MHB Rejecting the Hypothesis of a Fair Coin: Confidence Level?

  • Thread starter Thread starter Edward S
  • Start date Start date
Click For Summary
SUMMARY

The discussion centers on determining the confidence level required to reject the null hypothesis that a coin is fair, defined as having a 50% chance of landing heads. After flipping the coin 41 times and observing 31 heads, the consensus is that the null hypothesis can be rejected at an 80% confidence level. This conclusion is drawn from statistical analysis of the observed outcomes compared to expected probabilities.

PREREQUISITES
  • Understanding of null hypothesis and alternative hypothesis
  • Basic knowledge of confidence levels in statistics
  • Familiarity with binomial distribution
  • Ability to perform hypothesis testing
NEXT STEPS
  • Study the concept of p-values in hypothesis testing
  • Learn about binomial distribution calculations
  • Explore the implications of different confidence levels on hypothesis testing
  • Review statistical software tools for performing hypothesis tests
USEFUL FOR

Statisticians, data analysts, researchers, and anyone involved in hypothesis testing and statistical inference.

Edward S
Messages
1
Reaction score
0
Hi. At what level of confidence can I reject the hypothesis that a coin is "fair"? Meaning, the odds of a head is 50%. The coin is flipped 41 times and 31 are heads. Thank you!
 
Mathematics news on Phys.org
Edward S said:
Hi. At what level of confidence can I reject the hypothesis that a coin is "fair"? Meaning, the odds of a head is 50%. The coin is flipped 41 times and 31 are heads. Thank you!
I shall reject the null hypothesis that " The coin is fair" at even 80% confidence level.
1646032635013.png
 

Similar threads

High School Is the Coin Biased Towards Heads? Statistical Test and Conclusion
  • · Replies 21 ·
Replies
21
Views
3K
MHB The Probability of a Biased Coin: n Flips, m Heads
  • · Replies 4 ·
Replies
4
Views
3K
High School A simple trigonometry problem: Put eight coins around a central coin
  • · Replies 37 ·
2
Replies
37
Views
8K
High School Understanding Probability of Bias in Coin and Dice Tosses
  • · Replies 3 ·
Replies
3
Views
2K
MHB Left-Tailed Test Rejects Null Hypothesis at 0.05 Level
  • · Replies 1 ·
Replies
1
Views
2K
MHB Probability Function of Z: 1/4 & 1/2 Explained
  • · Replies 4 ·
Replies
4
Views
2K
MHB How Do You Calculate Expected Values in Probability Games?
  • · Replies 6 ·
Replies
6
Views
4K
Graduate Two Bernoulli distribution- test hypothesis for biased coins
  • · Replies 21 ·
Replies
21
Views
4K
Undergrad Type 1 Error Increases with Sample Size?
  • · Replies 9 ·
Replies
9
Views
4K
MHB Calculating overall percentage/probability from multiple categories?
  • · Replies 3 ·
Replies
3
Views
4K