Two-sided p-value of a mean test

MediumStatistics~4m

A desk claims its execution algo has zero average slippage (H0:μ=0H_0:\mu=0 ticks). Over n=36n=36 independent trades you observe a mean slippage of xˉ=2\bar x=2 ticks; the per-trade slippage standard deviation is known to be σ=6\sigma=6 ticks. Compute the two-sided pp-value for H0H_0. Give a decimal to three places. (Use Φ(2)=0.9772\Phi(2)=0.9772.)

Show hints (2)+
  1. Standardize by the SE of the mean, σ/n=1\sigma/\sqrt n=1, not by σ\sigma.
  2. Two-sided: p=2(1−Φ(z))p=2(1-\Phi(z)) with z=2z=2.

Answer

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0.046 (± 0.002)

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