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IAI Actuarial Core Principles · Actuarial Statistics · Hypothesis testing and goodness of fit

A test of H0: μ = 50 against H1: μ > 50 is carried out at the 5% significance level. Which statement correctly describes the probability of a Type I error for this test?

A Type I error means rejecting the null hypothesis when it is actually true. The significance level is exactly this probability, so at 5% the chance of rejecting H0 when μ = 50 is 5%. Failing to reject when H1 holds is a Type II error.

  1. AThe probability of rejecting H0 when μ = 50, which equals 5%Correct
  2. BThe probability of accepting H0 when μ > 50, which equals 5%
  3. CThe probability of rejecting H0 when μ > 50, which equals 5%
  4. DThe probability that H0 is true given that it has been rejected, which equals 5%
  5. The probability of accepting H0 when μ = 50, which equals 5%

Explanation

A Type I error is rejecting H0 when it is true. The significance level is the probability of this error, so at 5% it is P(reject H0 | μ = 50) = 5%. Accepting H0 when H1 is true is a Type II error, so the second option is wrong.

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