The Food and Drug Administration (FDA) is asked to approve a newdrug. The new drug should contain less than 25mg of the activeingredient “toxinâ€, which is assumed to have dangerous sideeffects. The FDA would like to restrict the error of “approving thedrug despite its too high content of toxin†to a maximum risk of 5%(α ≤ 0.05). Let Xi : “ The content of toxin in the i-th pill [inmg].†∼ N(µ, σ2 ) ∼ N(µ, 4). A simple random sample of n = 50 pills( Xi ∼ i.i.d.) will be used for the test.
7. Given a significance level of α = 5% what is the highestprobability of making a type II error?
8. In the sample, x¯ = 24.6. Compute the p-value. What do youconclude? [Write down the probability that you computed.]
9. Has a type I error occurred? Explain your answer.
10. Has a type II error occurred? Explain your answer.
