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null hypothesis

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.

alternative hypothesis

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:

-Mutually exclusive

-Exhaustive

-Mutually exclusive

-Exhaustive

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.

H0: μ≤50

H1: μ>50

H0: μ≤50

H1: μ>50

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.

H0: μ≥50

H1: μ<50If

H0: μ≥50

H1: μ<50If

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.

H0: μ=50

H1: μ≠50

H0: μ=50

H1: μ≠50

test statistic

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.

decision rule

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

•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.

•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)

β = P(Accept H| H is false)

power function

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.