Can the null hypothesis contain an inequality?
The null hypothesis (denoted by H0) is a hypothesis that contains a statement of equality, =. The alternative hypothesis (denoted by H1or Ha) is the statement that contains a statement of inequality, such as >, <, . Identifying the null and alternative hypotheses: Example 1: Write the claim as a mathematical sentence.
What inequality utilize right tailed test?
A right tailed test (sometimes called an upper test) is where your hypothesis statement contains a greater than (>) symbol. In other words, the inequality points to the right. For example, you might be comparing the life of batteries before and after a manufacturing change.
Why does H0 have to be stated as an equality?
In the classical approach (which I believe your texts follow), as proposed by Pearson and Neyman long time ago, H0 must be stated as an equality (and it is fundamental assumption for how the maths here works), it is necessary to have parameter assumed at a particular value, to work out the test statistic distribution and probabilities.
When do null and alternative hypotheses have to be?
If the test is about a parameter θ with H0 being the restriction θ ∈ Θ0, the alternative Ha can be of any form θ ∈ Θa as long as Θ0 ∩ Θa = ∅. An example as to why exhaustivity does not make much sense is when comparing two families of models, H0: x ∼ f0(x | θ0) versus Ha: x ∼ f1(x | θ1).
Do you include the inequality in the null?
(That said, in practice many people – though far from everyone – do include the inequality in stating the null, rather than just the equality. Different books take different stances on it.)
What is the probability of Type 1 error?
This probability is called the probability of Type 1 error. You can compute the probability of Type 1 error for all configurations that correspond to the hypothesis μ ≥ 12. In the figure I plot the distributions of the test statistics under two different such configurations C 1: μ = 12 and C 2: μ = 13.