Unformatted text preview: Chapter 9: Statistical Inference: Signiﬁcance Tests About Hypotheses Signiﬁcance Test: A signiﬁcance test is a method of using data to summarize the evidence about a
hypothesis. A signiﬁcance test about a hypothesis has ﬁve steps.
1) Assumptions 2) Hypotheses 3) Test Statistic 4) P-value 5) Conclusion Step 1 : —
> A (signiﬁcance) test assumes that the data production used randomization
> Other assumptions may include: 0 Assumptions about the sample size or about the shape of the population distribution Step 2 : m
> A hypothesis is a statement about a population, usually of the form that a certain parameter takes a
particular numerical value or falls in a certain range of values
> The main goal in many research studies is to check whether the data support certain hypotheses > Each signiﬁcance test has two hypotheses:
* 0 The null hypothesis is a statement that the parameter takes a particular value. It has a single u_n parameter value. The symbol H denotes null hypothesis. This always has equality .- sign.
Ex: Ho: p = 0.72 Ho: u = 42.3 *0 The alternative hypothesis states that the parameter falls in some alternative range of values. The
' symbol H denotes alternative hypothesis. The alternative hypothesis should express what the
a researcher hopes to show. This always has one of “>”, “<”, or “¢” signs.
Ex: Ha: p < 0.47 Ha: u ¢ 42 Ha: n > 3.45 .30 The hypotheses should be formulated before viewing or analyzing the data! )K Step 3: m > A test statistic describes how 'far the point estimate falls from the parameter value given in the null hypothesis
> We use the test statistic to assess the evidence against the null hypothesis by giving a probability, the
Step 4: m. mm.“ “mm"-
3 Sampling taxman»:
> To interpret a test statistic value, we use a probability summary of a“..- 1‘3““ ....._..5 the evidence against the null hypothesis, H
0 0 First, we presume that H is true
0 0 Next, we consider the sampling distribution from which the test
statistic comes 0 We summarize how far out in the tail of this sampling
distribution the test statistic falls > We summarize how far out in the tail the test statistic falls by the
tail probability of that value and values even more extreme .
0 This probability is called a P-value as...“ ____ 0 The smaller the P-value, the stronger the evidence is against H
0 0 The P-value is the probability that the test statistic equals the
observed value or a value even more extreme ...
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- Spring '08