A null hypothesis, denoted by H0, is an assertion about one or more population parameters. This is the assertion we hold to be true until we have sufficient statistical evidence to conclude otherwise.
The alternative hypothesis, denoted by H1, is the assertion of all situations not covered by the null hypothesis.
compare h0 vs h1
H0and H1 are:
right tailed test
The tails of a statistical test are determined by the need for an action. If action is to be taken if a parameter is greater than some value a, then the alternative hypothesis is that the parameter is greater than a, and the test is a right-tailed test.
left tailed test
If action is to be taken if a parameter is less than some value a, then the alternative hypothesis is that the parameter is less than a, and the test is a left-tailedtest.
two tailed test
If action is to be taken if a parameter is either greater than or less than some value a, then the alternative hypothesis is that the parameter is not equal to a, and the test is a two two-tailedtest.
A test statistic is a sample statistic computed from sample data. The value of the test statistic is used in determining whether or not we may reject the null hypothesis.
The decision rule of a statistical hypothesis test is a rule that specifies the conditions under which the null hypothesis may be rejected.
Type 1 Error
Type I Error: Reject a true H0
•The Probability of a Type I error is denoted by α
-α is called the level of significance of the test
Type 2 Error
Type II Error: Fail to reject a false H0
•The Probability of a Type II error is denoted by β.
* (1-β) is called the power of the test.
conditional probabilities of alpha and beta
α= P(Reject H |H is true)
β = P(Accept H| H is false)
The probability of a type II error, and the power of a test, depends on the actual value of the unknown population parameter. The relationship between the population mean and the power of the test is called the power function.