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← 32-24 Verify_Fair_1

32-24 Verify_Fair_1

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Showing Revision 2 created 11/02/2015 by Udacity Robot.

  1. Now, let's look at one more example and this time we go to a bank and hope to get a fair coin
  2. This going coin over here and our alternate hypothesis is a two-sided hypothesis
  3. with a probability either is smaller than 0.5 or larger than 0.5 which provide us p≠0.5.
  4. The way to know where this concept will lead, in all we've done so far,
  5. we assume that H₀ is correct and we've computed some sort of distribution and then we cut out
  6. a critical region such as the volume underneath with smaller input of 5%,
  7. assuming you a 5% confidence.
  8. Now in the two-sided test, what we do is cover the smaller region on the left but also one on the right,
  9. such that the area on the left doesn't exceed half of 5%
  10. that is 2.5% and the same for the area on the right.
  11. Now, we've moved the critical region into two areas.
  12. We have a two-sided test now that's called a two-tailed test
  13. and in totality, the two critical regions on the left and right don't exceed 5%.
  14. This looks awfully like a confidence interval, right?
  15. Let's flip the coin. In 14 experiments, heads comes out exactly 3 times
  16. and 11 times it comes out tails.
  17. Let's do the analysis. So in this table, I've graphed to you the probabilities
  18. under the binomial distribution for each possible outcome, from 0 to 14 as before.
  19. We go 0, 0.005, 0.22, 0.06, 0.12, 0.18, 0.21--this is obviously
  20. the most likely outcome for the null hypothesis and then it goes down
  21. exactly the way it went up over here.
  22. I've also added check boxes. I want you to check exactly those that define the critical region,
  23. so the total probability in the critical region does not exceed 5% and remember this is a two-tailed test.