1. P-value Approach for Test Conclusion
Under the assumption that H0 is true, the probability that the
test statistic would take a value as extreme or more extreme
than that actually observed is called the P-value of the test.
Small P-value gives evidence against H0. Large P-value gives
no evidence against H0. In general, the smaller the P-value the
stronger the evidence against H0 provided by the data.
The decisive value of the P is the significance level .
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2. Example
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3. Decision Errors
When we perform a hypothesis test we hope that our decision
will be correct, but sometimes it will be wrong. There are two
possible errors that can be made in hypothesis test.
The error made by rejecting the null hypothesis H0 when in
fact H0 is true is called a type I error. The probability of
making a type I error is denoted by .
The error made by failing to reject the null hypothesis H0 when in fact H0 is false is called a type II error. The probability of
making a type II error is denoted by .
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4. Significance level and type I error
The significance level  of any test is the P(Type I error).
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5. Power The probability of rejecting H0 when a particular alternative
value of the parameter is true is called the power of the test to
detect that alternative.
The power of a test against a particular alternative is
Power = 1- β = 1- P( not rejecting H0 when H0 is false) =
= P( rejecting H0 when H0 is false)
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6. Example
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