If we are flipping a coin, how large a proportion of heads do we need to get in

Question

If we are flipping a coin, how large a proportion of heads do we need to get in order to claim evidence that the coin is biased to give more heads than tails? If the coin is fair, the proportion of heads should be 0.5, so our null and alternative hypotheses are H0: p = 0.5 vs Ha: p > 0.5, where p is the proportion of heads.

For each situation below, make a guess about whether or not you think that sample outcome would give evidence for a biased coin (Yes or No)

                (7 heads in 10 flips)

                (14 heads in 20 flips)

                 (21 heads in 30 flips)

                (18 heads in 30 flips)

                (30 heads in 50 flips)

                (27 heads in 50 flips)

                (53 heads in 100 flips)

                (530 heads in 1000 flips)

                (510 heads in 1000 flips)

Explanation / Answer

7/10-No

14/20-No

21/30-Yes

18/30-No

30/50-yes

27/50-No

53/100-No

530/1000-Yes

510/1000-No

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