Testing max pain

In the 31 Nifty expiries of 9A.16, max pain predicted the direction of the settlement relative to the previous close correctly 16 times. (a) Compute the two-sided binomial $p$-value against a hit rate of 0.5. (b) How many independent expiries are needed to detect a true hit rate of 0.6 with a two-sided 5% test and 80% power (normal approximation)? (c) A buyer of the day-before ATM straddle lost 28.64 points per expiry on average with a sample standard deviation of 111.10. Compute the $t$-statistic and state what it does and does not show.