Jerry desperately wants to cure diseases but he is terrible at designing effective
treatments. He is however a careful scientist and statistician, so he randomly divides his patients into control and treatment groups. The control group gets a placebo and the treatment group gets the experimental treatment. His null hypothesis H0 is that the treatment is no better than the placebo. He uses a significance level of α =0.05. If his p-value is less than α he publishes a paper claiming the treatment is significantly better than a placebo.
(a) Since his treatments are never, in fact, effective what percentage of his
experiments result in published papers? (Hint: rejecting a true hypothesis i.e.
claiming treatment is effective but actually it isn’t)
(b) What percentage of his published papers contains type-1 error i.e. describe
treatments that are no better than placebo?
Efrat is a genius at designing treatments, so all of her proposed treatments are effective. She’s also a careful scientist and statistician so she too runs double-blind, placebo controlled, randomized studies. Her null hypothesis is always that the new treatment is no better than the placebo. She also uses a significance level of α =0.05 and publishes a paper if p <α.
(c) What percentage of her published papers contain type I errors, i.e. describe treatments that are no better than placebo?
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