Question

Q.

(a) Tegan is trying to decide if a coin is fair. She flips it 100 times and gets 63 heads. Please explain why it might make sense to view 63 heads as enough evidence to conclude the coin is unfair.

(b) Leela is trying to decide if a coin is fair. She flips it 100 times and gets 63 heads. Please explain why it might NOT make sense to view 63 heads as enough evidence to conclude the coin is unfair.

Answer 1

So to answer this we will do a hypothesis test initially

Let p denote the proportion of heads in 100 toss of coin

If the coin is unbiased then the proportion P would be 0.5

So to test

vs

Test statistic

  

So the p value is

a) So if the type 1 error is set to 0.01 or 1% We would reject the null hyothesis that that coin is unbiased or fair, hence we can conclude it is unfair.

b) So now in this case if we set type 1 error or alpha to be 0.001 or 0.1% then we would reject the null hypothesis that is we won't have enough evidence to show it is unbiased or unfair.

So depending on the alpha value or the type 1 error our conclusions would change.

Do comment id you have any doubt

Thank you !!!