# P-Value

p-value: probability of observing an outcome which is at least as hostile (or adversarial) to the null hypothesis as the one observed

Example
Null hypothesis: mean lifetime of a manufacturing device = 9.4 years
Accepted: within 0.396 units

50 elements with sample mean of 8.96
What is the probability that when we generate a different and independent sample average of 50 observations, we get the value <8.96 if the null hypothesis is true?

Worse than 8.96
1. Getting a number smaller than 8.96
2. Getting a number larger than 9.84

$P(Z\leq-\frac{0.44}{1.43/\sqrt{50}})+P(Z\geq\frac{0.44}{1.43/\sqrt{50}})=2\times P(Z\leq-2.175)=3\%$

Conclusion: the larger the p-value, the stronger the evidence supporting the hypothesis.

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