HYPOTHESIS TESTING

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HYPOTHESIS TESTING

Statistical Hypothesis: A claim about the value of some parameter.

NULL HYPOTHESIS (H₀): A claim that is initially favored as true.
ALTERNATIVE HYPOTHESIS (H_a): An alternative claim that is a direct contradiction of H₀.
Format for H₀: q = q₀
Format for H_a: q ¹q₀ OR q>q₀OR q<q₀
Two-tailed Test: When H_a is of the form q¹ q₀
One-tailed Test: When H_a is of the form q>q₀ (upper-tailed test) or q<q₀ (lower-tailed test)

Objective: To conduct a statistical test so as to decide whether (1) H₀ should be rejected in favor of H_a, or (2) H₀ should not be rejected. The test will have

a test statistic: some function of the sample data
a rejection region: all values for the test statistic for which H₀ will be rejected

Errors associated with a test: Since the test is based on a random sample there is always a possibility that the test might lead us to an erroneous conclusion. More specifically, we define

Type I Error: H₀ is erroneously rejected (when it is actually true)
Type II Error: H₀ is erroneously accepted (when H₀ is actually false)
NOTATION: P(Type I Error) = a
P(Type II Error) = b
Suppose we specify
a =Maximum Acceptable Type I Error Probability
Then this is the significance level of the test, and the test is called a level-a test.

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Jayant Rajgopal