PARAMETRIC STATISTICAL INFERENCE

We are now going to test these statements

• Examine the likelihood (probability) that a suspected claim would occur if an existing claim were true

• What is the claim being challenged?• What is the alternate claim?

– If we get an outcome that would be unlikely if Ho were true and is in the direction suggested by Ha, we have evidence against Ho in favor of Ha.

– Make “unlikely” precise by calculating the probability that an alternate (suspected) event is observed assuming Ho to be true (default or existing claim is true)

n

xZ

PARAMETRIC STATISTICAL INFERENCE

• The probability, computed assuming Ho is true, that the observed outcome would take a value as extreme or more extreme than that actually observed is called the P-VALUE of the test.

– The smaller the p-value the stronger is the evidence against Ho provided by the data.

1-SAMPLE Z STATISTIC FOR , known    

• the test statistic assesses the evidence against the null hypothesis by allowing the calculation of p-value

 • If the test statistic (Z-value) falls far from

the value suggested by the null hypothesis in the direction specified by the alternative hypothesis, it is good evidence against Ho and in favor of Ha.

 P-value describes how strong the evidence is

n

xZ