Homework Help is Here – Start Your Trial Now!
Math
Statistics
(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 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 2 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-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. (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 2 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.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.3: Conditional Probability; Independent Events; Bayes' Theorem
Problem 39E: The following problem submitted by Daniel Hahn of Blairstown, Iowa, appeared in the Ask Marilyn...
See similar textbooks
icon
Related questions
Question

1- c)d)e)f)

(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 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 0.01. Use the Normal approximation to the Binomial.
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 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 0.01. Use the Normal approximation to the Binomial.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
SEE MORE TEXTBOOKS