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A machine produces parts on an assembly line for an automotive manufacturer. If a part is defective, it must be scrapped. Every hour, the manager takes a random sample of 15 parts to test whether the process is "out of control" (i.e., to test whether the average proportion of defective parts exceeds 10%). Which of the following is a Type I error for this situation?a. A Type I error for this situation would be to incorrectly conclude that the process is out of control. b. A Type I error for this situation would be to conclude that an out of control process is out of control. c. A Type I error for this situation would be to conclude that an out of control process is in control. d. A Type I error for this situation would be to correctly conclude that the process is in control.

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Answer:

Option A) A Type I error for this situation would be to incorrectly conclude that the process is out of control.                  

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 15

Test:

average proportion of defective parts exceeds 10% that is whether the process is "out of control" or not.

Type I error:

  • Also known as false positive error.
  • It is the error of rejecting the null hypothesis when it is true.

We can design the null and alternate hypothesis as:

[tex]H_{0}: p \leq 0.10\\H_A: p > 0.10[/tex]

Type I error would be rejecting that the fact average proportion of defective parts is less than equal to 10% when it is true.

That is we accept the alternate hypothesis that average proportion of defective parts exceeds 10% when actually it does not.

Thus, we conclude that the process is out of control when it is not by committing a type I error.

Thus, the correct answer is:

Option A) A Type I error for this situation would be to incorrectly conclude that the process is out of control.