(1) According to your roommate, they have inherited a special coin from their great-grandmoth which is "magic" and "comes up heads WAaAaAaY more often than it comes up tails". You give your roommate the benefit of the doubt, and will devise a hypothesis test to try and support their claim that the coin is biased in favor of heads. (a) What is a sensible choice for a null and alternative hypothesis for this test? (b) If you are only able to flip the coin 10 times, and will only conclude that the coin is biased if all 10 flips come up heads, what is the probability of a Type I error for this test? Use exact Binomial probabilities. (c) If you will flip the coin 25 times, determine the rejection region corresponding to a test with a 0.05. Use Table I of cumulative Binomial probabilities. (d) If you will flip the coin 25 times, determine the rejection region corresponding to a test with a 0.01. Use Table I of cumulative Binomial probabilities. (е) If a test with a 0.05. Use the Normal approximation to the Binomial. you will flip the coin 100 times, determine the rejection region corresponding to (f) If you will flip the coin 100 times, determine the rejection region corresponding to a test with a 0.01. Use the Normal approximation to the Binomial.
(1) According to your roommate, they have inherited a special coin from their great-grandmoth which is "magic" and "comes up heads WAaAaAaY more often than it comes up tails". You give your roommate the benefit of the doubt, and will devise a hypothesis test to try and support their claim that the coin is biased in favor of heads. (a) What is a sensible choice for a null and alternative hypothesis for this test? (b) If you are only able to flip the coin 10 times, and will only conclude that the coin is biased if all 10 flips come up heads, what is the probability of a Type I error for this test? Use exact Binomial probabilities. (c) If you will flip the coin 25 times, determine the rejection region corresponding to a test with a 0.05. Use Table I of cumulative Binomial probabilities. (d) If you will flip the coin 25 times, determine the rejection region corresponding to a test with a 0.01. Use Table I of cumulative Binomial probabilities. (е) If a test with a 0.05. Use the Normal approximation to the Binomial. you will flip the coin 100 times, determine the rejection region corresponding to (f) If you will flip the coin 100 times, determine the rejection region corresponding to a test with a 0.01. Use the Normal approximation to the Binomial.
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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1)
Transcribed Image Text:(1) According to your roommate, they have inherited a special coin from their great-grandmoth
which is "magic" and "comes up heads WAaAaAaY more often than it comes up tails".
You give your roommate the benefit of the doubt, and will devise a hypothesis test to
try and support their claim that the coin is biased in favor of heads.
(a) What is a sensible choice for a null and alternative hypothesis for this test?
(b) If you are only able to flip the coin 10 times, and will only conclude that the coin
is biased if all 10 flips come up heads, what is the probability of a Type I error for
this test? Use exact Binomial probabilities.
(c) If you will flip the coin 25 times, determine the rejection region corresponding to a
test with a 0.05. Use Table I of cumulative Binomial probabilities.
(d) If you will flip the coin 25 times, determine the rejection region corresponding to a
test with a 0.01. Use Table I of cumulative Binomial probabilities.
(e) If you will flip the coin 100 times, determine the rejection region corresponding to
a test with a ~ 0.05. Use the Normal approximation to the Binomial.
(f) If you will flip the coin 100 times, determine the rejection region corresponding to
a test with a 2 0.01. Use the Normal approximation to the Binomial.
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