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
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
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
Expert Solution
steps

Step by step

Solved in 3 steps with 1 images

Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman