According to your roommate, they have inherited a special coin from their great-grandmother 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.
According to your roommate, they have inherited a special coin from their great-grandmother 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.
Chapter9: Sequences, Probability And Counting Theory
Section9.7: Probability
Problem 1SE: What term is used to express the likelihood of an event occurring? Are there restrictions on its...
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1- D)E)F)
Transcribed Image Text:(1) According to your roommate, they have inherited a special coin from their great-grandmother
which is "magic" and "comes up heads WAAAAAAY more often than it comes
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.
up
tails".
(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 0.01. Use the Normal approximation to the Binomial.
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