Question

In: Math

A regular type of laminate is currently being used by a manufacturer of circuit boards. A...

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: μregular > μspecial
Ha: μregular = μspecial
H0: μregular = μspecial
Ha: μregular < μspecial
H0: μregular = μspecial
Ha: μregular > μspecial
H0: μregular = μspecial
Ha: μregular

Solutions

Expert Solution

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: μregular = μspecial
Ha: μregular > μspecial

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.


Related Solutions

1. A regular type of laminate is currently being used by a manufacturer of circuit boards....
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 circuit boards and the special laminate on another independent sample of circuit boards. The amount of warpage will then be determined for each circuit board. The manufacturer will then switch to the special laminate only if it can be demonstrated that the true average amount...
A semiconductor manufacturer produces printed circuit boards that are sampled to determine the thickness of their...
A semiconductor manufacturer produces printed circuit boards that are sampled to determine the thickness of their copper plating. The following statements create a data set named Trans, which contains the plating thicknesses (Thick) of 50 boards: 3.412 3.45 3.551 3.451 3.60 3.462 3.586 3.645 3.252 3.62 3.606 3.634 3.852 3.56 3.342 3.341 3.444 3.774 3.632 3.199 3.71 3.654 3.723 3.981 3.934 3.708 3.934 3.315 3.762 3.223 3.469 3.481 3.515 3.535 3.46 3.575 3.488 3.515 3.484 3.482 3.517 3.483 3.467 3.467...
A manufacturer of printed circuit boards is considering purchasing a new surface mount technology component placement...
A manufacturer of printed circuit boards is considering purchasing a new surface mount technology component placement system. Two machines are under consideration and the following information is prepared for the economic evaluation. If the company's after-tax MARR of 12% per year and MACRS with a 7-year recovery period is used, compute the after-tax cash flow(ATCF) at the end of year 8 for the Machine Q. Assume an effective tax of 35% per year. Machine Q R First costs $392,248 $395,000...
show all work 2) A semiconductor manufacturer produces printed circuit boards that are sampled to determine...
show all work 2) A semiconductor manufacturer produces printed circuit boards that are sampled to determine the thickness of their copper plating. The following statements create a data set named Trans, which contains the plating thicknesses (Thick) of 50 boards: 3.412 3.45 3.551 3.451 3.60 3.462 3.586 3.645 3.252 3.62 3.606 3.634 3.852 3.56 3.342 3.341 3.444 3.774 3.632 3.199 3.71 3.654 3.723 3.981 3.934 3.708 3.934 3.315 3.762 3.223 3.469 3.481 3.515 3.535 3.46 3.575 3.488 3.515 3.484 3.482...
When circuit boards used in the manufacture of CD players are tested, the long-run percentage of...
When circuit boards used in the manufacture of CD players are tested, the long-run percentage of defectives is 3%. A random sample of size n=23 of boards have been selected and checked. The chance that the number of defective boards will exceed the mean by 2 standard deviation is: ?
Assume that 15% of circuit boards used in manufacturing compact displayers are defective. Off a batch...
Assume that 15% of circuit boards used in manufacturing compact displayers are defective. Off a batch of 200 randomly selected such circuit boards, use the normal approximation with the continuity correction to find the probability that at most 30 of these boards are defective. Is your answer approximate or exact. b. find exact probability using R code to compare answer on the previous question?
When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage...
When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%. Let ? = the number of defective boards in a random sample of size ? = 25. a. Determine ? (? = 2) (Using the formula of the pmf) b. Determine ? (1 ≤ ? ≤ 4) (Using the table). c. Calculate the expected value d. Calculate variance and standard deviation of ?.
When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage...
When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 10%. Let X = the number of defective boards in a random sample of size n = 25, so X ~ Bin(25, 0.1). (Round your probabilities to three decimal places.) (a) Determine P(X ≤ 2). (b) Determine P(X ≥ 5). (c) Determine P(1 ≤ X ≤ 4). (d) What is the probability that none of the 25 boards is defective? (e)...
When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage...
When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 10%. Let X = the number of defective boards in a random sample of size n = 20, so X ~ Bin(20, 0.1). (Round your probabilities to three decimal places.) (a) Determine P(X ≤ 2). (b) Determine P(X ≥ 5). (c) Determine P(1 ≤ X ≤ 4). (d) What is the probability that none of the 20 boards is defective? (e)...
When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage...
When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 10%. Let X = the number of defective boards in a random sample of size n = 20, so X ~ Bin(20, 0.1). (Round your probabilities to three decimal places.) (a) Determine P(X ≤ 2). b. Determine P(X ≥ 5). c. Determine P(1 ≤ X ≤ 4). d. What is the probability that none of the 20 boards is defective? e....
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT