Exam MAS-I Practice Question 34
Study guide: Exam MAS-I
An actuary suspects that average claim cost has risen above its filed value of 500. Claim costs are normally distributed with known standard deviation \sigma = 120. She tests H_0: \mu = 500 against H_1: \mu > 500 with a one-sided z-test on the sample mean, at significance level \alpha = 0.05. Use z_{0.05} = 1.645 and z_{0.10} = 1.282.
Part a (1 point)
The test uses n = 36 claims. Calculate the probability of a Type II error if the true mean is 540.
- A) Less than 0.20
- B) At least 0.20, but less than 0.40
- C) At least 0.40, but less than 0.60
- D) At least 0.60, but less than 0.80
- E) At least 0.80
Part b (1 point)
Calculate the smallest sample size n for which the probability of a Type II error at \mu = 540 is at most 0.10, keeping \alpha = 0.05. Give your answer as a whole number.
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