be used on one sample of specimens and the special laminate on another sample, and the amount of warpage will then be determined for each specimen. The manufacturer will then switch to the special laminate only if it can be demonstrated that the true average amount of warpage for that laminate is less than for the regular laminate. State the relevant hypotheses.

H₀: μ_regular < μ_special
H_a: μ_regular = μ_special

H₀: μ_regular = μ_special
H_a: μ_regular > μ_special    

H₀: μ_regular = μ_special
H_a: μ_regular < μ_special

H₀: μ_regular = μ_special
H_a: μ_regular ≠ μ_special

H₀: μ_regular > μ_special
H_a: μ_regular = μ_special

Describe the type I error in the context of this situation.

The type I error would be declaring the special laminate as having more warpage when in fact the true warpages are equal.

The type I error would be declaring the true warpages of the laminates to be equal when in fact the special laminate has more warpage.    

The type I error would be declaring the special laminate as having less warpage when in fact the true warpages are equal.

The type I error would be declaring the true warpages of the laminates to be equal when in fact the special laminate has less warpage.

Describe the type II error in the context of this situation.

The type II error would be declaring the special laminate as having more warpage when in fact the true warpages are equal.

The type II error would be declaring the true warpages of the laminates to be equal when in fact the special laminate has more warpage.    

The type II error would be declaring the special laminate as having less warpage when in fact the true warpages are equal.

The type II error would be declaring the true warpages of the laminates to be equal when in fact the special laminate has less warpage.

Answer 1

1)

H₀: μ_regular = μ_special
H_a: μ_regular > μ_special    

2)

In statistical hypothesis testing, a type I error is the rejection of a true null hypothesis (also known as a "false positive" finding or conclusion), while a type II error is the failure to reject a false null hypothesis (also known as a "false negative" finding or conclusion).

The type I error would be declaring the special laminate as having less warpage when in fact the true warpages are equal.

3)

The type II error would be declaring the true warpages of the laminates to be equal when in fact the special laminate has less warpage.