A pharmaceutical company develops drugs to increase apoptosis in cancer cells. Each candidate drug is tested...

A pharmaceutical company develops drugs to increase apoptosis in cancer cells. Each candidate drug is tested in mice, using an experiment design that has 90% power at a = 1%. 1) For every 1000 drugs that have no real effect, about how many will the company mistakenly conclude work? 2) For every 1000 drugs that actually work, about how many will the company correctly conclude work?

Solutions

Expert Solution

Null Hypothesis H₀ is that the drugs have no real effect.

Alternative Hypothesis H₁ is that the drugs actually work to increase apoptosis in cancer cells.

Probability that when the drugs that have no real effect, the company will mistakenly conclude that the drugs work

= Probability that H₁ is accepted to be true when in reality H₀ is true

= Probability of Type I error = a = 1% = 0.01

Thus for every 1000 drugs that have no real effect, the company will mistakenly conclude that 0.011000 = 10 drugs work.

Probability that when the drugs actually work, the company will correctly conclude that the drugs work

= Probability that H₁ is accepted to be true when in reality H₁ is true

= 1 - Probability that H₀ is accepted to be true when in reality H₁ is true

= 1 - Probability of Type II error = Power = 90% = 0.9

Thus for every 1000 drugs that actually work, the company will correctly conclude that 0.91000 = 900 drugs work.

orchestra answered 1 year ago

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