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Probability, Statistics and Queueing

Whether a product lot meets its specification is tested using a sample taken from it. If the null hypothesis is "this lot meets the specification", which of the following is a type I error?

  1. AJudging a lot that meets the specification as not meeting it and rejecting it
  2. BJudging a lot that does not meet the specification as meeting it and accepting it
  3. CThe instrument measuring the samples is broken, so the measured values themselves are wrong
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Answer: A. Judging a lot that meets the specification as not meeting it and rejecting it

A type I error is rejecting the null hypothesis when it is true, here rejecting a good lot (producer's risk). Its probability is the significance level α, decided in advance as 5% or similar. A type II error is failing to reject the null hypothesis when it is false, here accepting a bad lot (consumer's risk). For the same sample size, making α smaller makes type II errors more likely.

  • A. Correct. It is the error of rejecting a true null hypothesis, and its probability is the significance level α.
  • B. This is a type II error, failing to reject a false null hypothesis.
  • C. This is a measurement error, not a type of error in the judgment of a test.
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