1. Parameter:  What is it about the population that we want to know? For us, µ, p, or regression coefficient (beta-sub 1).

2. True Value of Parameter:  What is the value we are testing for, the actual value for the population.  Do Not Use Values from the Sample here.

3. Mathematical Relationship Expression:  >, <, =, or not equal to.
    a. "=" always goes in H₀.
    b. For H₁:
      i. Make H₁ what the decision-maker thinks is true or wants to demonstrate.  Remember rejecting H₀ is the result that provides strong evidence in favor of H₁.  If we make H₁ what we think is true and cannot reject H₀, we're left with support for our hypotheses but weak support.  So make H₁ what you think is true.
     ii. If we say we test a hypothesis, that hypothesis is H₀.  If we are asked if there is evidence that a hypothesis is true, that hypothesis should be H₁.
    iii. Test for a change.  Make H₀ the old value.  We hold on to this value unless there is strong evidence of a change and need for adjustment.  For instance, we make H₁ that a production process is not working as expected while H₀ is that it is working properly.  We don't want to shut down the process and try to fix it unless there is strong evidence of a need for change.
 

If µ0 or p0 is the specific value that you test for in H0, then:
1. A two-tail test checks for significant differences from µ0 or p0 in both directions, and
2. A one-tail test checks for a significant difference from µ0 or p0 in a single direction.

If a problem indicates that you are only checking in one direction, then the math symbol for H1 must reflect:
1. What the decision-maker wants to demonstrate, or
2. A change from an established or standard value.

In practice:
   a. When a decision-maker is a researcher or someone trying to show something new, then he or she gives the benefit of the doubt to the opposite, often an old or accepted value.   Only strong evidence in opposition to H0 can overthrow the old or accepted value.  For instance, if p0 were the probability of getting cancer if you smoke, then a decision-maker who reasons that smoking increases the risk of cancer would make H1 that p > p0.  He or she hopes to reject H0 and provide strong evidence of H1.

    When a problem asks if there is evidence of a hypothesis or statement, then H1 should indicate the direction indicated by that hypothesis.  For instance, if we are given a sample of performances by an employee and asked if there is evidence that the employee’s average performance is at least average when compared to all employees, then H1 would be µ > µ0.

    Note here that we read the problem to determine direction not to detect a statement with “equality” in it directly or indirectly.  An employee’s average that is “at least” average when compared to all employees says “µ is equal to µ0 or greater than µ0”.  Consequently, you might think, at first, that this relation should be in H0 and “less than” in H1.  Not so, the decision-maker wants strong evidence to say the employee performs above average.  Put the “=” in H0.
 
b. When a decision-maker wants to stick with the established or standard value (µ0 or p0) to avoid unnecessary costs associated with deviation from this value, he or she gives it the benefit of the doubt. Then he or she only accepts that change has occurred when there is strong evidence of a new or different value.  For instance, we wouldn’t want to shut down a production process unless we had strong evidence that it was malfunctioning.