Question

QUESTIONS Say that you had to quickly determine if a bunch of coins were fair. What outcome of the 10-tip test would you use to reject the null hypothesis that would make you be right 18/20 times (or 95% of the time TTTA 3112) T-EE Path

Answer 1

Given the null hypothesis here that the coin is fair and therefore the probability of getting a heads is 0.5. Therefore, we have here:
p = P(heads) = 0.5

The number of outcomes which comes up heads out of 10 flips here is modelled as:

$X \sim Bin(n = 10, p = 0.5)$

Now as we want to be right 95% of the time and as this is a two tailed test, we have to have (1 - 0.95)/2 = 2.5% probabilities on either of the two tails here.

The probabilities here are computed as:
P(X = 0) = P(X = 10) = 0.5¹⁰ = 0.000977
P(X = 1) = P(X = 9) = 10*0.5¹⁰ = 0.00977
P(X = 2) = P(X = 8) = (10c2)*0.5¹⁰ = 0.04395

Now 0.000977 + 0.00977 = 0.02 < 0.025 but
0.000977 + 0.00977 + 0.04395 = 0.06 > 0.025

Therefore the test here should be given as:

We Reject the null hypothesis that the coin is fair when there are either 0, 1, 9 or 10 heads in the flip of 10 coins here.