The Food and Drug Administration (FDA) is asked to approve a new drug. The new drug should contain less than 25mg
of the active ingredient "toxin", which is assumed to have dangerous side effects. The FDA would like to restrict the error of "approving the drug 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 [in mg]." ∼ N(µ, σ2 ) ∼ N(µ, 4). A simple random sample of n = 50 pills ( Xi ∼ i.i.d.) will be used for the test.
Given a significance level of α = 5% what is the highest probability of making a type II error?
In the sample, x¯ = 24.6. Compute the p-value. What do you conclude? [Write down the probability that you computed.]
Has a type I error occurred? Explain your answer.
Has a type II error occurred? Explain your answer.