Hypothesis Tests

Also referred to as , the null hypothesis is what we assume is true unless we can prove otherwise.

Also referred to as , the alternate hypothesis is a statement about a population parameter we intend to demonstrate is true.

1. State the appropriate hypotheses
2. State the appropriate test-statistic
3. State the Critical Region
4. Conduct the experiment and calculate the test statistic
5. Draw your conclusion

Left tail test:

• Assume null hypothesis to be true
• Assume that actual value will be less than null hypothesis

Right tail test:

• Assume null hypothesis to be true
• Assume that actual value will be greater than null hypothesis

Two-sided (tailed) test:

• Assume null hypothesis to be true
• Assume alternative hypothesis to be false

Depending on the results of our test we may:

• Reject our null hypothesis
• Fail to reject our null hypothesis

The probability of a type 1 error is referred to as alpha (). It is called the significance level.

The probability of a type 2 error is referred to as beta (). The power of a test is defined as

Note that and are inversely related.

The test statistic measures compatibility between the null hypothesis and the data collected. It is used for the probability calculation needed for our hypothesis test.

If we know and CLT checks out, our test statistic should be:

The p-value method is preferred but it may be best to start with the critical value (CV) method.

• Find a critical value based on
• Define your rejection region based on the type of test you have (left, right, two)
• Asses where you test statistic falls:
  • If it falls in the rejection region, REJECT the null hypothesis
  • If it does not, then we FTR

The P-Value is a probability computed assumed the null hypothesis is true, that the test statistic would take a value as extreme or more extreme than that actually observed.