How to determine the width of the zone of acceptance in hypothesis testing?

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SUMMARY

This discussion focuses on determining the width of the zone of acceptance in hypothesis testing for a fair coin. When flipping a coin 100 times, the zone of acceptance should be calculated to ensure less than a 5% chance of erroneously rejecting the fair coin hypothesis. For 5 flips, the cumulative probability for 2 or 3 heads is 20/32, while for 1 to 4 heads, it is 30/32. The normal curve can be used as an approximation for larger sample sizes, such as 100 flips, instead of relying solely on the binomial formula.

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  • Understanding of hypothesis testing principles
  • Familiarity with binomial distribution
  • Knowledge of cumulative probability calculations
  • Basic statistics concepts, including normal distribution
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  • Study the Central Limit Theorem and its application in hypothesis testing
  • Learn about the normal approximation to the binomial distribution
  • Explore the concept of Type I and Type II errors in hypothesis testing
  • Review statistical software tools for performing hypothesis tests, such as R or Python's SciPy library
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amberglo
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First and foremost, I am terrible in Stats so bear w/ me on this one. This is my question, if anyone has an idea on how to figure out this problem that would be great! Here it is: Suppose you flip a coin 100 times and you want to test the hypothesis that the coin is fair, making sure there is less than a 5 percent chance of erroneously rejecting the fair coin hypothesis. How wide should the zone of acceptance be? How wide should the zone be if you flip the coin 5 times?
 
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What you want is a range balanced around the mean which has cumulative probability 95%. The chance of 2 or 3 heads out of 5 flips is
((5 choose 2) + (5 choose 3)) / 2^5 = 20/32
The chance of 1 to 4 heads is
((5 choose 1) + (5 choose 2) + (5 choose 3) + (5 choose 4)) / 2^5 = 30/32

With 100 flips, you are probably intended to use the normal curve as an approximation rather than the explicit binomial formula, although either would work.
 

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