### GIGAMIND

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115 CFA
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115.020.60.06 Reading 11 - 6. The Decision Rule

# 6. The Decision Rule

## f. explain and interpret the p-value as it relates to hypothesis testing;

What is a decision rule?
A decision rule is a statement of the conditions under which the null hypothesis will be rejected and under which it will not be rejected. In general:

What is a critical value?
The critical value (or rejection point) is the dividing point between the region where the null hypothesis is rejected and the region where it is not rejected.

What is the decision rule for a two-tailed test?
Reject `H_0` if `z < -z_{α/2}` or `z > z_{α/2}`

What is the decision rule for a one-tailed test?
Reject `H_0` if `z > z_α`

What is a statistical decision vs an economic decision?
A statistical decision is purely numbers-driven. An economic decision must also take into account external factors like txn costs, taxes, risk, etc)

What is a P-value and how is it interpreted?
- A P-value is the amount of area under a curve from a measured point to the end of the tail of interest. (I know it as a z-score)
- I.e., if you have a normal distribution and an outlier that is close to the tail, the P-value will be small, whereas a value close to the center will have a large P-value.
- E.g., P-value is normally compared against the Alpha (0.05). So a P-value `<.05` means the null hypothesis `H_0` is rejected, and `>0.05` means the null hypothesis is not rejected

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