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Problem 3, Colquhoun (2014) claimed that, "if you use p=0.05 to suggest that you have made a discovery, 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 to determine whether the drug truly is effective. You perform a hypothesis test that has a significance level of 0.05 and a power of 0.8. A Write the null and alternative hypothesis for this hypothesis test, using words only (no math). B What 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 the probability 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 the probability that your randomly chosen drug has an effect, given that you rejected the nullhypothesis

Problem 3, Colquhoun (2014) claimed that, "if you use p=0.05 to suggest that you have made a discovery, 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 to determine whether the drug truly is effective. You perform a hypothesis test that has a significance level of 0.05 and a power of 0.8. A Write the null and alternative hypothesis for this hypothesis test, using words only (no math). B What 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 the probability 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 the probability that your randomly chosen drug has an effect, given that you rejected the nullhypothesis

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Problem 3, Colquhoun (2014) claimed that, "if you use p=0.05 to suggest that you have made a discovery, 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 to determine whether the drug truly is effective. You perform a hypothesis test that has a significance level of 0.05 and a power of 0.8. A Write the null and alternative hypothesis for this hypothesis test, using words only (no math). B What 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 the probability 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 the probability that your randomly chosen drug has an effect, given that you rejected the nullhypothesis
Transcribed Image Text:Problem 3, Colquhoun (2014) claimed that, "if you use p=0.05 to suggest that you have made a discovery, 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 to determine whether the drug truly is effective. You perform a hypothesis test that has a significance level of 0.05 and a power of 0.8. A Write the null and alternative hypothesis for this hypothesis test, using words only (no math). B What 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 the probability 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 the probability that your randomly chosen drug has an effect, given that you rejected the nullhypothesis
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