The manipulation of statistical formulas is no substitute
for knowing what one is doing.
 Hubert M Blalock Jr

Chapter 10
    Sec 10.2

The second type of statistical inference about a population based on information from a sample is "TEST of SIGNIFICANCE".  These tests have a goal of assessing evidence provided by the data about "some claim" about the population.

Claim:  "I make 80% of my free throw attempts in basketball."
           "Cola drinks lose sweetness over time."
           "Student over the age of 30 have better attitudes toward school."

Validating these statements (or refuting them) is done through a significance test.

Significance tests answer two questions:
a)  does the sample results (however small) reflect the true parameter
b)  would the outcome result easily be explained by chance

Procedures:
1)  careful statement of alternatives
2)  identification of the parameter of interest
3)  clear statement of the alternatives:  "null hypothesis" and "alternative hypothesis"
 

The NULL HYPOTHESIS
(H0 pronounced "H-nought") declares that there is NO effect or change in the population.
The ALTERNATE HYPOTHESIS
(Ha) declares that there is some effect or change in the population.

A significance test works by asking..."How unlikely is the observed outcome if the null hypothesis were really true" by assigning a number called the P-value which designates the probability that the Null Hypothesis is true).

Remember "p" for probability.  The p values are calculated from Table A or by using normal cdf as before.

Generally, we begin by assuming that the null hypothesis is TRUE and attempt to disprove it by finding a very low likelihood that it is true, thereby making it false.  We then accept the alternate hypothesis as true.

LOGIC:  IF the probability of a result is very low then the result is SURPRISING, with a capital "S" and provides strong evidence against the original assumption (hypothesis).

Recap:

**Small p values are evidence against the Null Hypothesis because they say that observed result is unlikely
to occur just by chance.  Large P-values fail to give evidence against the Null Hypothesis.

How small must a P-value be to persuade us to reject the null hypothesis???

Rule of Thumb:  P-value less than .05 is called STATISTICALLY SIGNIFICANT.

Let's see how all this works.

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