How much evidence is in 56 intraday trades?

The corrected opening-range scan of 15.3.7 produced 56 trades with mean $0.165R$ and standard deviation $0.760R$ (3 bp slippage). (a) Compute the $t$-statistic. (b) Using M03 (3.2a) and (3.2b), compute the number of trades needed for $t \ge 2$ in expectation and for 80% power at these values of $E$ and $s$. (c) The mean was $0.200R$ at 0 bp and $0.090R$ at 10 bp slippage per side. Assuming the mean is linear in slippage, at what slippage per side does it reach zero? (d) A sceptic assigns a prior probability of 5% that the rule has a real edge with per-trade Sharpe ratio $0.2$ (and 95% that its edge is zero). Using the normal approximation $t \sim N(0.2\sqrt{56}, 1)$ under the alternative and $N(0,1)$ under the null, compute the posterior probability of a real edge given that $t$ is at least the value in (a). Repeat for a prior of 20%.