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The Food and Drug Administration (FDA) is asked to approve a new drug. The new drug...

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Basic Math

The Food and Drug Administration (FDA) is asked to approve a newdrug. The new drug should contain less than 25mg of the activeingredient “toxin”, 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.

Answer & Explanation Solved by verified expert
4.3 Ratings (809 Votes)
7 Given is the probability of type 1 error that is error of rejecting atrue null hypothesisType 2 error is the error of accepting a false nullhypothesisThe highest probability    See Answer
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