# Problem 3, Colquhoun (2014) claimed that, "if you use p=0.05 to suggest that you have made adiscovery, you will be wrong at least 30% of the time." He uses the following example.Suppose you pick a drug at random from 1000 candidate drugs and run a randomized controlled trial todetermine whether the drug truly is effective. You perform a hypothesis test that has a significance levelof 0.05 and a power of 0.8.A Write the null and alternative hypothesis for this hypothesis test, using words only (no math).BWhat is the probability of committing a Type l Error on this single hypothesis test?C. hat is the probability of committing a Type Il Error on this single hypothesis test?D. If you independently run experiments and hypothesis tests for four drugs, what is theprobability of committing at least one Type l Error when performing the four hypothesistests?E. 10% of the drugs truly have an effect, and the other 90% are no different from placebo. Find theprobability that your randomly chosen drug has an effect, given that you rejected the nullhypothesis

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Step 1

Hello. Since your question has multiple sub-parts, we will solve the first three sub-parts for you. If you want remaining sub-parts to be solved, then please resubmit the whole question and specify those sub-parts you want us to solve.

A.

The null and alternative hypothesis of the test are:

Null hypothesis (Ho) : The drug has no effect.

Alternative hypothesis (H1) : The drug is effective.

Step 2

B.

The significance level is the probability of committing type I error.

In the above case, significance level is 0.05.

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