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_specialH₀: μ_regular = μ_special
H_a: μ_regular < μ_special H₀: μ_regular = μ_special
H_a: μ_regular > μ_specialH₀: μ_regular = μ_special
H_a: μ_regular

Answer 1

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

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

Type I is rejecting the null when the null is true.

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

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

Type II is failing to reject the null when the null is false.

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.